IEEE Signal Processing Magazine

We review a result in modeling lower order (univariate and bivariate) probability densities of pixel values resulting from bandpass filtering of images. Assuming an object-based model for images, a parametric family of probabilities, called Bessel K forms, has been derived (Grenander and Srivastava 2001). This parametric family matches well with the observed histograms for a large variety of images (video, range, infrared, etc.) and filters (Gabor, Laplacian Gaussian, derivatives, etc). The Bessel parameters relate to certain characteristics of objects present in an image and provide fast tools either for object recognition directly or for an intermediate (pruning) step of a larger recognition system. Examples are presented to illustrate the estimation of Bessel forms and their applications in clutter classification and object recognition.

In this article, we consider the marked point process framework for image analysis. We first show that marked point processes are more adapted than Markov random fields (MRFs) including some geometrical constraints in the solution and dealing with strongly correlated noise. Then, we consider three applications in remote sensing: road network extraction, building extraction, and image segmentation. For each of them, we define a prior model, incorporating geometrical constraints on the solution. We also derive a reversible jump Monte Carlo Markov chains (RJMCMC) algorithm to obtain the optimal solution with respect to the defined models. Results show that this approach is promising and can be applied to a broad range of image processing problems.

Athanasios Papoulis, of Polytechnic University, Brooklyn, NY, a prominent author and passionate educator for four decades, died 25 April in Huntington, Long Island, New York, USA. He was 81. Papoulis distinguished himself in the scientific community for his more than 150 scholarly papers and nine books, including the classic Probability, Random Variables and Stochastic Processes, first published in 1965 and considered the standard textbook in the field. A brief bibliography of his texts is included.

A maximum a posteriori (MAP) estimator using a Markov or a maximum entropy random field model for a prior distribution may be viewed as a minimizer of a variational problem.Using notions from robust statistics, a variational filter referred to as a Huber gradient descent flow is proposed. It is a result of optimizing a Huber functional subject to some noise constraints and takes a hybrid form of a total variation diffusion for large gradient magnitudes and of a linear diffusion for small gradient magnitudes. Using the gained insight, and as a further extension, we propose an information-theoretic gradient descent flow which is a result of minimizing a functional that is a hybrid between a negentropy variational integral and a total variation. Illustrating examples demonstrate a much improved performance of the approach in the presence of Gaussian and heavy tailed noise. In this article, we present a variational approach to MAP estimation with a more qualitative and tutorial emphasis. The key idea behind this approach is to use geometric insight in helping construct regularizing functionals and avoiding a subjective choice of a prior in MAP estimation. Using tools from robust statistics and information theory, we show that we can extend this strategy and develop two gradient descent flows for image denoising with a demonstrated performance.

Nghiên cứu của chúng tôi về cảnh quan fractal bắt nguồn từ mô hình đơn giản nhưng hiệu quả nhất của chuyển động Brown phân đoạn và khám phá các biến thể hai chiều (2-D) của nó. Chúng tôi tập trung vào khả năng giới thiệu độ bất đối xứng trong mô hình này, và chúng tôi cũng quan tâm đến việc xem xét các đối tác trong không gian rời rạc của nó. Chúng tôi sau đó tiến tới các mô hình đa phân đoạn và đa fractal khác cung cấp nhiều bậc tự do hơn để phù hợp với các trường 2-D phức tạp. Chúng tôi lưu ý rằng nhiều mô hình và quá trình được thực hiện trong FracLab, một bộ công cụ phần mềm MATLAB/Scilab cho việc xử lý fractal của các tín hiệu và hình ảnh.

The ease with which early watermarking algorithms were broken has given rise to a new set of schemes that are usually robust to a wide variety of attacks. We argue that this has created an illusion of progress, when in reality there is none. Most published watermarking algorithms, like their predecessors, protect all objects in a neighborhood surrounding the marked object. We point out that while this is necessary, it is very far from being sufficient. To withstand adversarial attack, a watermarking scheme would have to protect all valuable variations of an object, not merely ones that are close to it.

In this article, we give an overview of scale-spaces and their application to noise suppression and segmentation of 1-D signals and 2-D images. Several prototypical problems serve as our motivation. We review several scale-spaces (linear Gaussian, Perona-Malik, and SIDE-stabilized inverse diffusion equation) and discuss their advantages and shortcomings. We describe our previous work and argue that a very simple nonlinear scale-space leads to a fast estimation algorithm which produces accurate segmentations and estimates of signals and images.