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

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

This publication represents a precis of the examine now we have been carrying out because the early Nineties, and describes a conceptual framework which addresses a few present shortcomings, and proposes a unified strategy for a extensive classification of difficulties. whereas the framework is outlined, our learn keeps, and a few of the weather provided the following will without doubt evolve within the coming years.It is geared up in 8 chapters. within the advent bankruptcy, we current the definition of the issues, and provides an outline of the proposed process and its implementation. particularly, we illustrate the constraints of the 2.5D cartoon, and encourage using a illustration by way of layers instead.
In bankruptcy 2, we evaluation the various proper learn within the literature. The dialogue makes a speciality of basic computational ways for early imaginative and prescient, and person tools are just stated as references. bankruptcy three is the elemental bankruptcy, because it provides the weather of our salient function inference engine, and their interplay. It brought tensors in order to characterize info, tensor fields in order to encode either constraints and effects, and tensor balloting because the communique scheme. bankruptcy four describes the function extraction steps, given the computations played via the engine defined previous. In bankruptcy five, we follow the primary 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 technique on a few examples, either easy and complex. In bankruptcy 6, we follow the framework to the inference of surfaces, curves and junctions in 3D. the following, the enter comprises a suite of 3D issues, without or with as linked common or tangent path. We express a couple of illustrative examples, and likewise aspect to a few functions of the procedure. 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 e-book with a couple of comments, and talk about destiny examine directions.
We comprise three appendices, one on Tensor Calculus, one facing proofs and information of the function Extraction approach, and one facing the spouse software program applications.

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Extra resources for A Computational Framework for Segmentation and Grouping

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Furthermore, because layers may overlap, a location may actually correspond to both a point and a curve, or even to a surface, a curve and a point at the same time. An example of such a case occurs at the intersection between 2 smooth curves: the intersection should be a point, that is, it represents a junction with no associated tangent information, but also represents 2 curve elements, as the curves do not stop there. We therefore propose to encode not the geometric information for a specific type of feature, but instead geometric information/6>r every possible type offeature, together with a confidence measure, which we call saliency, associated with each type of feature.

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. The second term evaluates the model. It expresses prior beliefs about what we think is a good model, which corresponds to the regularization term ||Gfxj|| in the regularization theory.

E. e. i||Gfxj|| ). In particular, regularization theory provides techniques to determine the best X [85, 86]. There also exists a large body of results dealing with the form of the stabilizing function G that ensures both uniqueness of the result and convergence of the iterative search for a solution. In the case of early vision, the problem is transformed into the non-linear, scalar functional optimization framework, which can then be solved using standard numerical techniques, namely the variational principles [27, 36, 37, 40, 80].

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