다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)

On robust estimation of the location parameter

Preface Through many centuries physics has been one of the most fruitful sources of inspiration for mathematics. As a consequence, mathematics has become an economic language providing a few basic principles which allow to explain a large variety of physical phenomena. Many of them are described in terms of partial diierential equations (PDEs). In recent years, however, mathematics also has been stimulated by other novel elds such as image processing. Goals like image segmentation, multiscale image representation, or image restoration cause a lot of challenging mathematical questions. Nevertheless, these problems frequently have been tackled with a pool of heuristical recipes. Since the treatment of digital images requires very much computing power, these methods had to be fairly simple. With the tremendous advances in computer technology in the last decade, it has become possible to apply more sophisticated techniques such as PDE-based methods which have been inspired by physical processes. Among these techniques, parabolic PDEs have found a lot of attention for smoothing and restoration purposes, see e.g. 113]. To restore images these equations frequently arise from gradient descent methods applied to variational problems. Image smoothing by parabolic PDEs is closely related to the scale-space concept where one embeds the original image into a family of subsequently simpler , more global representations of it. This idea plays a fundamental role for extracting semantically important information. The pioneering work of Alvarez, Guichard, Lions and Morel 11] has demonstrated that all scale-spaces fulllling a few fairly natural axioms are governed by parabolic PDEs with the original image as initial condition. Within this framework, two classes can be justiied in a rigorous way as scale-spaces: the linear diiusion equation with constant dif-fusivity and nonlinear so-called morphological PDEs. All these methods satisfy a monotony axiom as smoothing requirement which states that, if one image is brighter than another, then this order is preserved during the entire scale-space evolution. An interesting class of parabolic equations which pursue both scale-space and restoration intentions is given by nonlinear diiusion lters. Methods of this type have been proposed for the rst time by Perona and Malik in 1987 190]. In v vi PREFACE order to smooth the image and to simultaneously enhance semantically important features such as edges, they apply a diiusion process whose diiusivity is steered by local image properties. These lters are diicult to analyse mathematically , as they may act locally like a backward diiusion process. …

/pdf/anisotropic-diffusion-in-image-processing-z13u09qvsm.pdf

Anisotropic diffusion in image processing

This book introduces the reader to a recent theory in Computer Vision yielding elementary techniques to analyse digital images. These techniques are inspired from and are a mathematical formalization of the Gestalt theory. Gestalt theory, which had never been formalized is a rigorous realm of vision psychology developped between 1923 and 1975. From the mathematical viewpoint the closest field to it is stochastic geometry, involving basic probability and statistics, in the context of image analysis. The authors maintain a public software, MegaWave, containing implementations of most of the image analysis techniques developped in the book. The book is intended for researchers and engineers. It is mathematically self-contained and requires only the basic notions in probability and calculus.

From Gestalt Theory to Image Analysis: A Probabilistic Approach

We propose a method for detecting geometric structures in an image, without any a priori information. Roughly speaking, we say that an observed geometric event is “meaningful” if the expectation of its occurences would be very small in a random image. We discuss the apories of this definition, solve several of them by introducing “maximal meaningful events” and analyzing their structure. This methodology is applied to the detection of alignments in images.

Meaningful Alignments

We apply to edge detection a recently introduced method for computing geometric structures in a digital image, without any a priori information. According to a basic principle of perception due to Helmholtz, an observed geometric structure is perceptually “meaningful” if its number of occurences would be very small in a random situation: in this context, geometric structures are characterized as large deviations from randomness. This leads us to define and compute edges and boundaries (closed edges) in an image by a parameter-free method. Maximal detectable boundaries and edges are defined, computed, and the results compared with the ones obtained by classical algorithms.

/pdf/edge-detection-by-helmholtz-principle-2rcrvdujlb.pdf

Edge Detection by Helmholtz Principle

/pdf/from-gestalt-theory-to-image-analysis-3najfm6u8y.pdf

From Gestalt Theory to Image Analysis

The perspective projections of n physical points on two views (stereovision) are constrained as soon as n ≥ 8 However, to prove in practice the existence of a rigid motion between two images, more than 8 point matches are desirable in order to compensate for the limited accuracy of the matches In this paper, we propose a computational definition of rigidity and a probabilistic criterion to rate the meaningfulness of a rigid set as a function of both the number of pairs of points (n) and the accuracy of the matches This criterion yields an objective way to compare, say, precise matches of a few points and approximate matches of a lot of points It gives a yes/no answer to the question: “could this rigid points correspondence have occurred by chance?”, since it guarantees that the expected number of meaningful rigid sets found by chance in a random distribution of points is as small as desired It also yields absolute accuracy requirements for rigidity detection in the case of non-matched points, and optimal values of n, depending on the expected accuracy of the matches and on the proportion of outliers We use it to build an optimized random sampling algorithm that is able to detect a rigid motion and estimate the fundamental matrix when the set of point matches contains up to 90% of outliers, which outperforms the best currently known methods like M-estimators, LMedS, classical RANSAC and Tensor Voting

Lionel Moisan

Papers

From Gestalt Theory to Image Analysis: A Probabilistic Approach

Meaningful Alignments

Edge Detection by Helmholtz Principle

From Gestalt Theory to Image Analysis

A Probabilistic Criterion to Detect Rigid Point Matches Between Two Images and Estimate the Fundamental Matrix