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Pyramidal Transforms in Image Processing and Computer Vision

  • Ph. W. Besslich
Part of the NATO ASI Series book series (volume 25)

Abstract

This chapter deals with a class of transform algorithms suitable for the generation and processing of pyramidal data. The transformations make use of radix-2k signal-flow graphs and “in-place” processing. The scheme is based on a hierarchical ordering of a 2n × 2n data array in memory for radix-2 signal-flow graph processing or, alternatively, on linewise stored data using incomplete radix-2 graphs (k=1, 2,…,n). The generation of pyramidal data structures is a special case of a more general class of 2-D transformations that calculate 2-D transform coefficients hierarchically, i.e. from the coefficients of subareas. Various useful global or local transformations maybe implemented under the hierarchical scheme.Pyramidal data structures are shown to be a special case of hierarchical transforms. For instance, each node level of an averaging pyramid corresponds to a hierarchy level of a reversible transformation. From the class of orthogonal transformations the 2-D Walsh-Hadamard transform (WHT) complies with the stipulations of hierarchical generation of coefficients. Local versions pyramidal radix-2k transformations provide windows of size 2k × 2k. Windows of odd-numbered dimensions require radix-p based transformations (p=prime number > 2). Local pyramids using weighted and overlapping window operations are shown to allow various weighting functions of the window, e.g. a Gaussian weighting. Pyramidal transform algorithms may be supported by special hardware. An architecture is proposed that uses spatially parallel processing for each pyramid layer and macro pipelining among the layers.

Keywords

Memory Location Iterative Step Single Instruction Multiple Data Picture Element Pyramid Level 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Ph. W. Besslich
    • 1
  1. 1.Electrical Engineering SectionUniversity of BremenBremen 33F. R. of Germany

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