Josiane Zerubia

Cellular neural network for Markov random field image segmentation

Statistical approaches to early vision processes need a huge amount of computing power. These algorithms can usually be implemented on parallel computing structures. CNN is a fast parallel processor array for image processing. However, CNN is basically a deterministic analog circuit. We use the CNN-UM architecture for statistical image segmentation. With a single random in-put signal, we were able to implement a (pseudo) random field generator using one layer (one memory/cell) of the CNN. The whole algorithm needs 8 memories/cell. We can introduce this pseudo-stochastic segmentation process in the CNN structure. Considering the simple structure of the analog VLSI design, we use simple arithmetic functions (addition, multiplication) and very simple nonlinear output functions (step, jigsaw). With this architecture, a real VLSI CNN chip can execute a pseudo-stochastic relaxation algorithm of about 100 iterations in about 1 msec. In the Markov random field (MRF) theory, one important problem is parameter estimation. The random segmentation process must be preceded by the estimation of the gray-level distribution of the different classes on small image segments. This process is basically supervised. Usually the histograms of noisy images can be modelled as simple Gaussian distributions. This approach cannot be held in a CNN structure, since there should be as many additional layers as the number of classes. We should follow another way. We have developed a pixel-level distribution model.

Deconvolution and Denoising for Confocal Microscopy

Fluorescence light microscopes, especially the confocal laser scanning microscopes, have become a powerful tool in life sciences for observing biological samples in order to detect the distribution of proteins or other molecules of interest. Using this tool, biologists can study cells and their sub-cellular structures, identify, and precisely localize cellular organelles and supra-molecular structures. The confocal microscope is a type of fluorescent light microscope that gives very good two-dimensional optical sections of three-dimensional specimens, rejects the background auto-fluorescence, and offers a good contrast. However, there are some inherent limitations in confocal images such as the blurring effects due to the diffraction limit of the optics, and the low signal levels. The aim of this chapter is to introduce the reader to the basics of the light and confocal microscopes, their imaging limitations, and the mathematics involved in the resolution and signal-to-noise ratio improvement methodologies. Although user-friendly restoration software packages are available in the market, image restoration by deconvolution remains a difficult task for many microscopist and choosing the right software is often a case of trial and error due to a lack of knowledge of the applied algorithm. It is with the objective of resolving this issue that the most recent developments are intuitively explained, with some concrete examples to explain the underlying principles. The current open problems in the field of microscopy and methodological challenges are mentioned towards the end of the chapter.

Mathematical Models for Remote Sensing Image Processing

This book maximizes reader insights into the field of mathematical models and methods for the processing of two-dimensional remote sensing images. It presents a broad analysis of the field, encompassing passive and active sensors, hyperspectral images, synthetic aperture radar (SAR), interferometric SAR, and polarimetric SAR data. At the same time, it addresses highly topical subjects involving remote sensing data types (e.g., very high-resolution images, multiangular or multiresolution data, and satellite image time series) and analysis methodologies (e.g., probabilistic graphical models, hierarchical image representations, kernel machines, data fusion, and compressive sensing) that currently have primary importance in the field of mathematical modelling for remote sensing and image processing. Each chapter focuses on a particular type of remote sensing data and/or on a specific methodological area, presenting both a thorough analysis of the previous literature and a methodological and experimental discussion of at least two advanced mathematical methods for information extraction from remote sensing data. This organization ensures that both tutorial information and advanced subjects are covered. With each chapter being written by research scientists from (at least) two different institutions, it offers multiple professional experiences and perspectives on each subject. The book also provides expert analysis and commentary from leading remote sensing and image processing researchers, many of whom serve on the editorial boards of prestigious international journals in these fields, and are actively involved in international scientific societies. Providing the reader with a comprehensive picture of the overall advances and the current cutting-edge developments in the field of mathematical models for remote sensing image analysis, this book is ideal as both a reference resource and a textbook for graduate and doctoral students as well as for remote sensing scientists and practitioners.