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Chapter 6:
Analysis of Bilateral Asymmetry in Mammograms via Directional Filtering with Gabor Wavelets
Editor(s): Jasjit Singh Suri; Rangaraj M. Rangayyan
Author(s): Rangayyan, Rangaraj M.; Ferrari, Ricardo J.; Desautels, J.E. Leo; Frère, Annie F.
Most of the concepts used in image processing and computer vision for oriented pattern analysis have their roots in neurophysiological studies of the mammalian visual system. Campbell and Robson suggested that the human visual system decomposes retinal images into a number of filtered images, each of which contains intensity variations over a narrow range of frequency and orientation. Marcelja, and Jones and Palmer demonstrated that simple cells in the primary visual cortex have receptive fields that are restricted to small regions of space and are highly structured, and that their behavior corresponds to local measurements of frequency. According to Daugman, one suitable model for the 2D receptive field profiles measured experimentally in mammalian cortical simple cells is the parameterized family of 2D Gabor functions. Jones and Palmer and Daugman showed that a majority of cortical cells have 2D receptive field profiles that can be fitted well, in the sense of a statistical test, by members of the family of 2D Gabor elementary functions. Another important characteristic of Gabor functions or filters is their optimal joint resolution in both space and frequency, which suggests that Gabor filters are appropriate operators for tasks requiring simultaneous measurement in the two domains. Except for the optimal joint resolution possessed by the Gabor functions, the difference of Gaussian (DOG) and difference of offset Gaussian (DOOG) filters used by Malik and Perona have similar properties. Gabor filters have been presented in several works on image processing; however, most of these works are related to segmentation and analysis of texture. Rolston and Rangayyan, and Rolston proposed methods for directional decomposition and analysis of linear components in images using multiresolution Gabor filters. Multiresolution analysis using Gabor filters has natural and desirable properties for analysis of directional information in images; most of these properties are based on biological vision studies as described previously. Other multiresolution techniques have also been used with success in addressing related topics such as texture analysis and segmentation, and image enhancement. Chang and Kuo, for instance, developed a new method for texture classification that uses a tree-structured wavelet transform for decomposing an image. In their work, image decomposition is performed by taking into account the energy of each subimage instead of decomposing subsignals in the low-frequency channels. If the energy of a subimage is higher than a certain fixed threshold value C, then the decomposition procedure is applied again; otherwise, the decomposition is stopped in that region.
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