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Active contour model, also called snakes, is a framework in computer vision introduced by Michael Kass, Andrew Witkin, and Demetri Terzopoulos [1] for delineating an object outline from a possibly noisy 2D image.
In mathematics, a Hankel contour is a path in the complex plane which extends from (+∞,δ), around the origin counter clockwise and back to (+∞,−δ), where δ is an arbitrarily small positive number. The contour thus remains arbitrarily close to the real axis but without crossing the real axis except for negative values of x. The Hankel ...
Contour integration is closely related to the calculus of residues, [4] a method of complex analysis. One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods. [5] Contour integration methods include:
The principal application is to detect and track the contour of objects moving in a cluttered environment. Object tracking is one of the more basic and difficult aspects of computer vision and is generally a prerequisite to object recognition. Being able to identify which pixels in an image make up the contour of an object is a non-trivial problem.
Typical applications include the contour lines on topographic maps or the generation of isobars for weather maps. Marching squares takes a similar approach to the 3D marching cubes algorithm: Process each cell in the grid independently. Calculate a cell index using comparisons of the contour level(s) with the data values at the cell corners.
Then, the residue at the point c is calculated as: (,) = = = = using the results from contour integral of a monomial for counter clockwise contour integral around a point c. Hence, if a Laurent series representation of a function exists around c, then its residue around c is known by the coefficient of the ( z − c ) − 1 {\displaystyle ...
In image processing, computer vision and related fields, an image moment is a certain particular weighted average of the image pixels' intensities, or a function of such moments, usually chosen to have some attractive property or interpretation.
where the poles of (,;) lie to the left of the contour and the remaining poles lie to the right. There is a similar contour integral for r +1 φ r . This contour integral gives an analytic continuation of the basic hypergeometric function in z .