Non-linear coupled CNN models for multiscale image analysis

A CNN model of partial differential equations (PDEs) for image multiscale analysis is proposed. The model is based on a polynomial representation of the diffusivity function and defines a paradigm of polynomial CNNs,for approximating a large class of nonlinear isotropic and/or anisotropic PDEs. The global dynamics of spacediscrete polynomial CNN models is analyzed and compared with the dynamic behavior of the corresponding space-continuous PDE models. It is shown that in the isotropic case the two models are not topologically equivalent: in particular discrete CNN models allow one to obtain the output image without stopping the image evolution after a given time (scale). This property represents an advantage with respect to continuous PDE models and could simplify some image preprocessing algorithm

Scale space analysis by stabilized inverse diffusion equations

Caption title.Includes bibliographical references (p. 11).Supported by AFSOR. F49620-95-1-0083 Supported by ONR. N00014-91-J-1004 Supported in part by Boston University under the AFOSR Multidisciplinary Research Program on Reduced Signature Target Recognition. GC123919NGDIlya Pollak, Alan S. Willsky, Hamid Krim

Fast parallel algorithms for a broad class of nonlinear variational diffusion approaches

Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during the last years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implement at ions of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Numerical results confirm that, depending on the parametrization, this approximation can be made quite accurate. Our results provide a perspective for uniform implement at ions of both nonlinear variational models and diffusion filters on parallel architectures

Scale-Space Properties of Nonstationary Iterative Regularization Methods

Most scale-space concepts have been expressed as parabolic or hyperbolic partial differential equations (PDEs). In this paper we extend our work on scale-space properties of elliptic PDEs arising from regularization methods: we study linear and nonlinear regularization methods that are applied iteratively and with different regularization parameters. For these so-called nonstationary iterative regularization techniques we clarify their relations to both isotropic diffusion filters with a scalar-valued diffusivity and anisotropic diffusion filters with a diffusion tensor. We establish scale-space properties for iterative regularization methods that are in complete accordance with those for diffusion filtering. In particular, we show that nonstationary iterative regularization satisfies a causality property in terms of a maximum-minimum principle, possesses a large class of Lyapunov functionals, and converges to a constant image as the regularization parameters tend to infinity. We also establish continuous dependence of the result with respect to the sequence of regularization parameters. Numerical experiments in two and three space dimensions are presented that illustrate the scale-space behavior of regularization methods

An improved classification approach for echocardiograms embedding temporal information

Cardiovascular disease is an umbrella term for all diseases of the heart. At present, computer-aided echocardiogram diagnosis is becoming increasingly beneficial. For echocardiography, different cardiac views can be acquired depending on the location and angulations of the ultrasound transducer. Hence, the automatic echocardiogram view classification is the first step for echocardiogram diagnosis, especially for computer-aided system and even for automatic diagnosis in the future. In addition, heart views classification makes it possible to label images especially for large-scale echo videos, provide a facility for database management and collection. This thesis presents a framework for automatic cardiac viewpoints classification of echocardiogram video data. In this research, we aim to overcome the challenges facing this investigation while analyzing, recognizing and classifying echocardiogram videos from 3D (2D spatial and 1D temporal) space. Specifically, we extend 2D KAZE approach into 3D space for feature detection and propose a histogram of acceleration as feature descriptor. Subsequently, feature encoding follows before the application of SVM to classify echo videos. In addition, comparison with the state of the art methodologies also takes place, including 2D SIFT, 3D SIFT, and optical flow technique to extract temporal information sustained in the video images. As a result, the performance of 2D KAZE, 2D KAZE with Optical Flow, 3D KAZE, Optical Flow, 2D SIFT and 3D SIFT delivers accuracy rate of 89.4%, 84.3%, 87.9%, 79.4%, 83.8% and 73.8% respectively for the eight view classes of echo videos

Multidimensional Wavelets and Computer Vision

This report deals with the construction and the mathematical analysis of multidimensional nonseparable wavelets and their efficient application in computer vision. In the first part, the fundamental principles and ideas of multidimensional wavelet filter design such as the question for the existence of good scaling matrices and sensible design criteria are presented and extended in various directions. Afterwards, the analytical properties of these wavelets are investigated in some detail. It will turn out that they are especially well-suited to represent (discretized) data as well as large classes of operators in a sparse form - a property that directly yields efficient numerical algorithms. The final part of this work is dedicated to the application of the developed methods to the typical computer vision problems of nonlinear image regularization and the computation of optical flow in image sequences. It is demonstrated how the wavelet framework leads to stable and reliable results for these problems of generally ill-posed nature. Furthermore, all the algorithms are of order O(n) leading to fast processing

Stability and inference in discrete diffusion scale-spaces

Taking averages of observations is the most basic method to make inferences in the presence of uncertainty. In late 1980's, this simple idea has been extended to the principle of successively average less where the change is faster, and applied to the problem of revealing a signal with jump discontinuities in additive noise. Successive averaging results in a family of signals with progressively decreasing amount of details, which is called the scale-space and further conveniently formalized by viewing it as a solution to a certain diffusion-inspired evolutionary partial differential equation (PDE). Such a model is known as the diffusion scale-space and it possesses two long-standing problems: (i) model analysis which aims at establishing stability and guarantees that averaging does not distort important information, and (ii) model selection, such as identification of the optimal scale (diffusion stopping time) given an initial noisy signal and an incomplete model. This thesis studies both problems in the discrete space and time. Such a setting has been strongly advocated by Lindeberg [1991] and Weickert [1996] among others. The focus of the model analysis part is on necessary and sufficient conditions which guarantee that a discrete diffusion possesses the scale-space property in the sense of sign variation diminishing. Connections with the total variation diminishing and the open problem in a multivariate case are discussed too. Considering the model selection, the thesis unifies two optimal diffusion stopping principles: (i) the time when the Shannon entropy-based Liapunov function of Sporring and Weickert [1999] reaches its steady state, and (ii) the time when the diffusion outcome has the least correlation with the noise estimate, contributed by Mrázek and Navara [2003]. Both ideas are shown to be particular cases of the marginal likelihood inference. Moreover, the suggested formalism provides first principles behind such criteria, and removes a variety of inconsistencies. It is suggested that the outcome of the diffusion should be interpreted as a certain expectation conditioned on the initial signal of observations instead of being treated as a random sample or probabilities. This removes the need to normalize signals in the approach of Sporring and Weickert [1999], and it also better justifies application of the correlation criterion of Mrázek and Navara [2003]. Throughout this work, the emphasis is given on methods that enable to reduce the problem to that of establishing the positivity of a quadratic form. The necessary and sufficient conditions can then be approached via positivity of matrix minors. A supplementary appendix is provided which summarizes a novel method of evaluating matrix minors. Intuitive examples of difficulties with statistical inference conclude the thesis.reviewe