| 11 | | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S V G 202 3 GEODETSKI VESTNIK | letn. / Vol. 67 | št. / No. 1 | SI | EN ABSTRACT IZVLEČEK KLJUČNE BESEDE KEY WORDS indoor navigation, navigation network, wayfinding, indoor path, space syntax, isovist, visibility graph analysis navigacija v zaprtih prostorih, model navigacijskega omrežja, iskanje poti, notranje poti, sintaksa prostora, analiza grafa vidljivosti UDK: 629.072.1 Klasifikacija prispevka po COBISS.SI: 1.01 Prispelo: 21. 7. 2022 Sprejeto: 1. 2. 2023 DOI: 10.15292/geodetski-vestnik.2023.01.11-39 SCIENTIFIC ARTICLE Received: 21. 7. 2022 Accepted: 1. 2. 2023 Atakan Bilgili, Alper Sen, Melih Basaraner VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES Notranja navigacijska omrežja (modeli) so bistven način za karakterizacijo dejanskih navigacijskih vzorcev pešcev. Da bi našli najprimernejšo pot skozi notranja navigacijska omrežja, se obstoječe študije tradicionalno osredotočajo predvsem na zmanjšanje dolžine in spremembo smeri. Žal pogosto ne najdejo poti, saj upoštevajo le prostorsko strukturo zgradbe. Mere prostorske sintakse podajajo interakcijo med konfiguracijo prostora prostorskim razmišljanjem pešca, ki temelji na vidljivosti. V tej študiji smo mere prilagodili za oceno notranjih poti. V praktičnem preizkusu smo zbirali dejanske navigacijske vzorce pešcev in jih na to primerjali z notranjimi potmi prek statistične primerjave glede na mere prostorske sintakse. Za najprimernejše navigacijsko omrežje se je pokazalo t.i. Universal Circulation Network, ki temelji na vidljivosti. Mere prostorske sintakse kažejo, da so navigacijska omrežja, ki temeljijo na središčnici, primernejša, če se upošteva vloga prostorske konfiguracije. Zato se je kot najprimernejše izkazalo navigacijsko omrežje Middle Point Relation Structure Segment Entrance. Indoor navigation networks (models) are an essential way to characterize the navigation patterns of pedestrians. To find the most suitable path existing studies concentrate mostly on the minimization of length and turns. However, they alone may fall short to support one in wayfinding as they only consider the spatial structure of a building. Space syntax measures can reveal the interaction among spatial configurations and visibility-based spatial reasoning of pedestrians. In this paper, our original contribution is to adapt them to evaluate indoor paths. To demonstrate our approach, we first conducted a user experiment to collect the navigation patterns. Then, these navigation patterns were compared with the indoor paths through statistical comparison with respect to space syntax measures. Also, all door-from-door paths were compared by traditional and space syntax measures. The findings of the experimental study show that the visibility-based UCN is the more suitable navigation network by traditional measures. However, space syntax measures suggest that centerline-based navigation networks are more suitable. Considering traditional and space syntax measures together, the centerline-based MPRSSE is found to be the more suitable navigation network to assist one in the wayfinding process for our experimental study. Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 12 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N 1 INTRODUCTION The usage of outdoor navigation systems has grown rapidly over a decade (Vanclooster et al., 2019). In the case of an outdoor environment, Global Navigation Satellite Systems (GNSS) pave the way for the implementation of navigation, providing sufficiently high accuracy and precision in positioning. Also, outdoor environments surrounded by street networks make it easier to establish a navigation network and implement routing algorithms (Rüetschi and Timpf, 2005). However, indoor environments are often much more complex (fragmented, less visible, and enclosed) (Fellner, Huang, and Gartner, 2017; Giudice, Walton, and Worboys, 2010) and wayfinding can be challenging for many people (Arthur and Passini, 1992). Due to the current methods for indoor positioning have reached a certain stage of accuracy and preci- sion, indoor navigation finds a place for itself in applications such as customer tracking and guidance in shopping malls, facility management, building evacuation, terror scenarios, and wheelchair navigation (Choi and Lee, 2009; Gunduz, Isikdag, and Basaraner, 2016; Kwan and Lee, 2005; Park, Goldberg, and Hammond, 2020). Indoor navigation networks serve as a basis for realizing indoor navigation (Karas et al., 2006; Lee and Kwan, 2005; Park et al., 2020) as they enable to conceptualize indoor spaces and characterize actual navigation patterns of pedestrians to a certain extent (Kneidl, Borrmann, and Hartmann, 2012; Pang et al., 2020; Park et al., 2020). Due to the lack of pre-defined paths within an indoor environment, the movement patterns of a pedestrian can vary much more in indoor spaces and the wide range of movement hampers the establishment of a comprehensive navigation network to support wayfinding for level (floor) and non-level paths (e.g., stairs, elevators, ramps, etc.) in line with human spatial cog- nition (Lin and Lin, 2018; Rüetschi and Timpf, 2005). Considering the lack of pre-defined paths, the chance of disorientation is rather high in an indoor environment (De Cock et al., 2020). Therefore, the indoor paths that are conveyed to the end-users should be cognitively reasonable to retain convenience and orientation. From the aspect of path-planning, studies on indoor navigation mainly adopted routing algorithms such as Dijkstra (Dijkstra, 1959) which is commonly used for outdoor navigation studies to detect the shortest path distance between a pair of origin-destination nodes. Vanclooster et al. (2019) stated most existing navigation systems focus on minimizing path length, but ideal routes are not always the shortest, and users of these systems do not always prefer them. They also stated that minimiz- ing turns is crucial to providing less challenging route instructions as typically route directions are generated at turns so it can lead to cognitive load. Since a turn made on a path can lead to increased wayfinding time and disorientation, minimizing the turns is an important factor in the route guidance context (Park et al., 2020; Vanclooster et al., 2019) along with distance minimization. Vanclooster et al. (2014a) also stated pedestrians value the form and complexity of a route as much as its total length. Park et al. (2020) stated more criteria should be involved in comparison to evaluate naviga- tion networks to support indoor navigation. A path derived from navigation networks should be cognitively reasonable so that the cognitive load induced on the user could be minimized. Therefore, evaluating the indoor paths alone by traditional measures (length of a path and the number of turns made along a path) may fall short. These paths can overlook the visual perception of pedestrians in Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 13 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N the spatial configuration of buildings. De Cock et al. (2020) stated that the architectural properties of a building have a significant influence on the spatial reasoning of pedestrians. The interaction among them can be revealed with space syntax, which is a set of methods to analyze the relationship between spatial layouts and human behaviors (De Cock et al., 2020; Van Nes and Yamu, 2021). Furthermore, Vanclooster et al. (2014a) provided some measures from space syntax theory (i.e., in- tegration, choice, and the number of visible decision points) that contribute to defining the risk of getting lost in a building. However, they have not included these measures to evaluate their proposed algorithm in their study and stated they can be used in future studies. To the best of our knowledge, a study that compares indoor paths with actual navigation patterns of pedestrians through space syntax measures has not been reported yet. Given these research gaps, this paper aims to: (1) refine the most commonly used navigation networks in a way that better matches with navigation patterns of pedestrians, (2) include the cognitive aspects in the evaluation of the indoor paths through the use of space syntax measures, (3) provide a comparison of indoor paths and actual navigation patterns of pedestrians through space syntax measures in addition to traditional measures. In this study, the five most commonly used navigation networks which are Medial Axis Transform (MAT), Conformal Constrained Delaunay Triangulation (CCDT), Grid, Middle Point Relation Structure Seg- ment Entrance (MPRSSE), and Universal Circulation Network (UCN) (Lee, 1982; Lee et al., 2010; Lewandowicz, Lisowski, and Flisek, 2019; Park et al., 2020; Li, Claramunt, and Ray, 2010) are utilized each with slight refinements to better reflect actual navigation patterns of the pedestrian. Space syntax measures that reflect the visual perception of pedestrians and spatial configuration of buildings are then assigned to the indoor paths. Since pedestrians are the main user of indoor navigation networks (models), the actual navigation patterns of users are compared with the indoor paths via a user experiment. Thus, the wayfinding results (i.e., computed indoor paths) are quantified not only by traditional measures but also by considering visual access and spatial configuration via the space syntax measures. The remainder of the paper is organized as follows. The next section describes the background and key concepts of indoor navigation networks and space syntax theory with related works. Section 3 describes the methodology conducted in this study. Section 4 provides a case study and presents the experimental results. Section 5 provides a discussion and the last section concludes the main findings and presents future works. 