Introduction to linear and nonlinear programming

Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables systematic development of optimal vision algorithms when used with optimization principles. This detailed and thoroughly enhanced third edition presents a comprehensive study / reference to theories, methodologies and recent developments in solving computer vision problems based on MRFs, statistics and optimisation. It treats various problems in low- and high-level computational vision in a systematic and unified way within the MAP-MRF framework. Among the main issues covered are: how to use MRFs to encode contextual constraints that are indispensable to image understanding; how to derive the objective function for the optimal solution to a problem; and how to design computational algorithms for finding an optimal solution. Easy-to-follow and coherent, the revised edition is accessible, includes the most recent advances, and has new and expanded sections on such topics as: Discriminative Random Fields (DRF) Strong Random Fields (SRF) Spatial-Temporal Models Total Variation Models Learning MRF for Classification (motivation + DRF) Relation to Graphic Models Graph Cuts Belief Propagation Features: Focuses on the application of Markov random fields to computer vision problems, such as image restoration and edge detection in the low-level domain, and object matching and recognition in the high-level domain Presents various vision models in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation Uses a variety of examples to illustrate how to convert a specific vision problem involving uncertainties and constraints into essentially an optimization problem under the MRF setting Introduces readers to the basic concepts, important models and various special classes of MRFs on the regular image lattice and MRFs on relational graphs derived from images Examines the problems of parameter estimation and function optimization Includes an extensive list of references This broad-ranging and comprehensive volume is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition and applications of MRFs. It has been class-tested and is suitable as a textbook for advanced courses relating to these areas.

Markov Random Field Modeling in Image Analysis

From the Publisher:
Markov random field (MRF) theory provides a basis for modeling contextual constraints in visual processing and interpretation. It enables us to develop optimal vision algorithms systematically when used with optimization principles. This book presents a comprehensive study on the use of MRFs for solving computer vision problems. The book covers the following parts essential to the subject: introduction to fundamental theories, formulations of MRF vision models, MRF parameter estimation, and optimization algorithms. Various vision models are presented in a unified framework, including image restoration and reconstruction, edge and region segmentation, texture, stereo and motion, object matching and recognition, and pose estimation. This book is an excellent reference for researchers working in computer vision, image processing, statistical pattern recognition, and applications of MRFs. It is also suitable as a text for advanced courses in these areas.

Markov Random Field Modeling in Computer Vision

Presents a new method to match a 2D image to a translated, rotated and scaled reference image. The approach consists of two steps: the calculation of a Fourier-Mellin invariant (FMI) descriptor for each image to be matched, and the matching of the FMI descriptors. The FMI descriptor is translation invariant, and represents rotation and scaling as translations in parameter space. The matching of the FMI descriptors is achieved using symmetric phase-only matched filtering (SPOMF). The performance of the FMI-SPOMF algorithm is the same or similar to that of phase-only matched filtering when dealing with image translations. The significant advantage of the new technique is its capability to match rotated and scaled images accurately and efficiently. The innovation is the application of SPOMF to the FMI descriptors, which guarantees high discriminating power and excellent robustness in the presence of noise. This paper describes the principle of the new method and its discrete implementation for either image detection problems or image registration problems. Practical results are presented for various applications in medical imaging, remote sensing, fingerprint recognition and multiobject identification. >

Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition

We introduce the Adaptive Hough Transform, AHT, as an efficient way of implementing the Hough Transform, HT, method for the detection of 2-D shapes. The AHT uses a small accumulator array and the idea of a flexible iterative "coarse to fine" accumulation and search strategy to identify significant peaks in the Hough parameter spaces. The method is substantially superior to the standard HT implementation in both storage and computational requirements. In this correspondence we illustrate the ideas of the AHT by tackling the problem of identifying linear and circular segments in images by searching for clusters of evidence in 2-D parameter spaces. We show that the method is robust to the addition of extraneous noise and can be used to analyze complex images containing more than one shape.

The Adaptive Hough Transform

In this paper we present results in the areas of shape matching of nonoccluded and occluded two-dimensional objects. Shape matching is viewed as a ``segment matching'' problem. Unlike the previous work, the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification. To reduce the computation time, the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels. This basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion. In such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects. These techniques have been applied to two-dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic, aerial, industrial and biological images where the matching is done after using the actual segmentation methods.

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Olivier D. Faugeras

Papers

Shape Matching of Two-Dimensional Objects

Correction to "Segmentation of Images Having Unimodal Distributions''