Moshe Porat

The generalized Gabor scheme of image representation in biological and machine vision

A scheme suitable for visual information representation in a combined frequency-position space is investigated through image decomposition into a finite set of two-dimensional Gabor elementary functions (GEF). The scheme is generalized to account for the position-dependent Gabor-sampling rate, oversampling, logarithmic frequency scaling and phase-quantization characteristic of the visual system. Comparison of reconstructed signal highlights the advantages of the generalized Gabor scheme in coding typical bandlimited images. It is shown that there exists a tradeoff between the number of frequency components used per position and the number of such clusters (sampling rate) utilized along the spatial coordinate. >

The farthest point strategy for progressive image sampling

A new method of farthest point strategy (FPS) for progressive image acquisition-an acquisition process that enables an approximation of the whole image at each sampling stage-is presented. Its main advantage is in retaining its uniformity with the increased density, providing efficient means for sparse image sampling and display. In contrast to previously presented stochastic approaches, the FPS guarantees the uniformity in a deterministic min-max sense. Within this uniformity criterion, the sampling points are irregularly spaced, exhibiting anti-aliasing properties comparable to those characteristic of the best available method (Poisson disk). A straightforward modification of the FPS yields an image-dependent adaptive sampling scheme. An efficient O(N log N) algorithm for both versions is introduced, and several applications of the FPS are discussed.

Localized texture processing in vision: analysis and synthesis in the Gaborian space

Recent studies of cortical simple cell function suggest that the primitives of image representation in vision have a wavelet form similar to Gabor elementary functions (EFs). It is shown that textures and fully textured images can be practically decomposed into, and synthesized from, a finite set of EFs. Textured-images can be synthesized from a set of EFs using an image coefficient library. Alternatively, texturing of contoured (cartoonlike) images is analogous to adding chromaticity information to contoured images. A method for texture discrimination and image segmentation using local features based on the Gabor approach is introduced. Features related to the EFs parameters provide efficient means for texture discrimination and classification. This method is invariant under rotation and translation. The performance of the classification appears to be robust with respect to noisy conditions. The results show the insensitivity of the discrimination to relatively high noise levels, comparable to the performances of the human observer.<<ETX>>

Analysis and synthesis of multicomponent signals using positive time-frequency distributions

A new approach to the analysis and reconstruction of multicomponent nonstationary signals from their time-frequency distribution (TFD) is presented. Specifically, we consider a TFD based on the recently introduced minimum cross entropy principle (MCE). This positive TFD is cross-terms free and, hence, has an advantage over the family of bilinear distributions. Based on the MCE-TFD, a new algorithm for reconstructing the phase and amplitude parameters of each component of the signal is developed. To evaluate the accuracy of the algorithm. Monte Carlo simulations are presented and compared with the corresponding Cramer-Rao bound. It is shown that the new algorithm is superior to presently available methods in both efficiency and performance. It is concluded that together with the MCE-TFD representation, the proposed approach provides a powerful tool for analysis of nonstationary multicomponent signals embedded in additive Gaussian noise.

Color image compression using inter-color correlation

Natural images are characterized by high correlation between their RGB color components. Most representation and compression techniques reduce the redundancies between color components by transforming the color primaries into a decorrelated color space, such as YIQ or YUV. In this paper a different approach to color information analysis is considered. Since the high correlation of color channels implicitly suggests a localized functional relation between the components, it could be used in an alternative framework by approximating subordinate colors as functions of a base color. This way, only a reduced number of parameters is required for coding the color information. Compression results are presented and compared with JPEG, and the parameters that affect the coding quality are studied and discussed. The results show the advantages of the new correlation-based approach over the YIQ/YUV decorrelation techniques as used in JPEG and related applications.

