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Lectures on Numerical Methods in Bifurcation Problems
Methods for Finding Zeros in Polynomials
Lectures on Stochastic Flows and Applications
Educational Psychology by Edward L. Thorndike
The Last Days of Tolstoy by V. G. Chertkov
Globalization and Responsibility
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A Short Biographical Dictionary of English Literature
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The Theory of the Theatre by Clayton Hamilton
The Mathematics of Investment
Occupiers of Wall Street: Losers or Game Changers
The Solution of the Pyramid Problem
Lectures on Moduli of Curves
Walden by Henry David Thoreau
Methods for Finding Zeros in Polynomials
Lectures on Stochastic Flows and Applications
Educational Psychology by Edward L. Thorndike
The Last Days of Tolstoy by V. G. Chertkov
Globalization and Responsibility
Lectures on Siegel Modular Forms and Representation by Quadratic Forms
Lectures on Topics In One-Parameter Bifurcation Problems
History of the Incas by Pedro Sarmiento de Gamboa
Linear Algebra: Theorems and Applications
Lectures on Stochastic Differential Equations and Malliavin Calculus
A Short Biographical Dictionary of English Literature
Lectures on Sieve Methods and Prime Number Theory
Dollars and Sense by William Crosbie Hunter
The Theory of the Theatre by Clayton Hamilton
The Mathematics of Investment
Occupiers of Wall Street: Losers or Game Changers
The Solution of the Pyramid Problem
Lectures on Moduli of Curves
Walden by Henry David Thoreau
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Variational Models for Image Segmentation: with seven image processing experiments
Posted on 2010-12-09
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More (Progress in Nonlinear Differential Equations and Their Applications) By Jean-Michel Morel, Sergio Solimini This text contains a synthesis and a mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmentation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in variational form. Thanks to the formalization, mathematical questions about the soundness can be raised and answered. Perception theory has to deal with the complex interaction between regions and "edges" (or boundaries) in an image; in the variational segmentation energies, "edge" terms compete with "region" terms in a way which is intended to impose regularity on both regions and boundaries. The first part of the book presents a unified presentation of the evidence in favour of the conjecture. It is proven that the competition of one-dimensional and two-dimensional energy terms in a variational formulation cannot create fractal-like behaviour for the edges. The proof of regularity for the edges of a segmentation constantly involves concepts from geometric measure theory, which proves to be central in image processing theory. The second part of the book provides a fast and self-contained presentation of the classical theory of rectifiable sets (the "edges") and unrectifiable sets ("fractals").
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