2 RELATED WORK 2.1 Indoor navigation networks and wayfinding For decades, graphs have served as models for the mental representation of an environment (Franz, Mallot, and Wiener, 2005). Such graphs can briefly express indoor spaces as nodes and edges to explain their interrelations. A navigation model is a specific type of data structure that facilitates the execution of path planning algorithms. Two distinct types of navigation models can be identified, which are network-based navigation models and grid-based navigation models, which respectively correspond to vector and raster representation. Commonly, network-based navigation models (i.e., navigation networks) are considered Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 14 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N more efficient as they enable faster processing which is vital for the implementation of indoor navigation (Yan and Zlatanova, 2022). Vanclooster et al. (2016) classified the navigation networks that evolved from topological connec- tivity graphs into three main categories as corridor derivation, cell decomposition, and visibility partitioning. The corridor derivation category mainly emphasizes corridors, where most of the movement takes place. In this category, the centerline of a corridor is obtained through MAT methods (Lee, 1982; Lee, 2004; Taneja et al., 2011) or the Constrained Delaunay Triangulation (CDT). In the related studies, CDT- based methods are commonly used to form navigation networks (Lin and Lin, 2018; Mortari et al., 2014; Teo and Cho, 2016). CDT is improved by densifying the vertices along the boundary of a given geometry in the CCDT algorithm (Park et al., 2020). In the cell decomposition category, indoor space is divided into numerous cells and each cell is repre- sented by a node, and the nodes are connected based on the adjacency aspect of the cells. The grid-based model is one of the cell decomposition models. In grid-based models, each grid cell is expressed by its centroid and the adjacent centroids are connected to form the navigation network and the cells which intersect with the built-in features are eliminated. It is adopted by several studies (Li et al., 2010; Park et al., 2020; Wang et al., 2014; Xu et al., 2017; Xu et al., 2018). The MPRSSE is another navigation network that belongs to the cell decomposition category first used by Lewandowicz et al. (2019). The navigation network uses the centroids of the CDT to construct Voronoi tessellation from these centroids. Then, the Voronoi kernels are connected to each other to form the network edges based on the Poincaré Duality. Lewandowicz et al. (2019) concluded that the MPRSSE navigation network decreases fragments in the corridor centerline while retaining efficiency. Park et al. (2020) used the MPRSSEM navigation network to compare it with the common navigation networks according to the traditional measure. They concluded that MPRSSEM is the most suitable navigation network for minimizing turns made along the route although UCN does not differ significantly from MPRSSEM. A path planning algorithm which adapts the famous concept of the Travelling Sales Person problem to indoor spaces is proposed by Yan et al. (2021). Voronoi tessellation is employed as the basis for deriv- ing the navigation network based on Poincaré Duality for their proposed path planning algorithm. Yan et al. (2022a) also proposed a navigation network based on space subdivisions using Voronoi diagrams. They integrated QR code locations into indoor space to derive their navigation network. Another use of Voronoi tessellation (based on Poincaré Duality) to derive a navigation network is proposed by Yan et al. (2022b). In their study, service area analysis is adapted to indoor spaces, which is a common GIS analysis used mainly in street networks for outdoor spaces. They concluded the proposed method is able to accurately determine the accessible areas, assisting individuals in choosing and reaching the optimal location. The last category defined by Vanclooster et al. (2016) is visibility partitioning emerged from the concept of visibility graph (Turner et al., 2001). In visibility partitioning navigation networks, edges are formed by connecting the nodes using the shortest lines based on their inter-visibility (Pang et al., 2020; Yang and Worboys, 2015). In the case of non-direct visibility, concave corners of the cor- ridor structures are used as intermediate nodes to partition visibility to ensure connectivity within Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 15 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N the visibility graph (Vanclooster et al., 2016). Stoffel, Lorenz, and Ohlbach (2007) introduced a partitioning algorithm by using concave vertices of corridor space to divide indoor space into sub- convex spaces. They named door openings as “boundary nodes”, concave vertices as “reflex nodes” and in the case of non-direct visibility between boundary nodes, the line from the boundary node is connected to the centroid of the line segment between reflex nodes. Yuan and Schneider (2010) presented another visibility partitioning method. They used concave vertices to break the shortest straight lines into segments to retain the shortest distance as much as possible in the case of non- direct visibility between door openings. Although the end-users of the navigation networks are mostly pedestrians, wheel-chaired pedestrians, and robots, hence they all have a width, this factor is ignored in the navigation networks such as those introduced by Liu and Zlatanova (2011) and Yuan and Schneider (2010). As a result, users are forced to follow a path that is too close to built- in features such as walls and columns. Lee et al. (2010) proposed a navigation network based on visibility partitioning named UCN that utilizes buffer zones to shift door nodes to the inner buffer of corridor space to overcome the problem of walking too closely to built-in features. They used the navigation network to compute the walking distances of pedestrians in a building. Park et al. (2020) also utilized the same navigation network to compare it with commonly used navigation networks according to the traditional measures. They concluded that the UCN navigation network generates shorter walking distances. 2.2 Space syntax and wayfinding Evaluating indoor paths solely by distance traveled and turns made along a path gives a coarse solution. This can cause overlooking of the visual perception of pedestrians and the architectural properties of an indoor environment, which have a significant impact on how pedestrians perceive indoor space (Mah- dzar and Safari, 2014). Studies have shown that the legibility of a spatial configuration (i.e., how easily navigable a space is) depends on the differentiation of appearance, visual access, and layout complexity of a building (Mahdzar and Safari, 2014; Montello, 2014; De Cock et al., 2020). The overall properties of a spatial configuration can be quantified via isovists and visibility graph analysis (VGA) (Montello, 2014), which are commonly used methods in space syntax theory. Several studies have investigated the relationship between space syntax and wayfinding in indoor spaces. Peponis, Zimring, and Choi (1990) investigated the relationship between global VGA measure integration with wayfinding performance in a hospital. They found that the higher the integration value is, the higher the people spent time in those spaces. Choi (1999) made an effort to explain the relationship between museum visits and space syntax measures by tracking people in a museum. He found that integration is the best measure to explain museum visits. Haq and Girotto (2003) con- ducted a wayfinding experiment in two complex hospital buildings to evaluate the relationship between overall layout complexity and intelligibility (which is the correlation coefficient between connectivity and integration). They found that intelligibility is a good predictor to evaluate success in a wayfinding task. Haq and Zimring (2003) investigated the relationship between people’s topological knowledge of a space and space syntax measures. They concluded that as people get to know the space better, their movement can be predicted via a global measure such as integration. Li and Klippel (2012) used inter- connection density, axial analysis, and VGA. They found that spending time in a space correlates with Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 16 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N the integration value. They also observed that low visibility had a significant effect on the wayfinding performance of participants so it can be concluded that visual access is an important factor to evaluate wayfinding performance. All the mentioned studies made a significant effort to explain the relation between space syntax and wayfinding behavior within indoor spaces. However, they focus on relations between space and random walking patterns within space, they do not strict participants to follow pre-defined routes such as indoor paths that are computed from navigation networks. Hölscher, Brösamle, and Vrachliotis (2012) made an effort to explain the navigation patterns of novice and expert users within space by using connectiv- ity, visual step depth, and integration measures along the trajectories participants walked. They found that novice users tend to walk higher connected and more integrated paths, whereas since expert users generally know the exact location of space, they tend to move more directly to the destination resulting in less connected and integrated paths. 3 METHODOLOGY 3.1 An overview of the methodology The evaluation of indoor paths requires the generation of navigation networks. For this purpose, a GIS environment is used, which enables the processing of vector spatial data. The five most common naviga- tion networks, which are MAT (Lee, 1982), CCDT (Park et al., 2020), Grid (Li et al., 2010), MPRSSE (Lewandowicz et al., 2019), and UCN (Lee et al., 2010), are utilized with slight refinements to better express actual navigation patterns of the pedestrians. A common way to evaluate indoor paths is to compare the length of a path. In this context, Dijkstra’s shortest path algorithm is employed (Dijkstra, 1959). Vanclooster et al. (2019) and Park et al. (2020) suggested the number of turns made along the paths should also be considered when evaluating wayfinding results (i.e., indoor paths) as turns induce cognitive load in users. Therefore, the number of turns is computed with “node-coordinate based turn calculation algorithm” (Vanclooster et al., 2014b). These discrete measures are converted to raster sur- faces. A user experiment is also conducted to obtain actual navigation patterns. Then, the mean values of the computed space syntax measures along the paths are assigned to the indoor paths and collected navigation patterns of the pedestrians. Next, the collected navigation patterns and indoor paths that are computed from navigation networks are compared with respect to the space syntax measures to evaluate indoor paths. Statistical analyses are then performed to check whether the space syntax measures differ significantly among navigation networks for all door-from-door paths. Figure 1 illustrates the outline of the methodology. The details of the methodology are provided in the sub-sections. Subsection 3.2 describes the data pre- processing steps. The generation of indoor navigation networks and the computation of indoor paths are given in Subsection 3.3 and Subsection 3.4, respectively. Then, space syntax analysis is described in Subsection 3.5. The process of capturing actual navigational patterns is explained in Subsection 3.6. In Subsection 3.7, the comparison of the actual navigation patterns with indoor paths by related measures is described. Finally, the statistical methods for the comparison of all door-from-door paths are given in Subsection 3.8. Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 17 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N Figure 1: The overall methodology of the study 3.2 Data preprocessing An indoor spatial dataset that represents indoor space is needed to create indoor navigation networks. Typically, floorplans can be considered primitive indoor maps (Chen and Clarke, 2020). They contain necessary geometric information related to the structure of the buildings to extract indoor topology and thus construct indoor navigation networks (Yang and Worboys, 2015). However, floorplans usually contain layers that are unnecessary for the generation of indoor navigation networks and hence need to be eliminated (i.e., text, measures, materials, notations, axis). In this study, for the simplification of the floorplans, the model generalization approach is utilized. The semantic selection and semantic grouping operations are adopted to preprocess data in a CAD environment. Semantic selection is utilized by keep- ing built-in structures such as walls, columns, doors, and stairs, and they are grouped semantically for a clear transformation of the CAD floorplans into a GIS environment. The final form of indoor spaces (rooms and corridors), walls, columns and doors are formed via various GIS tools. An example of the model generalization process for the case study buildings is illustrated in Figure 2. Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 18 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N Figure 2: Model generalization process for case study buildings: (a), (b): university, (c), (d): hospital 3.3 Generation of the indoor navigation networks Since indoor paths are derived from indoor navigation networks, their generation plays a significant role in realizing indoor navigation. The generalized floorplans are used to create corresponding navigation net- works. An overall flowchart of the methodology to generate navigation networks is illustrated in Figure 3. Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 19 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N Figure 3: Overall methodology to generate indoor navigation networks Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 20 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N Commonly used navigation networks, especially those that adopt door-to-door approaches in the literature have the problem of network edges being too close to built-in features such as walls, columns, and stairs. To overcome this problem, Lee et al. (2010) proposed a method of shifting door centroids and start/ end centroids of the stairs to an inner buffered space from built-in features, using half of the shoulder width of the average human shoulder as the minimum inner buffer distance. Additionally, people tend to start and end their locomotion process perpendicular to the door and start/end centroids of the stairs (in this study, referred to as “door/stair connection”) (Vanclooster et al., 2014b). Considering these, an approach is proposed by shifting door centroids and start/end centroids to an inner buffer of the corridor. The buffer size is decided as 0.25 m by both observing the pedestrian’s behaviors for the test buildings and considering half of the shoulder width (McDowell et al., 2009) to retain comfort and to match human spatial cognition. Exceptionally, considering the restricted visibility of the door opening area that connects the doors in recesses of the walls to a corridor, which does not affect pedestrian way- finding decisions, the network edges in this area are eliminated. To achieve this, the wall corner vertices corresponding to the doors of the inner buffer are eliminated and the relevant recesses are removed. An example of the shifted door and stair nodes and the inner buffer of corridor space is illustrated for the case study buildings in Figure 4. Figure 4: Shifted Door/Stair nodes and inner buffer polygons for case study buildings (a) university (b) hospital 3.3.1 MAT navigation network MAT algorithm is originally proposed by Lee (1982). The algorithm extracts the medial axis by drawing centerlines having the same distance from the given geometry’s edges. In this study, Lee (1982)’s algorithm is adopted with slight differences. For the proposed approach, first, door/stair connection segments are generated between the doors/stairs and the inner buffer of the corridor. Second, the medial axis of the inner buffer is created using the MAT algorithm. Third, to create the main network, the branches of the medial axis are eliminated considering the Voronoi diagram segments that do not intersect with the boundary of the inner buffer. Then, route connection segments are created by linking the endpoints of the door/stair connection segments to the nearest points on the main network. Finally, the MAT network is created by linking the route connection segments and door/stair connection segments to the main network. An example of the proposed approach for the MAT navigation network is illustrated for the case study buildings in Figure 5. Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 21 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N Figure 5: MAT navigation network: (a) university, (b) hospital 3.3.2 CCDT navigation network Figure 6: CCDT navigation network: (a) university, (b) hospital CDT connects the centroids of triangle edges that compose Delaunay triangles. Thus, it calculates the centerline of the geometry (approximates the medial axis). The problem is that CDT can produce inadequate edges, especially in long and narrow corridors (Park et al., 2020), besides it can also lead to undesired spikes which hinder the centerline (Haunert and Sester, 2008). Hence, the CCDT algorithm is proposed by Park et al. (2020) to overcome inadequate edges by densifying the vertices along the bound- ary of a corridor polygon. The algorithm densifies the vertices along a given geometry’s edges and uses the vertices of built-in features (i.e., walls, doors, stairs, and columns) to construct constrained Delaunay triangles. The centroids of Delaunay triangles are then used to construct network edges. In this study, Park et al. (2020)’s algorithm is utilized with slight differences. For the proposed approach, first, door/stair connection segments are generated. Second, the new vertices along the boundary of the inner buffer are Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 22 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N linearly interpolated to retain conformal characteristics of the Delaunay triangulation that the centerline relies on. Third, CDT is generated based on the final state of the inner buffer, taking walls and columns as constrained edges. Fourth, the centroids of non-constrained edges of CDT are derived and the main CCDT network is formed by connecting them. Finally, the CCDT network is created by linking the route connection segments and door/stair connection segments to the main network. An example of the proposed approach for the CCDT navigation network is illustrated for the case study buildings in Figure 6. 3.3.3 Grid navigation network Grid-based navigation network creation algorithm proposed by Li et al. (2010) forms their network by putting a grid in the extent of indoor space, thus the indoor space is divided into a set of cells. Each cell in the grid is expressed by its centroid and the adjacent centroids are connected to form the navigation network, and the cells which intersect with the built-in features such as walls, columns, and doors are eliminated to ensure that there is no network edge across built-in features. The size of the grid (i.e., resolu- tion) determines the sensitivity of the modeling of movement and the efficiency of the algorithm. In this study, Li et al. (2010)’s algorithm is adopted with slight differences. For the proposed approach, first, door/ stair connection segments are generated. Second, the square grids are created within the inner buffer. For this purpose, the grid resolution is set to 0.5 m. In this way, a grid cell represents the shoulder width of an average-sized human, thus forming a more realistic navigation network (McDowell et al., 2009). Third, the directional routes from each grid centroid are formed by the queen’s case. Fourth, the intersecting grids with wall boundaries are eliminated, and thereby the main network is generated. Finally, the grid network is created by linking the door/stair connection segments to the main network. An example of the proposed approach for the grid navigation network is illustrated for the case study buildings in Figure 7. Figure 7: Grid navigation network: (a) university, (b) hospital 3.3.4 MPRSSE navigation network The MPRSSE algorithm is proposed by Lewandowicz et al. (2019). The algorithm uses the centroids of the CDT edges or the CCDT edges as Voronoi kernels and forms Voronoi polygons from these cen- Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 23 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N troids. The Voronoi polygons are then used to decompose indoor space into neighboring cells. Based on the adjacency of Voronoi polygons, the Voronoi kernels are connected to form corridor paths for all neighboring Voronoi polygons. To form entrance-corridor connections, the MPRSSE navigation network connects the centroid of the corresponding door to the nearest Voronoi kernel. In this study, Lewandowicz et al. (2019)'s algorithm is adopted with slight differences. For the proposed approach, first, door/stair connection segments are generated. Second, the main network is created through the Voronoi polygons obtained from the centroids of CDT edges. Third, the centroids in the Voronoi neighborhood are con- nected. Finally, the MPRSSE network is created by linking the route connection segments and door/ stair connection segments to the main network. An example of the proposed approach for the MPRSSE navigation network is illustrated for the case study buildings in Figure 8. Figure 8: MPRSSE navigation network: (a) university, (b) hospital 3.3.5 UCN navigation network Figure 9: UCN navigation network: (a) university, (b) hospital Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 24 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N The UCN algorithm utilizes buffer zones to shift door/stair nodes to an inner buffer of corridor space and the algorithm forms the network edges based on the inter-visibility of the shifted nodes (Lee et al., 2010). In the case of non-direct visibility, the algorithm uses concave vertices of the inner buffer to generate network edges. In this study, Lee et al. (2010)’s algorithm is used with slight differences. For the proposed approach, first, door/stair connection segments are generated. Second, the endpoints of the door/stair connection segments are connected if they had inter-visibility. Finally, in the case of non- direct visibility, the concave vertices of the inner buffer of the corridor are used as intermediate nodes to create the visibility lines. An example of the proposed approach for the UCN navigation network is illustrated for the case study buildings in Figure 9. 