# Download A Computational Framework for Segmentation and Grouping by G. Medioni, Mi-Suen Lee, Chi-Keung Tang PDF

By G. Medioni, Mi-Suen Lee, Chi-Keung Tang

This booklet represents a precis of the examine now we have been undertaking because the early Nineties, and describes a conceptual framework which addresses a few present shortcomings, and proposes a unified method for a extensive type of difficulties. whereas the framework is outlined, our learn maintains, and a few of the weather awarded the following will without doubt evolve within the coming years.It is equipped in 8 chapters. within the advent bankruptcy, we current the definition of the issues, and provides an outline of the proposed strategy and its implementation. particularly, we illustrate the constraints of the 2.5D cartoon, and inspire using a illustration by way of layers instead.
In bankruptcy 2, we assessment a few of the correct study within the literature. The dialogue makes a speciality of normal computational methods for early imaginative and prescient, and person tools are just mentioned as references. bankruptcy three is the elemental bankruptcy, because it offers the weather of our salient characteristic inference engine, and their interplay. It brought tensors so as to signify info, tensor fields for you to encode either constraints and effects, and tensor vote casting because the communique scheme. bankruptcy four describes the characteristic extraction steps, given the computations played through the engine defined previous. In bankruptcy five, we follow the everyday framework to the inference of areas, curves, and junctions in 2-D. The enter might take the shape of 2-D issues, without or with orientation. We illustrate the method on a couple of examples, either uncomplicated and complicated. In bankruptcy 6, we observe the framework to the inference of surfaces, curves and junctions in 3-D. right here, the enter contains a collection of 3-D issues, without or with as linked general or tangent path. We exhibit a couple of illustrative examples, and in addition aspect to a couple purposes of the method. In bankruptcy 7, we use our framework to take on three early imaginative and prescient difficulties, form from shading, stereo matching, and optical circulation computation. In bankruptcy eight, we finish this ebook with a couple of comments, and talk about destiny learn directions.
We comprise three appendices, one on Tensor Calculus, one facing proofs and information of the characteristic Extraction procedure, and one facing the spouse software program applications.

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Additional info for A Computational Framework for Segmentation and Grouping

Sample text

Inverse problems can usually be obtained from the direct problem by exchanging the role of solution and data. For instance, we are given a problem expressed by the equation y = F(x), where F is a known operator. The direct problem is to determine y from x, the inverse problem is to obtain x when 3; (data) is given. Since imaging is a known operator, early vision problems are inverse problems. They are ill-posed because the solution is not unique. 2 Regularization methods To deal with ill-posed problems, Tikhonov has developed a rigorous theory, termed regularization, for the derivation of solutions to these problems [84, 85].

Recall that, in an inverse problem, one has to look for the most likely model M given a set of data D. In 'Bayesian language', this task can be described as the maximization problem of a probability density function. 1) The model M which maximizes P{M\D) also maximizes log[P(M\D)]. 2) = max{\og{P{D\M)) + log(P(M)) - log(P(D))} Hence, the problem is characterized by a trade-off between three terms. The first term evaluates how well a model describes the data, which is equivalent to the ||F(x)-}^|| term in the functional regularization framework.

By doing so, we avoid all the problems related to optimum searching, including modeling the search space, initializing the search, selecting the size and direction of the search step for each iteration, and deciding the terminating conditions. The scene description we produce is in terms of layers in object-centered coordinates, side-stepping problems due to image partitioning in viewer-centered coordinates. Our method is non-iterative, does not use explicit parametric models, can handle dense or sparse input, requires no initialization and thresholding, and the only free parameter is scale.