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Proceedings Paper

Equivalent weighting functions to equivalent contraction kernels
Author(s): Walter G. Kropatsch
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Paper Abstract

Burt introduced 1983 'equivalent weighting function': 'Iterative pyramid generation is equivalent to convolving the image g0 with a set of 'equivalent weighting functions' hl' gl equals hl * g0 equals h * gl-1, l > 1. It allowed him to study the effects of iterated reduction using the single parameter hl without giving up the efficient iterative computation. A similar concept applies to graph pyramids built by dual graph contraction. This new algorithm reduces the number of vertices and of edges of a pair of dual image graphs while, at he same time, the topological relations among the 'surviving' components are preserved. Repeated application produces a stack of successively smaller graphs: a pari of dual irregular pyramids. The process is controlled by selected decimation parameters which consist of a subset of surviving vertices and associated contraction kernels. These pay a similar role for graph pyramids than the convolution kernels of Gaussian pyramids. Equivalent contraction kernels combine two or more contraction kernels int one single dual contraction. The basic concepts are elaborated and discussed. The new theory opens a large variety of possibilities to explore the domain of 'all' graph pyramids.

Paper Details

Date Published: 1 February 1998
PDF: 11 pages
Proc. SPIE 3346, Sixth International Workshop on Digital Image Processing and Computer Graphics: Applications in Humanities and Natural Sciences, (1 February 1998); doi: 10.1117/12.301380
Show Author Affiliations
Walter G. Kropatsch, Vienna Univ. of Technology (Austria)


Published in SPIE Proceedings Vol. 3346:
Sixth International Workshop on Digital Image Processing and Computer Graphics: Applications in Humanities and Natural Sciences
Emanuel Wenger; Leonid I. Dimitrov, Editor(s)

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