We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and stochastic auto-regressive models, and exploit it for optimally choosing Sobolev parameters from available pixel values. To this aim, we use exact continuous-to-discrete mapping of the auto-regressive model that is based on symmetric exponential splines. The mapping is computationally efficient, and we exploit it for maximizing an approximated Gaussian likelihood function.We account for non-Gaussian Lévy-type processes by deriving a more robust estimator that is based on the sample auto-correlation sequence. Both estimators use multiple initialization values for overcoming the local minima structure of the fitting criteria. Experimental image resizing results indicate that the auto-correlation criterion can cope better with non-Gaussian processes and model mismatch. Our work demonstrates the importance of the auto-correlation function in adaptive image interpolation and image modeling tasks, and we believe it is instrumental in other image processing tasks as well.

In this work we introduce a new algorithm for color image compression based on inter-color correlations of the RGB (red, green and blue) primary colors of images and video. We employ the Bayer pattern, widely used in digital cameras and mobile phones, for its compression software. Our proposed method outperforms JPEG2000 for all the images tested, with a gain of more than 1dB in peak signal-to-noise ratio (PSNR) on average. Our conclusion is that the new algorithm could be useful in efficient visual communication.

Real-time multimedia applications often require efficient bit-rate reduction. This is mainly done by requantization, usually in the DCT domain. This work introduces theoretical rate-distortion analysis that allows for straightforward selection of the quantization step needed to achieve a given bit-rate. The analysis is based on the Laplace-like distribution of DCT coefficients in the transform domain and on the structure of the quantizers commonly used in image coding. We show that the proposed transcoding design achieves efficient compression at relatively low distortion, while keeping the computational complexity very low, allowing for real-time implementation.

Most demosaicing algorithms today are based on first reconstructing the green (G) color component followed by the reconstruction of the red (R) and the blue (B) components using the green. This approach and associated methods of using the differences R-G and B-G are arbitrary and in most cases not optimal. Instead, we propose optimal color spaces for demosaicing. Our optimization is based on energy compactness and smoothness of the color components. We compare the performance of the proposed algorithms to presently available demosaicing methods and show that the new approaches are superior both visually and quantitatively. Our conclusion is that the new color spaces improve the performance of demosaicing algorithms.

We introduce a new exponential-based shift-invariant approach to image interpolation using stochastic modeling. Our model stems from Sobolev reproducing kernels of exponential type, motivated by their role in continuous-domain stochastic autoregressive processes. An algorithm based on these tools is developed and tested. Experimental results of image and texture scaling show that these exponential kernels outperform currently available polynomial B-spline models. Our conclusion is that the proposed Sobolev-based image modeling could be instrumental and a preferred alternative in major image processing tasks.

A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks.

Many sources of information are of analogue or continuous-time nature. However, digital signal processing applications rely on discrete data. We consider the problem of approximating L2inner products, i.e., representation coefficients of a continuous-time signal, while having the possibly non-ideal signal samples, as the only available data. By adopting a generalized sampling scheme, a minimax solution is suggested. We then compare our approach with the piecewise-constant approximation method, commonly used for this problem

A new class of features for wavelet-based texture classification is introduced using a new feature-weighting scheme adapted to non-Euclidean similarity measures. The feature extraction is based on the histogram of the local second moment estimates of the wavelet transform. It is shown that the bins' centers of such histograms should be scaled logarithmically rather than linearly. The distance between two texture features is measured using the x/sup 2/ similarity measure, weighted according to the feature's degree of dispersion within the training dataset. Classification experiments of the proposed approach using an orthonormal wavelet transform show improved classification results compared to presently available methods.

A new low complexity transcoder for pre-encoded MPEG2 video is introduced. Based on the various architectures for video bit-rate reducer, we optimize the compression on the macro-block (MB) level and analyze the resulted quantization errors. We propose a low complexity rate-control algorithm accordingly. Finally, we examine coded video data in order to evaluate our model.

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.

Fourier transform magnitude is, in many cases, the only measurable data in fields such as optics, X-ray imaging, crystallography and astronomy. Spectral phase information is impractical to obtain in these instances, due to the relatively short wavelength involved. In this paper a new algorithm for image reconstruction from localized spectral magnitude is presented. The algorithm is based on localized Fourier transform magnitudes and a single spatial sample to fully reconstruct an image. The process reconstructs successively larger image blocks, until the entire image is restored, using the spatial sample as initial data. It is shown, that even in cases where the spatial sample is badly corrupted, it has little effect on the reconstructed image. The algorithm is analyzed in the presence of noise, and simulation results are presented.

Ultrasound images exhibit inherent geometric distortions due to variations in sound speed within the body. Other distortions include missing surfaces parallel to the direction of the ultrasonic rays, intense speckle noise, shadows and resolution inconsistency. These depend on the positioning of the transducer relative to the scanned organs, and considerably degrade the quality of the images obtained. We introduce a new algorithm that combines ultrasound images taken from different angles using spatial warping and compounding to obtain a quality-enhanced image. The algorithm is iterative: in each iteration the B-Mode images are divided into blocks and a matching procedure is performed between blocks of the reference images. The pixels are translated according to inter-block interpolation, subject to physical and medical constraints, resulting in warped images that function as the input signal to the following iteration. The algorithm was implemented and tested in-vitro and the results are presented and discussed.

