Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression

Abstract

Abstract-A three-layered neural network is described for transforming two-dimensional discrete signals into generalized nonorthogonal 2-D "Gabor" representations for image analysis, segmentation, and compression. These transforms are conjoint spatiahpectral representations [lo], [15], which provide a complete image description in terms of locally windowed 2-D spectral coordinates embedded within global 2-D spatial coordinates. Because intrinsic redundancies within images are extracted, the resulting image codes can be very compact. However, these conjoint transforms are inherently difficult to compute because t e elementary expansion functions are not orthogonal. One o r t h o g o n k i n g approach developed for 1-D signals by Bastiaans [SI, based on biorthonormal expansions, is restricted by constraints on the conjoint sampling rates and invariance of the windowing function, as well as by the fact that the auxiliary orthogonalizing functions are nonlocal infinite series. In the present "neural network" approach, based upon interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights, the network finds coefficients for complete conjoint 2-D Gabor transforms without these restrictive conditions. For arbitrary noncomplete transforms, in which the coefficients might be interpreted simply as signifying the presence of certain features in the image, the network finds optimal coefficients in the sense of minimal mean-squared-error in representing the image. I n one algebraically complete scheme permitting exact reconstruction, the network finds expansion coefficients that reduce entropy from 7.57 in the pixel representation to 2.55 in the complete 2-D Gabor transform. In "wavelet" expansions based on a biologically inspired log-polar ensemble of dilations, rotations, and translations of a single underlying 2-D Gabor wavelet template, image compression is illustrated with ratios up to 20: 1. Also demonstrated is image segmentation based on the clustering of coefficients in the complete 2-D Gabor transform. This coefficient-finding network for implementing useful nonorthogonal image transforms may also have neuroscientific relevance, because the network layers with fixed weights use empirical 2-D receptive field profiles obtained from orientation-selective neurons in cat visual cortex as the weighting functions, and the resulting transform mimics the biological visual strategy of embedding angular and spectral analysis within global spatial coordinates.

Biometric identification systems

“…Preprocessing consists of the application of pseudo-polar coordinates (taking into account that the inner and outer circular boundaries may not be completely concentric) and standardizing the radial size of the iris (so that possible dilation of the pupil does not a ect the system) [19]. As for feature extraction, 2D Gabor wavelets [26] are used to perform a multiscale analysis of the iris [17,16,15]. A set of quadrature pair frequency-selective ÿlters are used to analyze regions of the image at di erent scales.…”

Evaluating the Effect of Image Preprocessing on an Information-Theoretic CAD System in Mammography

“…Specifically, it has been shown that Gabor filters model the spatial frequency and orientation responses of simple cells in the primary visual cortex [39,40]. The Gabor representation has been shown to be optimal in the sense of minimizing the joint two-dimensional uncertainty in space and frequency [41]. Since the Gabor filter bank is derived from a wavelet basis with dilations and orientations, they are essentially bandpass filters.…”

Distributed computing methodology for training neural networks in an image-guided diagnostic application

“…structural [24], statistical [25][26][27] and random process [28], this work uses statistical measurements based on second order statistics [27]. These statistical descriptors have been estimated using the method of cooccurrence matrices applied to each region of an image.…”