ImageAnalStereol2009;28:195-203
TechnicalNote
TOUCHINGGRAINKERNELS SEPARATIONBY GAP-FILLING
MATTHIEU FAESSEL1ANDFRANCISCOURTOIS2
1MINES Paristech,Centre deMorphologieMath´ ematique,Mat h´ ematiquesetSyst` emes,35rue SaintHonor´ e,
77305FontainebleauCedex,France,2UMR 1145,INRA, AgroParisTech,1 AvenuedesOlympiades,917 44
MassyCedex,France
e-mail: matthieu.faessel@ensmp.fr,francis.courtois@a groparistech.fr
(AcceptedSeptember29,2009)
ABSTRACT
Separation of touching grain kernels is a recurring problem in image analysis. Morphological methods to
separatemergedobjectsinbinaryimagesaregenerallybase donthewatershedtransformappliedtotheinverse
of the distance function. This method is efficient with rough ly circular objects, but cannot separate objects
beyonda certainelliptic shapenorwhen thecontact zonesar e toonumerousor toolarge. Thispaperpresents
a gap-fillingmethodappliedto the skeletonofthe imageback groundasan alternativetechniqueto gofurther
in the fused objects separation process. Open lines resulti ng from skeletonizationare prolongedaccordingto
theirdirectionfromcorrespondingendpoints. Ifthedista ncebetweentwolinesissmallerthanacertainvalue,
theirrespectiveendpointsareconnected. Resultsofcombi neduseofwatershedandgap-fillingbasedmethods
are presented on sample binary images. An example of its use o n an particularly complex image containing
rice grains shows that it allows to segment up to 90% of the gra ins when classical watershed methods allow
onlyto segment25% of the grains. An applicationto breakage and cracksassessing of parboiledrice kernels
ispresented.
Keywords:gap-filling,mathematicalmorphology,overlapp inggrains,segmentation,skeleton.
INTRODUCTION
Fused grain kernels separation is a classical
problem in binary images segmentation. For the
general case, solutions are proposed with different
approches (Schmitt and Hasse, 2009): contour or
active contour based techniques, graph or level
set approaches, parametric fitting or morphological
methods. Morphological methods used to separate
fused objects in binary images are generally based
on the watershed transform (Beucher, 1990) on the
complementary of the distance function (Talbot and
Appleton, 2002). However, when fused particles have
elliptic shape or when they are fused beyond a certain
point, watershed algorithms may be insufficient to
produce an appropriate segmentation (Shatadal et al.,
1995; Talbot and Appleton, 2002; Wang and Paliwal,
2006). Fig. 1 shows the watershed transform on
couples of circular fused objects with decreasing
distances between their centers. As we can see,
classicalwatershedbasedalgorithmsareeffectiveeven
foranimportantdegreeofoverlap( d=1.2R).Indeed,
we knowthataslong asthe centersoftwo diskslie on
each side of their disecting line, watershed algorithm
willsucceedinseparatingthem(BeucherandVincent,
1990).
d=1.8R1.7R 1.6R 1.5R1.4R1.3R1.2R
Fig. 1.Watershed based segmentation on circular
fusedobjects.
On the contrary, Fig. 2 shows the result of
watershed based segmentation on elliptical fused
objects with a constant distance between their centers
andagrowing Rmax/Rminratio.
Rmax
Rmin=11.11.21.31.41.5 1 .6d=1.5Rmin
Fig. 2.Watershed based segmentation on elliptical
fusedobjects.
It appears that above a certain shape factor,
watershed algorithm fails to separate two overlapping
objects.
Those functions operate on markers (intrinsic
markers such as the maxima of the euclidean distance
function, or markers defined arbitrarly by means of
more elaboarted technics) of fused objects and their
success depends on the ability to obtain as many
markers as the number of fused kernels. Fig. 3
represents the ultimate points (the maxima of the
distancefunction)oftheelliptical fusedkernels.
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FAESSELMET AL:Touchinggrainkernelsseparationbygap-filling
Fig. 3.Ultimate points (white) of elliptical fused
objects(black).
It appears that the more the objects have an
important Rmax/Rminratio, the more their markers
position convergeuntil they merge. From that point, it
is impossible for watershed based algorithm to detect
more thanasinglekernel.
