This book introduces a new theory in Computer Vision yielding elementary techniques to analyze digital images. These techniques are a mathematical formalization of the Gestalt theory. From the mathematical viewpoint the closest field to it is stochastic geometry, involving basic probability and statistics, in the context of image analysis. The book is mathematically self-contained, needing only basic understanding of probability and calculus. The text includes more than 130 illustrations, and numerous examples based on specific images on which the theory is tested. Detailed exercises at the end of each chapter help the reader develop a firm understanding of the concepts imparted.

From Gestalt Theory to Image Analysis: A Probabilistic Approach (Interdisciplinary Applied Mathematics, 34)

Computers & Technology

Desolneux, Agnès

Morel, Jean-Michel

Moisan, Lionel

Computer Science

Springer

This book introduces a new theory in Computer Vision yielding elementary techniques to analyze digital images. These techniques are a mathematical formalization of the Gestalt theory. The text includes numerous illustrations, and chapter-end exercises, to reinforce understanding.

This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmen­ tation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in a variational form. Thank to this formalization, mathematical questions about the soundness of algorithms 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 seg­ mentation energies, "edge" terms compete with "region" terms in a way which is supposed to impose regularity on both regions and boundaries. This fact was an experimental guess in perception phenomenology and computer vision until it was proposed as a mathematical conjecture by Mumford and Shah. The third part of the book presents a unified presentation of the evi­ dences in favour of the conjecture. It is proved that the competition of one-dimensional and two-dimensional energy terms in a variational for­ mulation cannot create fractal-like behaviour for the edges. The proof of regularity for the edges of a segmentation constantly involves con­ cepts from geometric measure theory, which proves to be central in im­ age 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").

Variational Methods in Image Segmentation: with seven image processing experiments (Progress in Nonlinear Differential Equations and Their Applications)

Solimini, Sergio

Birkhauser

Nouveau guide de phytotherapie broche

Grancher

Remarques sur les Theoremes de Bochner et P.Levy.- Recent developments in axiomatic potential theory.- Über wesentlich indefinite Spiele.- La Topologie fine en Théorie du Potentiel.- Lois Stables et Espaces Lp.- Comments on the Martingale Convergence Theorem.- Faktorisierung von Differentialoperatoren.- Die Anzahl der Niveaudurchgänge und der lokalen Maximalstellen von Gaußschen Prozessen.- Vektorwertige Masse und Zufallsvariable auf Booleschen Algebren und der Satz von Radon-Nikodym.- Toward a theory of patterns.- On the potential theory of linear, homogeneous parabolic partial differential equations of second order.- Invariant and non-invariant measures.- Representation of abstract L-spaces.- Extension of stationary processes.- Renewal sequences and their arithmetic.- Optimal bounded control with linear stochastic equations and quadratic cost.- On a Fourier transform in infinitely many dimensions.- Some problems arising from spectral analysis.- Analytical methods in probability theory.- Martingales à Valeurs Vectorielles Application à la dérivation.- Atomes Conditionnels d'Espaces de Probalite et Theorie de l'Information.- On Markov processes whose shift transformation is quasi-mixing.- Remarks on the Poisson process.- Sums of Markov-chains on finite semigroups.- On superefficiency.- Two explicit Martin boundary constructions.- Structure des Lois Indefiniment Divisibles (? ? ?=? (X)) dans un Espace Vectoriel Topologique (separe) X.- On a paper of J.G. Sinai on dynamical systems.

Symposium on Probability Methods in Analysis: Lectures Delivered at a Symposium at Loutraki, Greece, 22.5. - 4.6.66 (Lecture Notes in Mathematics, 31)

Science & Math

Teissier, Bernard

Mathematics

Recent years have seen dramatic progress in shape recognition algorithms applied to ever-growing image databases. They have been applied to image stitching, stereo vision, image mosaics, solid object recognition and video or web image retrieval. More fundamentally, the ability of humans and animals to detect and recognize shapes is one of the enigmas of perception. The book describes a complete method that starts from a query image and an image database and yields a list of the images in the database containing shapes present in the query image. A false alarm number is associated to each detection. Many experiments will show that familiar simple shapes or images can reliably be identified with false alarm numbers ranging from 10-5 to less than 10-300. Technically speaking, there are two main issues. The first is extracting invariant shape descriptors from digital images. Indeed, a shape can be seen from various angles and distances and in various lights.

A Theory of Shape Identification (Lecture Notes in Mathematics, 1948)

Cao, Frédéric

Lisani, José-Luis

Musé, Pablo

Sur, Frédéric

The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems, and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties, empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.

Optimal Transportation Networks: Models and Theory (Lecture Notes in Mathematics, 1955)

Business & Money

Caselles, Vicent

Bernot, Marc

Management & Leadership

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