Image reconstruction from localized phase

The authors present a novel approach to image representation using partial information defined by the localized phase. The scheme is implemented using the short-time (short-distance) Fourier transform. This is a generalization of the Gabor scheme which is well-established with regard to biological representation of visual information at the level of the visual cortex. Similar to processing in vision, the DC component is first extracted from the signal and treated separately. Computational results and theoretical analysis indicate that image reconstruction from the localized phase representation requires fewer computer operations and yields an improved rate of convergence compared to reconstruction from the global phase representation. It is also implementable with fast algorithms using highly parallel architecture. >

Similarity-invariant signatures for partially occluded planar shapes

A methodology is described for associating local invariant signature functions to smooth planar curves in order to enable their translation, rotation, and scale-invariant recognition from arbitrarily clipped portions. The suggested framework incorporates previous approaches, based on locating inflections, curvature extrema, breakpoints, and other singular points on planar object boundaries, and provides a systematic way of deriving novel invariant signature functions based on curvature or cumulative turn angle of curves. These new signatures allow the specification of arbitrarily dense feature points on smooth curves, whose locations are invariant under similarity transformations. The results are useful for detecting and recognizing partially occluded planar objects, a key task in low-level robot vision.

Multi-window Gabor schemes in signal and image representations

Motivated by biological vision, schemes of signal and image representation by localized Gabor-type functions are introduced and analyzed. These schemes, suitable for information representation in a combined frequency-position space are investigated through signal decomposition into a set of elementary functions. Utilizing the Piecewise Zak transform (PZT), the theory of the multi-window approach is given in detail based on the mathematical concept of frames. The advantages of using more than a single window are analyzed and discussed. Applications to image processing and computer vision are presented with regard to texture images, and considered in the context of two typical tasks: image representation by partial information and pattern recognition. In both cases the results indicate that the multi-window approach is efficient and superior in major aspects to previously available methods. It is concluded that the new multi-window Gabor approach could be integrated efficiently into practical techniques of signal and image representation.

Color image coding using regional correlation of primary colors

Most color compression systems reduce the redundancies between the RGB color components by transforming the color primaries into a decorrelated color space, such as YIQ or YUV. In this paper a different compression approach is proposed. Since the high correlation of the RGB color channels implicitly suggests a localized functional relation between the components, it is used here in an alternative framework, by approximating subordinate colors as functions of a base color allowing that only a reduced number of parameters is required for coding the color information. Furthermore, since this correlation is particularly high locally, the image is first sub-divided into regions and for each region the correlation is analyzed and exploited separately. The size of the encoded regions is gradually reduced to allow progressively a more refined description of the transmitted image. Compression results of this progressive approach, which could be useful for slower communication channels, are presented and compared with JPEG as a typical example of the decorrelation approach. Our conclusion is that the proposed new approach to progressive image coding could be superior to presently available compression techniques.

Correlation-based approach to color image compression

Most coding techniques for color image compression employ a de-correlation approach-the RGB primaries are transformed into a de-correlated color space, such as YUV or YCbCr, then the de-correlated color components are encoded separately. Examples of this approach are the JPEG and JPEG2000 image compression standards. A different method, of a correlation-based approach (CBA), is presented in this paper. Instead of de-correlating the color primaries, we employ the existing inter-color correlation to approximate two of the components as a parametric function of the third one, called the base component. We then propose to encode the parameters of the approximation function and part of the approximation errors. We use the DCT (discrete cosine transform) block transform to enhance the algorithms performance. Thus the approximation of two of the color components based on the third color is performed for each DCT subband separately. We use the rate-distortion theory of subband transform coders to optimize the algorithms bits allocation for each subband and to find the optimal color components transform to be applied prior to coding. This pre-processing stage is similar to the use of the RGB to YUV transform in JPEG and may further enhance the algorithms performance. We introduce and compare two versions of the new algorithm and show that by using a Laplacian probability model for the DCT coefficients as well as down-sampling the subordinate colors, the compression results are further improved. Simulation results are provided showing that the new CBA algorithms are superior to presently available algorithms based on the common de-correlation approach, such as JPEG.