Severaltechniqueshave been explored to improve
the determination of markers of elliptical objects:
the use of the elliptical distance in place of
Euclidean distance (Talbot and Appleton, 2002), the
bisector (Meyer, 1979) or conditional bisector (Talbot
and Vincent, 1992) functions, etc..., but those
methods are inefficient or difficult to use when fused
objects are numerous, not perfect disks, or when
contact zones are important. It is also possible to use
methodsbasedonellipse fitting (TalbotandAppleton,
2002; Evans et al., 2004; Zhang et al., 2005), which
appear efficient as long as clusters contain only a few
grains,orwhoseperformancedependsonthefitofthe
contourto anidealellipse (Baia etal.,2009).
When concavities corresponding to contact zones
areimportant,themostevidentsolutionremainstofind
a way to locate them and to link them together (Visen
et al., 2001; van den Berg et al., 2002; Schmitt and
Hasse,2007).Inthispaper,wepresentamethodusing
the skeleton of the background image to locate the
concavities and to draw clipping lines, in order to
improvethesegmentationofnon-circularfusedobjects
in binaryimages.
The initial scope of this work was to develop
image analysis techniques to quantify some quality
parameters on rice grains: global properties (amount
of broken kernels, ...), but also individual grain
properties (dimensions, degree of crack-free kernels,
...), which implies to be able to individualize each
grain ofasample.
MATERIALSANDMETHODS
The material used in this study is based on long
white rice grains of type “Ariete” (origin Camargue,
France). Thecharacteristic dimensionsfor this type of
grainsare2mmforthewidth and7mm forthelength
(which representsa Rmax/Rminratio of3.5).The main purpose of this work was to develop a
light and fast solution to extract individual properties
such as length, width or state (broken, cracked,...)
from a rice grain sample. Some studies give an
important initial effort to position manually grains
to make easier the stage of image analysis (Shatadal
etal.,1995;vanDalen,2004).Inourcase,theprocess
had to be as simple and as fast as extract a grain
sample from a batch, place it on the acquision system
and launch the acquisition and analysis process.
Furthermore, samples sometimes contain hundreds of
grainsandmanualgrainplacementwouldleadtoanon
negligible waste of time and a need of an important
surfacefor imageacquisition.
Theacquisitionsystemisasimplestandardflatbed
scanner. Grains are tabled directly on the glass of the
scannerandarequicklyapportionedtoavoidexcessive
overlapping. Then a black box is used to recover
the grains and isolate them from ambient light. To
reducethesizeoftheimages,onlya115mm ×70mm
surface was used to place the grain sample (about 2–
3 g corresponding to about 200 grains) and a 300 dpi
resolutionand8bits depth(grayscale)wereused.
Fig.4.Sampleimageobtainedwiththeflatbedscanner
(850×800pixels).
Thealgorithmsweredeveloppedandimplemented
under Java using the ImageJ software1(Girish and
Vijayalakshmi,2004). ImageJ is a public domain Java
image processing program inspired by NIH Image for
the Macintosh and developped by Wayne Rasband at
the Research Services Branch, National Institute of
MentalHealth,Bethesda,Maryland,USA.
1http://rsbweb.nih.gov/ij/index.html
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ImageAnalStereol2009;28:195-203
IMAGE BINARIZATION
It is important to notice that the information
contained in the grey-level image is generally useful
in order to split fused objects. In Fig. 5 is represented
the morphological gradient calculated on the grey-
level image. As we can see, gradient between grains
isveryweakcomparedtothevariationscorresponding
to internal grain fissures and therefore can not be
exploitedto splitgrains.
Fig.5.Morphologicalgradientcalculatedonthegrey-
levelimage ofFig.4 (detail).
As our images have two distinct classes of
pixels (grains and background), we use the Otsu
algorithm (Otsu, 1979), which allows to find
automatically an optimum threshold. Ostu algorithm
consists in separating the two classes so that their
combined spread (within-class variance) is maximal.
Theresulting binaryimageis presentedin Fig. 6.
Fig. 6.Binaryimageobtainedwith theOtsualgorithm
appliedonthe grey-levelimage (Fig.4).CONCAVITIESLOCATION
In order to locate concavities between grains, it
is possible to use the cluster convex hull. Another
possibility is to analyse the concavity of the contours
of thegrain clusters (Baia etal., 2009),but becauseof
noise or of the image grid along contours, it is usual
to detect false concave regions, and to obtain an over-
estimationofthe numberofconcavepoints.
In our case, we use the morphological skeleton to
detect the corners of the complementary image and
then,extracttheconcavepointsfromtheskeletonopen
lines. The use of the morphological skeleton to detect
object corners in a binary image can be found with
different implementations (Dinesh and Guru, 2006).
