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Probability density functions for the components of the first and second derivatives of localized phase are derived.

The derivation of bounds on the structural similarity (SSIM) index as a function of quantization rate for fixed-rate uniform quantization is discussed. Findings reveal the importance of the proposed bounds for rate allocation problems in practical image and video coding applications.

An algorithm for designing linear equalizers, which maximizes the structural similarity (SSIM) index between the reference and restored signals, is proposed. Findings reveal the achievement of higher SSIM index and superior perceptual quality.

A foveated, multifixating strategy is presented for locating corners in natural images. The results have shown that the algorithm performs well on strong edges with sharp corners and less well in areas of fine detail.

A performance evaluation study of ten image quality assessment (QA) algorithms are presented, which involved 779 distorted images derived from 29 source images using five different distortion types. The study was diverse in terms of image content, distortion types, distortion strength and the number of human subjects ranking each image, and results and data from the study are made publicly available to facilitate future research in image quality assessment.

The concept of extracting features of the original high-quality images and embedding into the image data as invisible hidden messages and can provide an objective measure of the quality of the distorted images known as quality-aware image is described. A practical quality-aware image encoding, decoding and quality analysis system is formulated which uses a unique reduced-reference image quality assessment technique based on a statistical model of natural images and quantization watermarking-based data hiding method in wavelet transform domain.

The goal of quality assessment (QA) research is to design algorithms that can automatically assess the quality of images or videos in a perceptually consistent manner. The problem of image QA is approached by proposing a novel information fidelity criterion that is based on natural scene statistics.

A model that accounts for the properties of the imaging system and of the tissues is developed to get a better understanding of confocal reflectance microscopy images of cervical tissues, and to supply a basis for parameter selection in a classification algorithm. The algorithm was applied to an extensive set of cervical images and it was found that it detects 90% of hand-segmented nuclei with an average of 6 false positive per frame.

Theorems are developed that place limits on the point-wise approximation of the responses of filters, both linear shift invariant (LSI) and linear shift variant (LSV) to input signals and images that are LSV. The application of the theory was found to defoveation of images, deblurring of shift-variant blurs, and shift-variant edge detection.

A study of the objective method for assessing perceptual image quality that attempted to quantify the visibility of errors between distorted and reference images according to known characteristics of the human visual system (HVS) is presented. The development of the structural similarity index (SSIM) for quality assessment based on the assumption that HVS is highly adapted to extract structural information is discussed.

A wavelet-based, scalable video coding system, foveation scalable video coding (FSVC, is described and discussed.

It is shown that formulating the nullspace-based approach to eigenstructure-based direct multichannel blind image restoration methods implies a subspace-based approach that relies on matrix operations. The new approach has the same advantages as the nullspace-based one but requires less computational complexity.

An embedded foveation image coding (EFIC) algorithm is proposed. The algorithm orders the encoded bitstream to optimize foveated visual quality at arbitrary bit rates.

Multidimensional multicomponent and quasi-Eigenfunction approximation AM-FM models are discussed. Techniques on several images of general interest in practical applications have been demonstrated. Reconstructions that establish validity of characterizing the type of images as sums of locally narrowband modulated components have been made. Two discrete computational paradigms were used. Dominant component analysis does one thing and channelized components analysis does another.

We develop a general formalism for computing high quality, low-cost solutions to nonconvex combinatorial optimization problems expressible as distributed interacting local constraints. For problems of this type, generalized deterministic annealing (GDA) avoids the performance-related sacrifices of current techniques. GDA exploits the localized structure of such problems by assigning K-state neurons to each optimization variable. The neuron values correspond to the probability densities of K-state local Markov chains and may be updated serially or in parallel; the Markov model is derived from the Markov model of simulated annealing (SA), although it is greatly simplified. Theorems are presented that firmly establish the convergence properties of GDA, as well as supplying practical guidelines for selecting the initial and final temperatures in the annealing process. A benchmark image enhancement application is provided where the performance of GDA is compared to other optimization methods. The empirical data taken in conjunction with the formal analytical results suggest that GDA enjoys significant performance advantages relative to current methods for combinatorial optimization.

Natural scene statistics (NSS) is used for blindly measuring the quality of images compressed by JPEG2000 image coder. An average error of 8.05 is achieved from the mean opinion scores.

Foveation has been investigated as a tool for exploring techniques for optimal rate control of foveated video. It is concluded that foveated compression and rate control offers significant potential with regard to compression performance, speed and visual quality.

Partial differential equations and AM-FM image modeling was used to achieve an automated method for repairing broken, occluded oriented image textures.

An AM-FM surface model was developed to study the projection of surface patterns seen through a binocular camera system. The proposed model also proved to be useful in the design of a modulation-based stereo matching framework where local image phase was used to compute stereo disparities. The combined concepts of the phase-based matching and AM-FM image model and use powerful multichannel Gabor image demodulation techniques led to the development of a systematic approach for coarse-to-coarse disparity computation of disparities in stereoscopic images.

Novel smoothing constraints have been developed for use in the regularized image restoration problem with the aid of two broad classes of physically significant models. The models, called piecewise image models and local image models, capture distinct image properties that can be adapted to the image and that reflect structurally important surface properties. Numerical results are presented to illustrate the mechanism of model selection, image restoration and parameter selection.