Wavelet transform and lip model - Courbebaisse, Guy (Image analysis and stereology, 2002)
The Fourier transform is well suited to the study of stationary functions. Yet, it is superseded by the Wavelet transform for the powerful characterizations of function features such as singularities. On the other hand, the LIP (Logarithmic Image Processing) model is a mathematical frameworkdeveloped by Jourlin and Pinoli, dedicated to the representation and processing of gray tones images called hereafter logarithmic images. This mathematically well defined model, comprising a Fourier Transform "of its own", provides an effective tool for the representation of images obtained by transmitted light, such as microscope images. This paper presents a Wavelet transform within the LIP framework, with preservation of the classical WaveletTransform properties. We show that the fast computation algorithm due to Mallat can be easily used. An application is given for the detection of crests.
Keywords: Fourierjeva analiza; Image Processing, Computer-Assisted; Slika, obdelava z računalnikom; Fourier Analysis; Wavelet transformacija; analiza slik