The main advantages are that it is a robust and non-
parametricmethod.
The skeleton is calculated on the background
of the binary image. It is obtained by means of a
morphological thinning (Serra, 1982). The algorithm
used here is the single pass thinning algorithm
developped by Zhou et al.(1995). The result is
presentedin Fig.7.
a b c
Fig. 7.Skeleton of the background image. (a) Binary
image,(b) Backgroundimageskeleton(c)a overb.
GAP-FILLINGMETHOD
Automatic reconnection of linear segments is also
a classical problem in image analysis. When portions
of missing lines are sufficiently small, morphological
operations such as closing (dilation followed by
erosion) or localisation of nearest neighbours are
commonlyusedinordertoconnectthem(Zhang etal.,
1999; Visen et al., 2001). In our case, the distance
betweenthe endpointsof the lines we wantto connect
is often larger than the width of the grains, and the
size of closing necessary to link them would lead to
completelyfillskeletoncells.
The pairing procedure used here to join endpoints
is quite similar to the “linking edge-chains” method
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FAESSELMET AL:Touchinggrainkernelsseparationbygap-filling
described by Ferrari et al.(2006), except that we
use 2D spherocylinders in place of isocele trapezia to
extend and join open-lines. First, segment endpoints
arelocalized.An“average”directionofthesegmentis
calculated on a given length from its endpoint. Open
linesarethenlinearlyextendedfrom theirendpointon
a specified distance until they join (or until another
extending line reach their neighborhood in a given
radius).
ENDPOINTSDETERMINATION
Endpoints are detected from the skeleton thanks
to the morphological hit-or-miss operation (Serra,
1982).Consideringacoupleoftwodisjointstructuring
elements T={T′,T′′}, the hit-or-miss operation is
defineduponimage Xas:
ηT(X) ={z:T′′(z)⊆Xc;T′(z)⊆X}
=εT′(X)∩εT′′(Xc),
whereεT′(X)andεT′′(Xc)arerespectivelytheerosion
ofXwithT′and the erosion of the complementary
imageXcwith thestructuring element T′′.
In order to extract the extremity of open lines
(Fig. 9a), we use the hit-or-miss operation with a “U”
structuring element and its seven successive rotations
(Fig. 8).
T′: T′′: T:
r1 r2 r3 r4 ...
Fig. 8.Definition of the “U” structuring element and
its firstrotations.
LINESDIRECTIONCALCULATION
Starting from the endpoints, we apply successive
morphological thinnings (Serra, 1982) with the same
“U” structuring element (and rotations) to thin the
openlinesonacertainlength,oruntilidempotence(in
this case, the junction of several lines). The thinning
operationcorrespondstotheresiduebetweenanimage
andits hit-or-miss transformation:
ΘT(X) =X\ηT(X) =X\[εT′(X)∩εT′′(Xc)]
The “average” direction of a line is calculated
between an end point and the last point obtained by
thinningthe correspondingline (Fig. 9b).a b
c d
Fig. 9.Gap-Filling steps. a) End-points localisation.
b) Open-lines direction evaluation. c) Open-lines
prolongation.d)End-pointsjunction.
LINESPROLONGATION
This line of average direction is then extended
fromterminalpointsonafixedlength.Ateverystepof
reconstruction,weextendthelineofapoint(pixel)and
determineifit intersectswith anotherone(Fig. 9c).
Inordertodetecttheintersectionbetweendifferent
lines, each line is represented on a black image with a
different value. Each time we extenda line ifrom one
pixel,wecheckifthecorrespondingpixelontheblack
imagehasthevalue0orthe valueofanotherline j. In
thefirstcase,wecontinuetheextendingprocess,andin
the second one, we define a new contact pair between
linesiandj.Whenacontactpairhasbeenestablished,
we draw as straight line between the corresponding
endpoints. This line is then subtracted to the binary
imageto splittheconnexgrains.
Note that line crossings are banned: when
prolongatingaline,ifthenextpixelcorrespondstothe
skeleton or to a previous link, the prologation process
oftheline is stopped.
IMPLEMENTATION
During the pairing procedure, some problems can
occur:
–two corresponding lines may never connect ; this
happens if two lines are parallel or if they don’t
intersect between the two end-points. To ensure
that two corresponding contact zone lines join, at
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ImageAnalStereol2009;28:195-203
eachstepofprolongation,welookforthepresence
of a nearby line within a radius of fixed size Rn
(Fig. 10).