3.3.6 Computation of indoor paths and turns Dijkstra’s shortest path algorithm (Dijkstra, 1959) is utilized on the five navigation networks to com- pute all possible door-from-door paths and their distances. For the turns, the “node-coordinate based turn calculation algorithm” is utilized (Vanclooster et al., 2014b). The algorithm considers a change of direction as a turn only if the angle exceeds a given threshold (the commonly used threshold value is 45°, which is also used in this study). 3.4 Space Syntax analysis The legibility of a spatial configuration depends on the differentiation of appearance, visual access, and layout complexity of a building. The isovists and VGA, which are commonly used methods in space syntax theory, can quantify the overall properties of a spatial configuration. An isovist is defined as a polygon that reflects the visible area from a vantage point from the visual percep- tion of human cognition (Benedikt, 1979). The vantage point of an isovist represents a human observer hence they can be referred to as cognitive measurements of the visual perception of a pedestrian (Hölscher and Brösamle, 2007). Isovists focus on architectural layouts (Turner et al., 2001), thus isovists can be generated on floorplans to evaluate visual access from an observation point. Therefore, isovist measures are usually referred to as local measures (De Cock et al., 2020). To associate the related local isovist measures along a continuous path (e.g., to express how the user experiences space through movement), a set of isovists at regular intervals can be generated. This kind of isovist is referred to as the Minkowski model, and can potentially be used to evaluate indoor paths (Benedikt, 1979; Al-Sayed et al., 2014). VGA is a commonly used analysis in space syntax theory, originally emerged from the concept of isovists (Turner et al., 2001). Representing spatial space in a similar manner to axial lines (Hillier and Hanson, 1984), but in a more granular way by putting a grid to the extent of the spatial unit. The grid size defines the precision of the analysis, thus allowing modeling of the spatial relationships and space occupancy based on the resolution. The VGA measures such as mean visual depth and integration (normalized mean visual depth) can be used to evaluate a place’s centrality in a spatial configuration as it accounts for all other places in the spatial configuration. In this study, five local isovist measures (area, perimeter, occlusivity, vista length, and average radial) and five VGA measures as semi-global and global measures (overt control, covert control, choice, mean visual depth (MVD), and integration) are computed for corridor space (McElhinney, 2020) to evaluate Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 25 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N visual access and the characteristics of spatial configuration. An overview of the local, semi-global and global measures is given in Table 1 and Table 2, respectively. In Table 1, L is radial length, E is edge lengths between the ends of radials, n is the total number of radial samples and k is the sample number in a 360° cycle (McElhinney, 2020). In addition to these measures, through vision (Turner, 2007) is computed. The measure is defined as for each cell in the grid, the number of times a cell is crossed by the inter-visibility lines drawn between the centroid of grid cells. Thus, the places that are most probable to be traveled can be identified (Koutsolampros et al., 2019). Table 1: Equations and short descriptions of local isovist measures (Benedikt, 1979) Local Measures Equation Description Area 2 1 n v i i A L n π = = ∑ The area of the isovist generated from a vantage point. Perimeter 1 n v i i kP E n = = ∑ The sum of the length of edges of an isovist. Occlusivity 2_ 1 n v i occ i iv kO E L nP = = ⋅∑ The proportion of the isovist edges that do not intersect with physical objects within the environment. It indicates the potential to see a space that cannot previously be seen along with the movement. Vista Length Hv = max (Hv, Li ) The length of the longest view of an isovist. Average Radial v iQ L∑ The mean value of all possible view lengths of an isovist. In Table 2, n is the total number of isovist samples, Wv is directed visibility (see McElhinney, 2020), B is the number of points belonging to random walking routes falling within isovists, F is the shortest distance from sample location to all other locations in a spatial configuration and G is the least number of visual steps from sample location to all other locations in a spatial configuration. Table 2: Equations and short descriptions of VGA measures Category Equation Description Semi- Global Overt Control 1 1 1n v i i X n A=   =     ∑ The area of visible space concerning the immediate neighbors. Indicates places where the observer’s view is large (McElhinney, 2020). Covert Control 1 1 . n v i i Y A nWv = = ∑ Mean area of visible space within one visual step divided by Directed Visibility (McElhinney, 2020). Global Choice 1 1 n v i i Z B n = = ∑ The average number of times the given location stands on the shortest path between all other spaces (Hillier et al., 1987). MVD 1 1 n v i i MVD G n = = ∑ The average number of visual steps from a sample point to all other locations (Hillier, 1996). Integration 22 . 2 1 1 3 ( 1)( 2) kk log dValue k k  +   − +      = − − v v dValue kIng MeanVisualDepth .( 2) 2( 1) − = − A normalized version of MVD by using d-value, allowing comparison between spatial layouts independent from their size (Hillier and Hanson, 1984). It indicates the centrality of a place in the layout. Usually, isovist and VGA measures are computed for a set of grid coordinates in the space syntax analysis. To assign these measures to indoor paths, these discrete points should be converted into continuous Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 26 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N data. Therefore, these discrete measures are converted to the raster surfaces (in this study, the resolution is utilized as 0.1 m) and the mean value of the raster cells for each measure is assigned to the respective indoor paths. An example of the raster surfaces is illustrated for the case study buildings in Figure 10. Figure 10: Raster surfaces for area measure: (a) university, (b) hospital 3.5 Collection of the actual navigation patterns An individual's actual navigation pattern can be defined as their preference to move in a certain area or zone while they locomote in an environment (Jamshidi et al., 2020). A user experiment is conducted to capture the actual navigation patterns of pedestrians and to compare them with indoor paths. 3.5.1 Recruitment of the participants A self-report questionnaire to collect fundamental information about the participants (i.e., age, gender, degree of education) is conducted. Spatial abilities are important in the wayfinding process (Li and Klippel, 2016). Therefore, participants are asked to complete the Santa Barbara Sense of Direction scale (SBSOD) (Hegarty et al., 2002), to ensure that there is no significant difference between male and female participants. Also, since the familiarity of a pedestrian with a building has an impact on their wayfinding decisions, their degree of familiarity with the related test buildings is considered (see Section 4.2 for details). 3.5.2 Experiment procedure The experiment procedure is briefly introduced to the participants, and they are accompanied to the main entrance of the related area. At the starting point, the floorplans of the buildings are shown to the participants, and they are asked to find some spaces in the study area. The tasks are chosen as they broadly cover the environment. The participants are not allowed to look further into the floorplan or any kind of map and they are not allowed to ask any questions during the experiment. Each task is assigned by giving semantic information related to indoor spaces (e.g., office Z-067, the stairs that lead to the 1st floor, kitchen, class DZ-132, class DZ-135, WC, etc.). Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 27 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N The participants are invited to the experiment one by one, and the tasks are assigned to the participants step by step; after they reach a goal, the following task is assigned to them and their walking patterns are collected (Hölscher and Brösamle, 2007; Hölscher et al., 2012; Li and Klippel, 2016) and then regener- ated in the GIS environment for further analysis. 3.6 Comparison of the actual navigation patterns To determine substantial isovist and VGA measures for human spatial cognition and link them with navigation patterns of pedestrians; first, Jenks Natural Breaks (JNB) classification is used to classify isovist and VGA measures into three ordinal categories, i.e., “low”, “mid” and “high”. Next, to compare them with the actual navigation patterns of pedestrians, the mean values of the space syntax measures are as- signed to the actual navigation patterns of the pedestrians. After that, the paths are categorized by their values. In this way, the preferences of pedestrians for related isovist and VGA measures are determined. Finally, the mean differences between the actual navigation patterns and indoor paths are evaluated to determine the closest navigation network to the actual navigation patterns for the related routes. 