The importance of localized phase in signal representation is investigated. The convergence rate of the POCS algorithm (projection onto convex sets) used for image reconstruction from spectral phase is defined and analyzed, and the characteristics of images optimally reconstructed from phase-only information are presented. It is concluded that images of geometric form are most efficiently reconstructed from their spectral phase, whereas images of symmetric form have the poorest convergence characteristics. The transition between the two extremes is shown to be continuous. The results provide a new approach and analysis of the previously reported advantages of the localized phase representation over the global approach, and suggest possible compression schemes.

A new localized approach to video teleconferencing is introduced using three-dimensional vector quantization (VQ). According to the proposed model, recent localized history of the sequences is used to encode present frames based on a hierarchical approach. The results indicate a high compression ratio of over 100:1 with a high quality of the perceived sequence.

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.

The POCS algorithm (projection onto convex sets) used for image reconstruction from spectral phase is investigated. The convergence rate of the algorithm is defined and analyzed, and the characteristics of images optimally represented by phase-only information are presented. It is concluded that images of geometric form are most efficiently represented by their spectral phase whereas images of symmetric form have the poorest convergence characteristics. The transition between the two extremes is shown to be continuous. The results provide a new approach and analysis of the reported advantages of the localized phase representation over the global approach, and suggest possible compression schemes.

The representation of images by phase-only information is investigated. The iterative algorithm used for image reconstruction from phase is analyzed, and the characteristics of images optimally represented by phase-only information are presented. It is concluded that images of geometric structure are most efficiently represented by their spectral phase, whereas images of symmetric form have the poorest convergence characteristics.

A new method of "farthest point strategy" (FPS) for progressive image acquisition is presented. Its main advantage is in retaining its uniformity with the increased density, providing an 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 superior antialiasing properties. 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.

2-D shape boundary segmentation is required as a fundamental and important stage in the recognition of partially occluded objects. We introduce here a new segmentation method capable of extracting a controlled number of segments along a smooth boundary curve. This new approach is invariant to similarity transformation, and partial occlusion has only marginal influence on the segmentation of the visible part. The basic concept is to transform the curve into another one which intersects itself. Points of intersection of the new curve are re-transformed to the original curve and serve as endpoints of segments. Properties of the transform are discussed, and conditions for existence of intersection points are given. Simulation results of gray level images are presented, and advantages of our method over conventional approaches relying on singular points of the curvature are discussed.>

A method for image analysis, based on the formalism of functional analysis is proposed. This approach, which is employed for pattern recognition in the combined position-orientation space, is motivated by a variety of neurophysiological findings that emphasize the importance of the orientation feature in visual image processing and analysis. The approach is applied to the so-called Glass patterns, which are special cases of images characterized uniquely by their orientational feature of local correlations between pairs of corresponding dots. The approach can be of interest in the analysis of optical flow.>

The problem of signal approximation by partial sets of a given nonorthogonal basis is addressed, motivated by the essentially practical requirement of signal representation in infinite-dimensional spaces. Utilizing the biorthonormal approach, a general theorem for optimal vector approximation in Hilbert spaces is suggested, based on distinction between two biorthonormal sets related to a partial basis. A sufficient and necessary condition interrelating these sets is given, and a general systematic method for deriving finite biorthonormal sets is presented. This method uses an algebraic approach and thus obviates, in the case of function spaces, the need for solving integral equations. It is concluded that in cases of significant nonorthogonality, the optimal approximation approach has greater accuracy and calculation efficiency, from both the theoretical and numerical viewpoints.>

2D shape boundary segmentation is required as a fundamental and important stage in the recognition process of partially occluded objects. The authors introduce a segmentation approach which is invariant to similarity transformation and in which partial occlusion has only marginal influence on the segmentation of the visible part. The basic concept is to transform the curve into another curve which intersects itself. Points of intersection of the new curve are retransformed to the original curve and serve as endpoints of segments. Properties of the transform are discussed, and conditions for the existence of intersection points are given. Simulation results, showing substantial immunity to noise, are presented, and advantages of the proposed method over conventional approaches relying on singular points of the curvature are discussed.>

The Gram determinant technique is applied to signal representation by non-orthogonal bases. A special case of image representation in biological and machine vision using Gabor elementary functions (GEFs) is considered. It is shown that, in general, the Gram determinant is a better approach to computation of the expansion coefficients than the one using bi-orthonormal auxiliary functions. An optimal representation by finite sets of coefficients is attained without a significant computational effort and the resultant reconstruction error converges monotonically with the addition of basis’ components to the reconstruction set. The Gram approach appears to be in a better accord with biological findings, regarding information processing along the visual pathway, compared to the conventional bi-orthogonal scheme.

The basic biological principles of nonuniform image representation in the combined frequency-position space are utilized in an approach to image representation and processing. A scheme of image decomposition into optimal localized frequency operators, the so-called Gabor elementary functions which minimize the uncertainty inherent in image representation, is accordingly proposed. Applications to size-invariance and object-separable pattern analysis, localized texture discrimination, and representation by partial information are discussed, illustrating the advantages of the Gabor transform.>

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.>