homotopy

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homotopy

[hō′mäd·ə·pē]
(mathematics)
Between two mappings of the same topological spaces, a continuous function representing how, in a step-by-step fashion, the image of one mapping can be continuously deformed onto the image of the other.
References in periodicals archive ?
The definition of the homotopic thinning itself already provides an algorithm to compute the ultimate homotopic skeleton.
m]), x) is defined to be a group generated by all homotopic classes of closed d-pathes based at x.
If L is trim and nuclear, then its order complex is homotopic to a sphere, whose dimension is 2 less than the number of atoms of L.
The dynamical 3-space is different: here we have only a dynamical 3-space, which at a small scale is a quantum foam system without dimensions and described by fractal or nested homotopic mappings [2].
Different classes of methods allow computation of skeletons: "prairie fire" models (Blum, 1967), homotopic thinning (Lam et al.
Some specific topics explored include procedural glyphs for audio files, a Euclidean homotopic skeleton based on critical kernels, and detection of unusual motion using computer vision.
From the Quillen's fiber lemma we know that the function [phi] has a homotopic inverse, say [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Indeed, it is evident that in many cases, when resolution decreases, the resulting downsampled image cannot be homotopic to the original image.