As previously, each time we extend a line ifrom
one pixel, we checkon the black image (on which
extending lines are represented) the presence of a
pixel with a different value in a radius of Rn. If a
pixelwith a value jis found, we set a new contact
pairbetweenlines iandj.
Rn
Fig. 10.Detectionoftwo lines proximity.
–the average direction calculated from the end-
point to the open line root doesn’t fit the global
curvature of the line, which will be prolonged in
anunexpecteddirection.Forthisreason,itisoften
better to calculate the average direction on a fixed
lengthLcratherthanonthewholelengthoftheline
(Fig. 11a).
–if a line is prolonged on a too long distance,
unexpected contacts can occur between lines
correspondingto different contact zones.To avoid
this situation, lines are prolonged only on a fixed
distance Lp, generally smaller than the specific
lengthofa grain(Fig. 11b).
Lcroot
a b
Fig. 11. Lenght of direction calculation     a).
Prolongationlength b).
In order to obtain good results, it is necessary
to execute the procedure sequentially with growing
values for the parameters Lc,LpandRn. First, small
values of Lc,LpandRnare used in order to fill
small gaps.Thentheoperation is repeatedwith higher
values, to join progressively more distant lines. The
maximum values for the parameters are respectivelythe specific length and width of a grain for LpandRn
(Lcis limited bythelengthofthe open-line).
The figure 12 illustrates the sequence of pairing
procedures with growing parameters: at the first step,
we use small values of Lp,RnandLc. Only two lines
(on the bottom left) are linked. At the second step,
valueschosenfortheparametersallowtobuildthetwo
upperlinksofthefigure,andthelastlinkisdetermined
only at the third step. At each step, the particles
revealed by the new links are measured. If their width
and length are lower or equal to those of a typical
grain, they are considered as correctly segmented and
are removed from the image. The procedure is then
continued with higher parameters, until the image is
empty(oruntilthemaximumvaluesofparametersare
reached).
a b
c
Fig.12.Sequenceofpairingprocedures: a)Firststep
with low values of parameters L p, Rnand Lc. b)
Second step with medium values. c) Third step with
highvalues.
Theresultofsuchasequenceappliedontheimage
7a is observed in Fig. 13. As we can see, the result is
exactly what we expect to, except for the two grains
on the top of the image which are not separated. In
thisparticularconfiguration,theskeletondidnotreveal
two, but only one concavity (see Fig. 13a) and thus,
onlyoneopen-line.Then,theleft open-linecannotbe
pairedandnosplitline canappear.
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FAESSELMET AL:Touchinggrainkernelsseparationbygap-filling
(a) -Gap-Filling. (b)-Resulton binaryimage.
Fig.13.Resultofthegap-filling(a)andresultinggrain
splitting (b). Non  splitted grains(atthe top).
APPLICATION TO BREAKAGE AND
CRACKS ASSESSING OFPARBOILED
RICEKERNELS
The criterion used by industrials for evaluating
quality of paddy rice is the measurement of the head
rice yield (HRY, in %) after milling. The rice is
processed in an pilot rice-mill, generally consisting
of a husker with rubber disks and a mill with an
abrasive cone. Husked kernels are then separated in
two fractions using a grain sorter: a whole fraction
and a broken one. A kernel is considered broken if its
length is smaller than 3 /4 of this of a whole kernel.
The result is expressed in terms of rice processing
yield,whichistheratiooftheweightofwhite(husked)
kernels to the total weight and in terms of head rice
yield, corresponding also to the ratio of the weight of
whole kernels to the total weight of white rice (norm
ISO 6646:2000. Rice – Determination of the potential
milling yieldfrom paddyandfrom huskedrice).
Ouralgorithmusesthesameclassificationcriteria:
once the grains are individualized, they are classified
accordingtotheirdimensions.Thelengthofthegrains
is measured using the Feret’s diameter. A grain is
considered as broken if its length is smaller than 3/4
ofthis ofawholekernel.
Furthermore, in order to characterize the cracking
level of a grain, we evaluate the number of parts
it contains. As we can see in Fig. 4, when a grain
contains fissures, cracking zones present important
grey level contrasts (due to different cracking planes
orientation). Thus, parts can be easily identified using
information such as the gradient. In order to close
the contours corresponding to the different cracking
zones of a grain, the gradient image is flooded by a
watershed. To control the level of segmentation, the
number of local minima is reduced using a gaussian
filteronthegradientimagebeforethefloodingprocess.