3.7 Comparison of all door-from-door paths All door-from-door indoor paths are evaluated to compare navigation networks against each other by traditional measures as well as isovist and VGA measures with statistical tests. One way-ANOVA test is performed to check whether the mean of traditional measures differs significantly among the navigation networks (i.e., indoor paths for each navigation network). If ANOVA results are significant (p < .05), the Tukey HSD or Games-Howell post-hoc tests are implemented based on the assumption of homogeneity of variance for the data. Concerning isovist and VGA measures, first, a dimension reduction via factor analysis is executed on the interrelated measures (De Cock et al., 2020). Then, these measures are evaluated statistically as applied to the traditional measures. If they fail to fulfil the assumption of normality of one way-ANOVA test, non-parametric Kruskal-Wallis H test can be implemented. If the Kruskal-Wallis H test is significant (p < .05), pairwise Mann-Whitney U tests (with Bonferroni correction) can be implemented as post-hoc tests. Finally, the most suitable navigation network for traditional and space syntax measures is determined. 4 EXPERIMENTS AND CASE STUDY 4.1 Dataset and materials It is acknowledged within the literature that there exist some distinctions between outdoor and indoor environments with regards to navigation and wayfinding (Yan, Zlatanova, and Diakité, 2021). The configuration of indoor spaces (e.g. corridors) differs from the linear layout commonly observed in out- door environments (Diakité and Zlatanova, 2018). Hence, they vary much more than outdoor spaces (Fellner, Huang, and Gartner, 2017) which results in the lack of a comprehensive network model (Park et al., 2020). Furthermore, along with the spatial configuration, the function of an environment (e.g., educational, healthcare, airport, mall) plays a significant role in wayfinding tasks (Devlin, 2014). Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 28 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N Considering the aforementioned aspects, to understand how navigation networks respond to different forms of corridors (e.g., cross junction and complex combined junction), two distinct buildings with different functions, one designed for educational purposes (i.e., university) and the other for healthcare (i.e., hospital), were utilized for the experimental study. The basement floor of a university building was chosen as the first test area (Figure 11a). For the first building, the indoor spaces (e.g., rooms) have a common form. They vary in size, but the typical shape is a rectangle with each surrounded by walls and columns, with different-sized door apertures. The second building is a hospital (Figure 11b). The first floor was utilized as the test area because it contains an L-shaped and combined-shaped complex corridor structure. The corridor space has two square-shaped columns and two rectangular columns along with a sub-corridor that leads to staircases. They tend to cause inaccurate and non-linear paths according to the structural shape of the sub-corridor. Both buildings were chosen as they contain at least a sub-corridor to evaluate indoor paths. Generalized floorplans of the two buildings (see Section 3.2) were utilized as the indoor spatial dataset which is commonly used in the literature to derive indoor navigation networks. For the navigation net- works, the generalized floorplans were used as input data and all operations were performed with ArcPy and ArcGIS tools, additionally, for the MAT navigation network, the medial axis was created through the “centerline” Python library (https://github.com/fitodic/centerline). In addition, for the space syntax analysis, isovist and VGA measures were computed through open-source software Isovist_App (McElhin- ney, 2020) and depthmapX (Varoudis, 2012). Figure 11: Generalized floorplans used in the study: (a) university, (b) hospital 4.2 Results of collecting the actual navigation patterns We conducted a user experiment to capture the actual navigation patterns of pedestrians and to compare them with indoor paths. A total of 30 individuals (13 female and 17 male) aged 19 to 31 (M = 22.63 SD = 2.47) voluntarily participated in the experiment. All the participants provided a written consent Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 29 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N form, and they were informed that they could retreat any time from the experiment. Since there was no significant difference between the wayfinding ability of the male and female participants in accordance with SBSOD test, (t(28) = 1.947, p = .062), all participants were treated as equals. For the university building, most of the participants were students or staff, however, four participants had no prior or minor knowledge of the test area. For the hospital, all of the participants were unfamiliar with the building. The impact of familiarity on the results is discussed in the discussion section. In this study, the participants were asked to find six spaces sequentially in the test areas. After the experiment, the actual navigation patterns were regenerated in the GIS environment (see section 3.5.2). The resulting navigation pattern for a task is given in Figure 12. Figure 12: An example of an actual navigation pattern in the GIS environment 4.3 Results of the comparison for the actual navigation patterns The results of assigning actual navigation patterns (averaged across participants) to the related classes are given in Table 3. For the university, results show that participants prefer to walk on routes that have a “medium” level of isovist measures and overt control that quantifies visual access within the building. Participants tend to prefer “high” choice, and “medium” level of integration, which quantify a place’s centrality (betweenness and closeness centrality) in the spatial configuration of a building. For the hospital, results show that participants again prefer to walk on routes that have a “medium” level of isovist measures and overt control whereas they tend to walk routes with “high” choice and integration. Table 3: Class labels for isovist and VGA measures derived from actual navigation patterns of pedestrians for the university and the hospital Measure University Hospital Value Class Value Class Area 14.111 Medium 23.743 Medium Occlusivity 0.425 Medium 0.403 Medium Overt Control 6.839 Medium 6.010 Medium Choice 0.400 High 0.357 High Integration 21.069 Medium 36.401 High The results for mean differences in isovist and VGA measures between the actual navigation patterns and the navigation networks are given in Table 4. For the university, in terms of isovist measures, the navigation network closest to the actual navigation patterns is the MPRSSE navigation network fol- lowed by CCDT, MAT, Grid and UCN in decreasing order. In terms of VGA measures, the MPRSSE Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 30 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N navigation network is the closest followed by CCDT, MAT, Grid and UCN, except for overt control, where MPRSSE and CCDT switch the orders with a slight difference. For the hospital, with respect to isovist measures, the CCDT navigation network is the closest to the actual navigation patterns, followed by MAT, MPRSSE, Grid and UCN in decreasing order. Concerning VGA measures, for integration, the MAT navigation network is closer to the actual navigation patterns, followed by CCDT, MPRSSE, UCN and Grid in decreasing order. Concerning overt control, CCDT is the closest navigation network followed by MAT, UCN, Grid and MPRSSE. Table 4: Mean differences of actual navigation patterns and navigation networks for the six tasks Measure Movement Model University Hospital Mean Value Mean Difference Mean Value Mean Difference Area Actual 14.111 23.743 MAT 14.719 -0.608 23.331 0.412 CCDT 14.359 -0.248 23.344 0.399 Grid 13.048 1.063 22.786 0.957 MPRSSE 14.155 -0.044 23.090 0.653 UCN 12.938 1.173 22.744 0.999 Occlusivity Actual 0.425 0.403 MAT 0.421 0.004 0.413 -0.010 CCDT 0.426 -0.001 0.413 -0.010 Grid 0.446 -0.021 0.429 -0.026 MPRSSE 0.424 0.001 0.426 -0.023 UCN 0.451 -0.026 0.435 -0.032 Overt Control Actual 6.839 6.010 MAT 6.967 -0.128 5.810 0.200 CCDT 6.848 -0.009 5.812 0.198 Grid 6.194 0.645 5.728 0.282 MPRSSE 6.795 0.044 5.723 0.287 UCN 6.128 0.711 5.763 0.247 Choice Actual 0.400 0.357 MAT 0.403 -0.003 0.350 0.007 CCDT 0.402 -0.002 0.350 0.007 Grid 0.394 0.006 0.351 0.006 MPRSSE 0.401 -0.001 0.349 0.008 UCN 0.393 0.007 0.354 0.003 Integration Actual 21.069 36.401 MAT 22.283 -1.214 34.712 1.689 CCDT 21.733 -0.664 34.586 1.815 Grid 18.749 2.320 32.585 3.816 MPRSSE 20.988 0.081 33.225 3.176 UCN 18.628 2.441 32.788 3.613 Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 31 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N 4.3 Results of the comparison for all door-from-door paths for traditional measures The descriptive statistics for traditional measures and the one way-ANOVA results for traditional measures are given in Table 5 and Table 6, respectively. Table 5: Descriptive statistics for traditional measures Navigation network University Hospital Distance (m) Turn Distance(m) Turn Mean SD Mean SD Mean SD Mean SD MAT 52.428 30.678 4.32 1.806 11.635 5.072 4.26 1.664 CCDT 52.874 30.872 4.40 2.263 11.419 5.018 4.52 2.443 Grid 48.148 30.187 10.30 7.318 9.743 4.699 7.08 4.603 MPRSSE 50.673 29.995 2.85 0.958 10.969 4.932 2.89 1.676 UCN 46.948 29.659 2.18 0.709 9.331 4.514 1.41 0.830 Table 6: Results of one way-ANOVA test for traditional measures ANOVA University Hospital Distance Turn Distance Turn df (between groups) 4 4 4 4 df (within groups) 6625 3110.890 675 315.629 F-value 9.804 993.838 6.095 153.306 p-value p < .001 p < .001 p < .001 p < .001 Since ANOVA results were significant (p < .05) for both buildings, Tukey-HSD and Games-Howell post-hoc tests were executed for the traditional measures, respectively (see Table 7). Table 7: Results of post-hoc test for traditional measures (*p < .05, **p <.01, ***p < .001. MD = Mean Difference) Navigation network University Hospital Distance(MD) Turn(MD) Distance(MD) Turn(MD) MAT CCDT Grid 4.280** -5.98*** 1.892* -2.82*** MPRSSE 1.47*** 1.37*** UCN 5.480*** 2.14*** 2.304** 2.85*** CCDT MAT Grid 4.726** -5.90*** 1.676* -2.56*** MPRSSE 1.55*** 1.63*** UCN 5.926*** 2.22*** 2.088** 3.11*** Grid MAT -4.280** 5.98*** -1.892* 2.82*** CCDT -4.726** 5.90*** -1.676* 2.56*** MPRSSE 7.45*** 4.19*** UCN 8.12*** 5.67*** MPRSSE MAT -1.47*** -1.37*** CCDT -1.55*** -1.63*** Grid -7.45*** -4.19*** UCN 3.725* 0.67*** 1.638* 1.48*** UCN MAT -5.480*** -2.14*** -2.304** -2.85*** CCDT -5.926*** -2.22*** -2.088** -3.11*** Grid -8.12*** -5.67*** MPRSSE -3.725* -0.67*** -1.638* -1.48*** Note: MD values are shown if the p-value is significant (p < .05). Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 32 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N For indoor path distances, MD implies the amount of difference between the mean values of the naviga- tion networks in meters. For example, for the university, the average distance obtained from the MAT navigation network is 5.48 m longer than the UCN navigation network (shorter is better). For turns, MD implies the difference in the average number of turns between the navigation networks (lower is better). Regarding the average distances, the greatest of the significant differences occurred between UCN and CCDT for the university while between UCN and MAT for the hospital. The lowest significant difference was between UCN and MPRSSE for both the university and the hospital (see Table 7). For the hospital, the UCN navigation network yields shorter distances followed by Grid, MPRSSE, MAT and CCDT, while for the hospital MAT and CCDT switch the orders with a slight difference. Regarding the average turns, the highest significant difference occurred between UCN and Grid for both the university and the hospital. The lowest significant difference was between UCN and MPRSSE for the university and MAT and MPRSSE for the hospital (see Table 7). Since the average differences between the remaining models were insignificant, they were considered equivalent for both measures. For both buildings, the UCN navigation network yields a lower number of turns followed by MPRSSE, MAT, CCDT and Grid. 4.4 Results of the comparison for all door-from-door paths for space syntax measures Table 8: Descriptive statistics for isovist and VGA measures Measure Navigation network University Hospital Mean SD Mean SD Area MAT 16.114 3.418 23.088 4.930 CCDT 16.072 3.490 23.046 4.919 Grid 15.013 3.556 22.321 5.142 MPRSSE 15.439 3.579 22.722 4.684 UCN 15.150 3.617 22.564 5.115 Overt Control MAT 6.785 0.857 5.781 0.689 CCDT 6.759 0.857 5.751 0.727 Grid 6.346 0.802 5.515 0.732 MPRSSE 6.496 0.751 5.687 0.725 UCN 6.372 0.794 5.564 0.733 Integration MAT 23.947 4.801 33.775 8.271 CCDT 23.883 4.807 33.384 8.682 Grid 21.815 4.858 32.172 8.687 MPRSSE 22.490 4.835 32.498 8.475 UCN 21.923 4.946 32.355 8.843 Note: Only one measure from each category (local, semi-global, global) is given in the table. The descriptive statistics of all door-from-door indoor paths for isovist and VGA measures are given in Table 8. Since the distribution of the space syntax measures rejected the assumption of normality of one way-ANOVA test, the Kruskal-Wallis H test was used. The resulting significance values of the Kruskal- Wallis H test and the following pairwise Mann-Whitney U tests (with Bonferroni correction) on average ranks between navigation networks for isovist and VGA measures are summarized in Table 9 and Table Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 33 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N 10. For the university, the average ranks of all measures differed significantly among groups. For factor A (area, perimeter, vista length and average radial), factor B (overt control and covert control), factor C (through vision and choice) and integration, the MAT navigation network yields higher average ranks, followed by CCDT, MPRSSE, UCN and Grid navigation networks. For occlusivity, the Grid navigation network yields a higher average rank, followed by UCN, CCDT, MPRSSE and MAT (see Table 9). For the hospital, the measures that differed significantly were solely factor B and factor C. The MAT naviga- tion network yields a higher average rank, followed by CCDT, MPRSSE, UCN and Grid (see Table 10). Table 9: Results for Kruskal-Wallis H test and pairwise Mann-Whitney U tests (with Bonferroni correction) for isovist and VGA measures for the university (p < .05) Measure p-value (KW) Model University MAT CCDT Grid MPRSSE UCN Factor A p < .001 MAT -1218.112 -596.108 -914.569 CCDT -1184.587 -562.582 -881.044 Grid 1218.112 1184.587 -622.005 -303.543 MPRSSE 596.108 562.582 622.005 -318.462 UCN 914.569 881.044 303.543 318.462 Occlusivity p < .001 MAT -669.400 -622.925 CCDT -516.556 -470.081 Grid 669.400 516.556 -656.450 MPRSSE 656.450 -609.976 UCN 622.925 470.081 609.976 Factor B p < .001 MAT -1027.278 -617.446 -907.795 CCDT -988.235 -578.403 -868.752 Grid 1027.278 988.235 -409.832 MPRSSE 617.446 578.403 409.832 -290.349 UCN 907.795 868.752 290.349 Factor C p < .001 MAT -1504.581 -423.391 -1443.031 CCDT -1444.170 -362.980 -1382.620 Grid 1504.581 1444.17 -1081.189 MPRSSE 423.391 362.980 1081.189 -1019.64 UCN 1443.031 1382.620 1019.640 Integration p < .001 MAT -1224.845 -820.451 -1129.006 CCDT -1212.270 -807.876 -1116.431 Grid 1224.845 1212.270 -404.394 MPRSSE 820.451 807.876 404.394 -308.555 UCN 1129.006 1116.431 308.555 Factor A: Factor of interrelated measures, i.e., Area, Perimeter, Vista Length, Average Radial Factor B: Factor of interrelated measures, i.e., Overt Control, Covert Control Factor C: Factor of interrelated measures, i.e., Choice, Through Vision Note 1: The measures are given in the table if the Kruskal-Wallis H test is significant (p < .05) Note 2: Null columns mean that there is no significant difference for the Mann-Whitney U test Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 34 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N Table 10: Results for Kruskal-Wallis H test and pairwise Mann-Whitney U tests (with Bonferroni correction) for isovist and VGA measures for the hospital (p < .05) Measure p-value (KW) Model Hospital MAT CCDT Grid MPRSSE UCN Factor B 0.013 MAT -69.963 CCDT Grid 69.963 MPRSSE UCN Factor C p < .001 MAT -132.886 -109.923 CCDT -108.143 -85.180 Grid 132.886 108.143 -74.445 MPRSSE 74.445 UCN 109.923 85.180 Factor B: Factor of interrelated measures, i.e., Overt Control, Covert Control Factor C: Factor of interrelated measures, i.e., Choice, Through Vision Note 1: The measures are given in the table if the Kruskal-Wallis H test is significant (p < .05) Note 2: Null columns mean that there is no significant difference for the Mann-Whitney U test 5 DISCUSSION 5.1 Comparison of the actual navigation patterns Some noteworthy remarks can be drawn from the comparison of actual navigation patterns and naviga- tion networks. A priori outcome that can be inferred is that participants tend to prefer isovist measures, i.e., those pertaining to visual access, to be in the medium category since low or high visual access can induce cognitive load in users. For example, low occlusivity, i.e., the potential to see a space that cannot previously be seen along with the movement, can lead to uncertainty to decide where to head whereas high occlusivity can lead to a higher amount of information to be processed, thus demanding a higher cognitive load. Another outcome that can be drawn is that since people tend to walk routes that be- long to high choice and through vision categories (Factor C), these measures can be used to forecast where human’s movement flow may occur; therefore, it can come in handy when planning a path with navigation networks or when designing a building based on the occupancy. From the perspective of VGA measures, i.e., those related to the centrality of a place in a building, the university belongs to the medium category of integration whereas the hospital belongs to the high category of integration (see Table 3). The possible reason for this may be the individual's familiarity with the building (Hölscher et al., 2012). For the university, most of the participants have been in the building before whereas none of the participants has ever visited the hospital before. Another factor may be the shape of the corridor spaces of buildings. Since the hospital has a more complex corridor structure and some less visible areas than the university, it can be stated that people prefer walking through higher integrated spaces (higher integration indicates the centrality of a place) which complies with the prior studies in the literature (Haq and Girotto, 2003; Haq and Zimring, 2003; Li and Klippel, 2012). Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 35 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N Since isovist measures are a representation of human cognition from a vantage point, isovist measures are crucial to reflect human cognition when traveling along a path. Therefore, assessing the closeness between actual walking patterns and indoor paths by space syntax measures should be considered when evaluating the navigation networks (i.e., computed indoor paths), which has not been reported yet. In this study, the MPRSSE, CCDT and MAT navigation networks come closer to the actual navigation patterns in terms of space syntax measures, i.e., isovist and VGA measures except choice measure for the hospital where UCN is closer (see Table 4). Although they differ slightly, MPRSSE, CCDT and MAT navigation networks, being a kind of centerline approximation models, can be useful to reflect human perception when navigating indoors. Besides, for our experimental study, the building configuration does not significantly affects the results in terms of the comparison of the actual navigation patterns. Although we only compared them by six routes for both test buildings, the routes containing non-level paths such as stairs, elevators and ramps could also be employed to assess a complete coverage within the building. Also, the participants mostly are in the 20-30 age period and have similar levels of education. These factors can also influence the results as shown by De Cock et al. (2020). 