By G. Medioni, Mi-Suen Lee, Chi-Keung Tang
This booklet represents a precis of the learn we now have been engaging in because the early Nineteen Nineties, and describes a conceptual framework which addresses a few present shortcomings, and proposes a unified process for a wide category of difficulties. whereas the framework is outlined, our examine maintains, and a few of the weather provided the following will doubtless evolve within the coming years.It is prepared in 8 chapters. within the creation bankruptcy, we current the definition of the issues, and provides an summary of the proposed method and its implementation. specifically, we illustrate the constraints of the 2.5D cartoon, and inspire using a illustration when it comes to layers instead.
In bankruptcy 2, we evaluate the various correct study within the literature. The dialogue specializes in basic computational ways for early imaginative and prescient, and person equipment are just brought up as references. bankruptcy three is the basic bankruptcy, because it provides the weather of our salient function inference engine, and their interplay. It brought tensors in order to symbolize info, tensor fields that allows 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 via the engine defined prior. In bankruptcy five, we observe the usual framework to the inference of areas, curves, and junctions in 2-D. The enter may perhaps take the shape of 2-D issues, without or with orientation. We illustrate the technique on a few examples, either simple and complicated. In bankruptcy 6, we practice the framework to the inference of surfaces, curves and junctions in 3-D. the following, the enter involves a collection of 3-D issues, without or with as linked basic or tangent path. We convey a few illustrative examples, and in addition aspect to a couple functions of the process. In bankruptcy 7, we use our framework to take on three early imaginative and prescient difficulties, form from shading, stereo matching, and optical move computation. In bankruptcy eight, we finish this booklet with a number of feedback, and talk about destiny examine directions.
We comprise three appendices, one on Tensor Calculus, one facing proofs and information of the function Extraction technique, and one facing the significant other software program applications.
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Extra resources for A Computational Framework for Segmentation and Grouping
The tensor value at any given location in the domain is the tensor sum of all the tensor votes cast at this location. A somewhat subtle difference occurs in this second case, as ball tensors define isolated features, which therefore do not need to propagate their information, and thus do not vote. While they may be implemented differently for efficiency, these 2 operations are equivalent, and generalize convolution to tensor elements. 2 Mathematical formulation We now give the mathematical formulation of this communication scheme.
M are the carriers (basis functions). Two major issues need to be addressed: (1) parameter estimation (2) inlier/outlier classification (data error correction) Robust estimators often make use of the algebraic properties of the carrier functions and the constraint equation to handle parameters estimation, and apply statistical tools to tackle data error correction. While techniques such as the Hough Transform  can be very robust to noise, the parametric formalism of these techniques makes it hard to deliver the same robustness in solving early vision problems.
The resulting voting field is a plate tensor which describes the a plane with normal [0 0 1] in world coordinates. 9) e = 0, (|) = 0 This field encodes two complementary, different aspects of the smoothness constraint. The first one embodies surface smoothness in the direction normal to the direction of the tangent, the second expresses smoothness along a curve linking boundary points. 12 illustrate these fields. In practice, we use a finite discrete version of these characterizing saliency tensor fields to represent the voting function efficiently.
A Computational Framework for Segmentation and Grouping by G. Medioni, Mi-Suen Lee, Chi-Keung Tang