Once the different zones are revealed, the grains are
classified according to the number of zones theycontain: strongly cracked (more than 3 zones), slighly
cracked(between2 and3 zones)andintact(1zone).
h=0
h=1
h=4
Fig. 14. Result of the segmentation obtained using
the watershed transform on the distance function with
markerscorrespondingtotheh-minimaofthedistance
function.
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ImageAnalStereol2009;28:195-203
RESULTS
In Fig. 14, we can see the segmentation obtained
using the classical watershed transformation on
the distance function on a grain sample image
with a particularly difficult configuration: lots of
conglomerates, important contact zones (only 15% of
the grains are single). In order to control the level of
segmentation obtained by the watershed, the markers
used to perform the flooding are determined using the
h-minima (Soille, 1999) of the distance function. As
we cansee,evenwith arelativelyhighvalueof h(h=
4), there are still unwantedgrain clippings. In orderto
completely avoid any inappropriate cuttings, we have
to process the watershed with h≥5. This handles
onlyverysimplecontactcases(clusterscontainingtwo
or threee grains with small contact zones), and the
amountofmergedgrainsremainsverylarge.
Fig. 15 represents the result of our method on the
same image (resulting countours have been projected
ontheoriginalgrey-levelimage).Grainsconsideredas
successfullysegmentedare representedwith a colored
contour (in this example, grains are classified with
a color code according to their state: blue for intact
grains, green for broken, yellow and red for slightly
andstronglycrackedgrains).
Fig. 15. Gap-filling based segmentation on a
complex image of many touching rice grains. Grains
consideredassuccessfullysegmentedareanalysedand
represented with a colored contour: blue for intact
grains, green for broken, yellow and red for slightly
andstronglycrackedgrains.
We observe that most of the time, contours of
grains are perfectly detected. Only a few grains are
notcorrectlysegmented.Asitwassaidpreviously,this
happends generally when concavities are not clearlyrevealed by the skeleton (inexistant or too short open-
lines).
The rate of successfully segmented grains is
estimated using the ratio of the surface of correctly
segmentedgrainstothesurfaceofallthegrains(easily
determined by counting the foreground pixels on the
binary image). In this case, segmentation based on
watershed algorithms detects successfully only 25%
of the grains total surface, while gap-filling algorithm
reaches90% of correctly segmentedgrains surface. In
the case of more simple configurations, our algorithm
allows us to obtain from 95% to 100% of successful
segmentation(Fig. 16).
Fig. 16.Gap-filling based segmentation on a simpler
case(1000×1000pixels).
In order to validate the method, percentages
of broken kernels obtained using image analysis
were compared to measures obtained by manually
separating and counting broken and intact grains.
Different samples of processed, or not, parboiled rice
dried in various conditions were used. As previously,
each sample contains about 2–3 g (corresponding to
about 200 grains). As we can see in Fig. 17, the
estimates from the image analysis approach match
perfectly both the measures using the ISO norm and
the manualcounting.
This algorithm was used on several hundred
of images with more or less complicated cases,
containing from ten to one thousand rice grains, with
the same rate of success. The time needed to process
one image depends of the number of grains and of
the complexity of grains appointment, and is about
several seconds (the time for the segmentation of the
850×800 pixels image in Fig. 15, is about 8 seconds
ona standardlaptopcomputer).
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FAESSELMET AL:Touchinggrainkernelsseparationbygap-filling
0102030405060708090
0 10 20 30 40 50 60 70 80 90% Broken grains (Image Analysis)
% Broken grains (lab)parboiled paddy rice
linear fit
processed parboiled rice
Fig. 17. Comparison between breakage ratios as
obtained from laboratory visual inspection or ISO
norm analysis, and sorting and image analysis
estimation. The fitted slope of the line is 1.00434 ±
0.00898.
CONCLUSION
Separation of touching grains involves specific
problems when grains have an elliptic shape and
when clusters of grains contains many objects. We
have seen that classical watershed based algorithms
are not sufficient in this case. In this paper, a gap-
filling method using the skeleton of the background
image was introduced to draw clipping lines between
touching grains. Then, a concrete implementation of
the algorithm was presented in order to fulfil the
separation process. Therefore, for images composed
of many touching grain kernels with elliptic shapes,
the described “gap-filling” based algorithm allows us
to improve the segmentation process. More detailed
application of this algorithm in food industry is
presented in an upcoming article (Courtois et al.,
2009).
ACKNOWLEDGEMENTS
The work was financially supported by the Office
National Interprofessionel des C´ er´ eales (ONIC),
France.
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