5.2 Comparison of all door-from-door paths The results of traditional measures suggest that the UCN model is the most suitable for length and turn minimization (see Table 7). It is expectable since the UCN model mostly consists of shortest paths or slightly broken shortest paths between a node pair. In most of the previous studies, the visibility-based navigation networks were found the most suitable model; however, it is arguable because that is the case if people know the exact location of the destination. Moreover, in our case, although most of the par- ticipants knew the exact location of some destinations, they first tended to walk towards the centerline until they saw the destination. This indicates that visual access parameters may play a role and should be considered when evaluating navigation networks. From the perspective of isovist and VGA measures, one striking result is that the leading navigation network for traditional measures, which is UCN, falls behind the other navigation networks for space syntax measures (see Table 9 and Table 10). On the other hand, two centerline approximation navigation networks, i.e., CCDT and MAT outperform others. According to both traditional measures as well as isovist and VGA measures, the MPRSSE navigation network can be deemed the most feasible navigation network for indoor navigation as it stands between mid to top for concerned measures (See Table 4 and Tables 7-10). This may stem from the additional paths that come from the adjacency of Voronoi polygons, thus it both approximates the centerline and the break lines of visibility to some extent. However, it should be noted that we are aware of the prefer- ence level of participants for related space syntax measures for only six given tasks (given via the user experiment). Here, in this section, we have checked whether the related measures differ significantly for all indoor paths (for each navigation network). Therefore, we can only interpret the results in a general sense. Besides, for our experimental study, the building configuration does not significantly affects the results in terms of the comparison of the all door-from-door paths. Further research is needed to deter- mine whether preferences for space syntax measures change with task variation (i.e., other indoor paths via the collection of navigation patterns). Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 36 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N 6 CONCLUSION AND FUTURE WORK Indoor navigation networks are a significant way to implement indoor navigation since they concep- tualize indoor space, model the interrelations of structural components, and try to express the actual navigation patterns of pedestrians. Due to the lack of clear movement patterns in an indoor environ- ment, there is an ongoing debate to establish an indoor navigation network that is in line with human cognition to support the wayfinding process. However, existing studies mostly focus on length and turn minimization to evaluate navigation networks. In this study, to address the related gap, we utilized also space syntax measures to evaluate the five most commonly used navigation networks (MAT, CCDT, Grid, MPRSSE, and UCN) each with slight refinements, followed by a user experiment to assess the closeness between actual navigation patterns and the navigation networks as well as to determine user preferences for related space syntax measures. The findings of the experimental study show that according to the traditional measures, a visibility- based navigation network (UCN) is the most suitable. However, the user experiment suggests that the centerline approximation navigation networks (MAT, CCDT and MPRSSE) are better to reflect the visual perception of pedestrians and the preference for the centrality of a place according to the space syntax measures. When all measures are concerned, it can be concluded that the MPRSSE navigation network is the most feasible for indoor navigation for our test buildings. However, it should be noted that none of the examined navigation networks step forward for all the tested measures. Nevertheless, the MPRSSE model covers most of the aspects of our experimental study. For future studies, the variety of the user characteristics (age, gender, level of education), the participant’s degree of familiarity with the building, and the buildings with different configurations/functions (e.g., air- ports, shopping malls, metro stations, etc.) should be considered when evaluating indoor paths. In addition, the routes containing non-level paths can be investigated to assess complete coverage within a building. Despite the availability of various algorithms and studies, establishing an indoor navigation network that fully supports one’s wayfinding process remains challenging and the debate to determine the most proper navigation network seems to continue to grow. Literature and references: Al Sayed, K., Turner, A., Hillier, B., Iida, S., Penn, A. (2014). Space syntax methodology, 4th Edition. Bartlett School of Architecture, UCL, London. Arthur, P. L., Passini, R. (1992). Wayfinding: People, signs and architecture. McGraw Hill, New York. Benedikt, M. (1979). To take hold of space: Isovists and isovist fields. Environment and Planning B: Planning and Design 6 (1): 47–65. DOI: https://doi.org/10.1068/ b060047 Choi, J., Lee, J. (2009). 3D geo-network for agent-based building evacuation simulation. In S. Zlatanova (Ed.), J. Lee (Ed.), 3D Geo-Information Sciences, Lecture Notes In Geoinformation And Cartography (pp. 283-299). Springer. DOI: https://doi.org/10.1007/978-3-540-87395-2_18 Choi, Y. K. (1999). The morphology of exploration and encounter in museum layouts. Environment and Planning B 26 (2): 241–250. DOI: https://doi.org/10.1068/b4525 Chen, J., Clarke, K. C. (2020). Indoor cartography, Cartography and Geographic Information Science, 47 (2): 95-109. DOI: https://doi.org/10.1080/1523040 6.2019.1619482 De Cock, L., Ooms K., Van de Weghe, N., Vanhaeren, N., Pauwels, P., De Maeyer, P. (2020). Identifying what constitutes complexity perception of decision points during indoor route guidance. International Journal of Geographical Information Science 35 (6): 1232–1250. DOI: https://doi.org/10.1080/1365 8816.2020.1719109 Devlin, A. S. (2014). Wayfinding in healthcare facilities: Contributions from environmental psychology. Behavioral Sciences 4 (4): 423–436. DOI: https:// doi.org/10.3390/bs4040423 Diakité, A. A., Zlatanova, S. (2018). Spatial subdivision of complex indoor environments Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 37 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N for 3D indoor navigation. International Journal of Geographical Information Science 32(2): 213–235. DOI: https://doi.org/10.1080/13658816.2017.1376066 Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik 1: 269–271. DOI: https://doi.org/10.1007/BF01386390 Fellner I, Huang H, Gartner G. (2017). “Turn Left after the WC, and Use the Lift to Go to the 2nd Floor”—Generation of Landmark-Based Route Instructions for Indoor Navigation. ISPRS International Journal of Geo-Information 6(6):183. DOI: https://doi.org/10.3390/ijgi6060183 Franz, G., Mallot, H. A., Wiener, J. M. (2005). Graph-based models of space in architecture and cognitive Wangscience: a comparative analysis. In Y. Leong (Ed.), Architecture, Engineering and Construction of Build Environments (pp. 30-38). http://hdl.handle.net/11858/00-001M-0000-0013-D4B7-E, accessed 19.7.2022. Giudice, N. A., Walton, L. A., Worboys, M. (2010). The informatics of indoor and outdoor space: A research agenda. Proceedings of the Second ACM SIGSPATIAL International Workshop On Indoor Spatial Awareness, San Jose, CA (pp. 47–53). New York, NY: ACM. DOI: https://doi.org/10.1145/1865885.1865897 Gunduz, M., Isikdag, U., Basaraner, M. (2016). Trending technologies for indoor fm: Looking for ‘geo’ in information. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences IV-2/W1: 277–283. DOI: https://doi. org/10.5194/isprs-annals-IV-2-W1-277-2016 Haq, S., Girotto, S. (2003). Ability and intelligibility: Wayfinding and environmental cognition in the designed environment. The Bartlett School of Graduate Studies, University College London. Haq, S., Zimring, C. (2003). Just down the road a piece: The development of topological knowledge of building layouts. Environment and Behavior 35 (1): 132–160. DOI: https://doi.org/10.1177/0013916502238868 Haunert, J. H., Sester, M. (2008). Area collapse and road centerlines based on straight skeletons. GeoInformatica 12 (2): 169–191. DOI: https://doi.org/10.1007/ s10707-007-0028-x Hegarty, M., Richardson, A. E., Montello, D. R., Lovelace, K., Subbiah, I. (2002). Development of a self-report measure of environmental spatial ability. Intelligence 30 (5): 425–447. DOI: https://doi.org/10.1016/S0160- 2896(02)00116-2 Hillier, B., Hanson, J. (1984). The social logic of space. Cambridge University Press. DOI: https://doi.org/10.1017/CBO9780511597237 Hillier, B. (1996). Space is the machine: A configurational theory of architecture. Cambridge University Press. https://doi.org/10.1016/S0142-694X(97)89854-7 Hillier, B., Burdeau, R., Peponis, J., Penn, A. (1987). Creating life or does architecture create anything?. Architecture et Comportement/Architecture and Behaviour 3: 233-250. https://discovery.ucl.ac.uk/id/eprint/101, accessed 19.7.2022. Hölscher, C., Brösamle, M. (2007). Capturing indoor wayfinding strategies and differences in spatial knowledge with space syntax. Proceedings of the 6th International Space Syntax Symposium, Istanbul,2007. Hölscher, C., Brösamle, M., Vrachliotis, G. (2012). Challenges in multilevel wayfinding: A case study with the space syntax technique. Environment and Planning B: Planning and Design 39 (1): 63–82. DOI: https://doi.org/10.1068/b34050t Jamshidi, S., Ensafi, M., Pati, D. (2020). Wayfinding in Interior Environments: An Integrative Review. Frontiers in Psychology 11: 1-24. DOI: https://doi. org/10.3389/fpsyg.2020.549628 Karas, I. R., Batuk, F., Akay, A. E., Baz, I. (2006). Automatically Extracting 3D Models and Network Analysis for Indoors. In: A. Abdul-Rahman (Ed.), S. Zlatanova (Ed.), V. Coors (Ed.), Innovations in 3D Geo Information Systems. Lecture Notes in Geoinformation and Cartography. Springer, Berlin, Heidelberg. DOI: https:// doi.org/10.1007/978-3-540-36998-1_31 Kneidl, A., Borrmann, A., Hartmann, D. (2012). Generation and use of sparse navigation graphs for microscopic pedestrian simulation models. Advanced Engineering Informatics 26 (4): 669–680. DOI: https://doi.org/10.1016/j.aei.2012.03.006 Koutsolampros, P., Sailer, K., Varoudis, T., Haslem, R. (2019). Dissecting visibility graph analysis. Proceedings of the 12th Space Syntax Symposium, Beijing, China, 8-13 July 2019. Kwan, M. P., Lee, J. (2005). Emergency response after 9/11: The potential of real-time 3D GIS for quick emergency response in micro-spatial environments. Computers, Environment and Urban Systems 29 (2): 93–113. DOI: https://doi.org/10.1016/j. compenvurbsys.2003.08.002 Lee, D. T. (1982). Medial Axis Transformation of a planar shape. