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Pyramidal Transforms in Image Processing and Computer Vision

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Pyramidal Systems for Computer Vision

Part of the book series: NATO ASI Series ((NATO ASI F,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.

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Author information

Authors and Affiliations

  1. Electrical Engineering Section, University of Bremen, D- 2800, Bremen 33, F. R. of Germany

    Ph. W. Besslich

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  1. Ph. W. Besslich
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Editors and Affiliations

  1. Istituto di Informatica e Sistematica, Pavia University, Strada Nuova 106/C, 27100, Pavia, Italy

    Virginio Cantoni

  2. Dipartimento di Matematica, Rome University, Piazzale Aldo Moro 2, 00185, Rome, Italy

    Stefano Levialdi

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© 1986 Springer-Verlag Berlin Heidelberg

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Besslich, P.W. (1986). Pyramidal Transforms in Image Processing and Computer Vision. In: Cantoni, V., Levialdi, S. (eds) Pyramidal Systems for Computer Vision. NATO ASI Series, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82940-6_14

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  • DOI: https://doi.org/10.1007/978-3-642-82940-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82942-0

  • Online ISBN: 978-3-642-82940-6

  • eBook Packages: Springer Book Archive

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