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Multiresolution Design of Aperture Operators

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Abstract

The design of an aperture operator is based on adequately constraining the spatial domain and the graylevel range in order to diminish the space of operators and, consequently, the estimation error. The design of a resolution constrained operator is based on adequately combining information from two or more different resolutions and has the same motivation, that is, diminish the space of operators to facilitate design. This paper joins these approaches and studies multiresolution design of aperture operators for grayscale images. Spatial resolution constraint, range resolution constraint and the combination of both constraints are characterized, and the error increase by using the constrained filter in place of the optimal unconstrained one is analyzed. Pyramidal multiresolution design involves applying the resolution constraint approach hierarchically, from the higher to the lower resolution space. These approaches are also characterized and their error increase analyzed. The system that has been implemented to design pyramidal multiresolution operators is described and has its complexity (memory and runtime) analyzed. Several simulations and two applications for deblurring are shown and compared to optimal linear filters. The results confirm the usefulness of the approach.

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Authors and Affiliations

  1. SENAC College of Computer Science and Technology Rua Galvão Bueno, 430 - 01506-000, São Paulo, Brazil

    Roberto Hirata Junior

  2. Departamento de Ciência da Computação, Instituto de Matemática e Estatística - USP Rua do Matão, 1010 - 05508-900 -, São Paulo - SP, Brazil

    Marcel Brun & Junior Barrera

  3. Department of Electrical Engineering, Texas A&M University College Station, 77843-3128, TX, United States

    Edward R. Dougherty

Authors
  1. Roberto Hirata Junior
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  2. Marcel Brun
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  3. Junior Barrera
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  4. Edward R. Dougherty
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Hirata Junior, R., Brun, M., Barrera, J. et al. Multiresolution Design of Aperture Operators. Journal of Mathematical Imaging and Vision 16, 199–222 (2002). https://doi.org/10.1023/A:1020377610141

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