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-4 (4): 363–369. DOI: https:// doi.org/10.1109/TPAMI.1982.4767267 Lee, J., Kwan, M. P. (2005). A Combinatorial data model for representing topological relations among 3D geographical features in micro-spatial environments. International Journal of Geographical Information Science 19 (10): 1039–1056. DOI: https://doi.org/10.1080/13658810500399043 Lee, J. K., Eastman, C. M., Lee, J., Kannala, M., Jeong, Y. S. (2010). Computing walking distances within buildings using the Universal Circulation Network. Environment and Planning B: Planning and Design 37 (4): 628–645. DOI: https://doi.org/10.1068/b35124 Lewandowicz, E., Lisowski, P., Flisek, P. (2019). A modified methodology for generating indoor navigation models. ISPRS International Journal of Geo-Information 8 (2): 60. DOI: https://doi.org/10.3390/ijgi8020060 Li, R., Klippel, A. (2012). Wayfinding in libraries: Can problems be predicted? Journal of Map and Geography Libraries 8 (1): 21–38. DOI: https://doi.org/10.1080/ 15420353.2011.622456 Li, R., Klippel, A. (2016). Wayfinding Behaviors in Complex Buildings: The Impact of Environmental Legibility and Familiarity. Environment and Behavior 48 (3): 482–510. DOI: https://doi.org/10.1177%2F0013916514550243 Li, X., Claramunt, C., Ray, C. (2010). A grid graph-based model for the analysis of 2D indoor spaces. Computers, Environment and Urban Systems 34 (6): 532–540. DOI: https://doi.org/10.1016/j.compenvurbsys.2010.07.006 Lin, W. Y., Lin, P. H. (2018). Intelligent Generation of Indoor Topology (i-GIT) for human indoor pathfinding based on IFC models and 3D GIS technology. Automation in Construction 94: 340–359. DOI: https://doi.org/10.1016/j. autcon.2018.07.016 Liu, L, Zlatanova, S. (2011). A "door-to-door" path-finding approach for indoor navigation. Proceedings of the Gi4DM 2011: GeoInformation for Disaster Management, Antalya, Turkey, 3-8 May 2011. Mahdzar, S. S. S., Safari, H. (2014). Legibility as a result of geometry space: Analyzing Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 38 | | 67/1 | GEODETSKI VESTNIK RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N and Comparing hypothetical model and existing space by space syntax. Life Science Journal 11 (8): 309–317. McDowell, M. A., Fryar, C. D., Ogden, C. L., (2009). Anthropometric reference data for children and adults: United States, 1988-1994. Vital and Health Statistics. Series 11, Data from the National Health Survey 249: 1–68. McElhinney, S. (2020). The Isovist_App: A basic user guide. https://www.isovists. org/user_guide/, accessed 19.7.2022. Montello, D. R. (2014). Spatial cognition and architectural space: Research perspectives. Architectural Design 84 (5): 74–79. DOI: https://doi.org/10.1002/ad.1811 Mortari, F., Zlatanova, S., Liu, L., Clementini, E. (2014). "Improved Geometric Network Model" (IGNM): A novel approach for deriving connectivity graphs for indoor navigation. ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences II–4: 45–51. DOI: https://doi.org/10.5194/isprsannals-II-4-45-2014 Pang, Y., Zhou,L., Lin, B., Lv, G., Zhang, C. (2020). Generation of navigation networks for corridor spaces based on Indoor Visibility Map. International Journal of Geographical Information Science 34 (1): 177–201. DOI: https://doi.org/10. 1080/13658816.2019.1664741 Park, J., Goldberg, D. W., Hammond, T. (2020). A comparison of network model creation algorithms based on the quality of wayfinding results. Transactions in GIS 24 (3): 602–622. DOI: https://doi.org/10.1111/tgis.12632 Peponis, J., Zimring, C., Choi, Y. K. (1990). Finding the building in wayfinding. Environment and Behavior 22 (5): 555–590. DOI: https://doi . org/10.1177/0013916590225001 Rüetschi, U. J., Timpf, S. (2005). Modelling wayfinding in public transport: Network space and scene space. In T. Barkowsky (Ed.), C. Freksa (Ed.), M. Knauff (Ed.), B. Krieg-Brückner (Ed.), B. Nebel (Ed.), Spatial Cognition IV. Reasoning, Action, Interaction, Spatial Cognition 2004, Lecture Notes in Computer Science: Vol. 3343 (pp. 24–41). Springer. DOI: https://doi.org/10.1007/978-3-540- 32255-9_2 Stoffel, E. P., Lorenz, B., Ohlbach, H. J. (2007). Towards a semantic spatial model for pedestrian indoor navigation. Advances in Conceptual Modeling – Foundations and Applications. ER 2007. Lecture Notes in Computer Science: Vol. 4802 (pp. 328–337). Springer. DOI: https://doi.org/10.1007/978-3-540-76292-8_39 Taneja, S., Akinci, B., Garrett, J. H., Soibelman, L., East, B. (2011). Transforming an IFC-based building layout information into a geometric topology network for indoor navigation assistance. Proceedings of the 2011 International Workshop on Computing in Civil Engineering, Miami, FL (pp. 313–322). Reston, VA: ASCE. DOI: http://doi.org/10.1061/41182(416)39 Teo, T. A., Cho, K. H. (2016). BIM-oriented indoor network model for indoor and outdoor combined route planning. Advanced Engineering Informatics 30 (3): 268–282. DOI: https://doi.org/10.1016/j.aei.2016.04.007 Turner, A., Doxa, M., O’Sullivan, D., Penn, A. (2001). From isovists to visibility graphs: A methodology for the analysis of architectural space. Environment and Planning B: Planning and Design 28 (1): 103–121. DOI: https://doi.org/10.1068/b2684 Turner, A. (2007). To move through space: Lines of vision and movement. Proceedings of the 6th International Space Syntax Symposium, Istanbul, 2007. Van Nes, A., Yamu, C. (2021). Introduction to space syntax in urban studies. DOI: https://doi.org/10.1007/978-3-030-59140-3 Vanclooster, A., Ooms, K., Viaene, P., Fack, V., Van de Weghe, N., De Maeyer, P. (2014a). Evaluating suitability of the least risk path algorithm to support cognitive wayfinding in indoor spaces: An empirical study. Applied Geography 53: 128–140. DOI: https://doi.org/10.1016/j.apgeog.2014.06.009 Vanclooster, A., Van de Weghe, N., Fack, V., De Maeyer, P. (2014b). Comparing indoor and outdoor network models for automatically calculating turns. Journal of Location Based Services 8 (3: 11th International Symposium on Location-Based Services): 148–165. DOI: https://doi.org/10.1080/17489725.2014.975289 Vanclooster, A., Van de Weghe, N., De Maeyer, P. (2016). Integrating Indoor and outdoor spaces for pedestrian navigation guidance: A review. Transactions in GIS 20 (4): 491–525. DOI: https://doi.org/10.1111/tgis.12178 Vanclooster, A., Vanhaeren, N., Viaene, P., Ooms, K., De Cock, L., Fack, V., Van de Weghe, N., De Maeyer, P. (2019). Turn calculations for the indoor application of the fewest turns path algorithm. International Journal of Geographical Information Science 33 (11): 2284–2304. DOI: https://doi.org/10.1080/13658816.2019.1630629 Varoudis, T. (2012). DepthmapX - open source multi-platform spatial network analysis software. https://varoudis.github.io/depthmapX/, accessed 19.7.2022. Wang, B., Li, H., Rezgui, Y., Bradley, A., Ong, H. N. (2014). BIM based virtual environment for fire emergency evacuation. Scientific World Journal 2014. DOI: https://doi.org/10.1155/2014/589016 Xu, M., Wei, S., Zlatanova, S., Zhang, R. (2017). Bim-based indoor path planning considering obstacles. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences IV-2/W4: 417–423. DOI: https://doi. org/10.5194/isprs-annals-IV-2-W4-417-2017 Xu, W., Liu, L., Zlatanova, S., Penard, W., Xiong, Q. (2018). A pedestrian tracking algorithm using grid-based indoor model. Automation in Construction 92: 173–187. DOI: https://doi.org/10.1016/j.autcon.2018.03.031 Yan, J., Zlatanova, S., Diakité, A. (2021). A unified 3D spacebased navigation model for seamless navigation in indoor and outdoor. International Journal of Digital Earth 14 (8): 985-1003. DOI: https://doi.org/10.1080/17538947.2021.1913522 Yan, J., Zlatanova, S., Lee, J., Liu, Q. (2021). Indoor Traveling Salesman Problem (ITSP) path planning. ISPRS International Journal of Geo-Information 10 (9): 616. DOI: https://doi.org/10.3390/ijgi10090616 Yan, J., Lee, J. B., Zlatanova, S., Diakité, A. A., Kim, H. (2022a). Navigation network derivation for QR code based indoor pedestrian path planning. Transactions in GIS 26: 1240– 1255. DOI: https://doi.org/10.1111/tgis.12912 Yan, J., Zlatanova, S., Lee, J.B. (2022b). An indoor service area determination approach for pedestrian navigation path planning. Cartography and Geographic Information Science. DOI: https://doi.org/10.1080/15230406.2022.2142849 Yan, J., Zlatanova, S. (2022). Seamless 3D Navigation in Indoor and Outdoor Spaces. CRS Press. Yang, L., Worboys, M. (2015). Generation of navigation graphs for indoor space. International Journal of Geographical Information Science 29 (10): 1737–1756. DOI: https://doi.org/10.1080/13658816.2015.1041141 Yuan, W., Schneider, M. (2010). iNav: An indoor navigation model supporting length- dependent optimal routing. In Painho M. (Ed.), Santos M. (Ed.), Pundth H. (Ed.), Geospatial Thinking, Lecture Notes in Geoinformation and Cartography: Vol. 0 (pp. 299-313), Springer. DOI: https://doi.org/10.1007/978-3-642-12326-9_16 Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 | | 39 | GEODETSKI VESTNIK | 67/1 | RE CE NZ IRA NI ČL AN KI | P EE R- RE VIE W ED AR TIC LE S SI | E N Atakan Bilgili Yildiz Technical University, Faculty of Civil Engineering, Department of Geomatic Engineering Davutpasa Campus Esenler Istanbul 34220, TURKEY e-mail: atakanb@yildiz.edu.tr Assist. Prof. Dr. Alper Sen Yildiz Technical University, Faculty of Civil Engineering, Department of Geomatic Engineering Davutpasa Campus Esenler Istanbul 34220, TURKEY e-mail: alpersen@yildiz.edu.tr Prof. Dr. Melih Basaraner Yildiz Technical University, Faculty of Civil Engineering, Department of Geomatic Engineering Davutpasa Campus Esenler Istanbul 34220, TURKEY e-mail: mbasaran@yildiz.edu.tr Bilgili A., Sen A., Basaraner M. (2023). Evaluation of Indoor Paths based on Indoor Navigation Network Models and Space Syntax Measures. Geodetski vestnik, 67 (1), 11-39. DOI: https://doi.org/10.15292/geodetski-vestnik.2023.01.11-39 Atakan Bilgili, Alper Sen, Melih Basaraner | VREDNOTENJE NOTRANJIH POTI, IZRAČUNANIH Z MODELI NAVIGACIJSKIH OMREŽIJ V ZAPRTIH PROSTORIH IN MERAMI PROSTORSKE SINTAKSE | EVALUATION OF INDOOR PATHS BASED ON INDOOR NAVIGATION NETWORK MODELS AND SPACE SYNTAX MEASURES | 11-39 |