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Pattern matching in a digitized image

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Abstract

For motivation purpose, imagine the followingcontinuous pattern-matching problem. Two continuous pictures, each consisting of unicolor regions, are given; one picture is called thescene and the other thepattern. The problem is to find all occurrences of the pattern in the scene.

As a step toward efficient algorithmic handling of the continuous pattern-matching problem by computers, where discretized representations are involved, we consider pattern-matching problems where the pattern and the text are specified either in terms of the “continuous” properties, or through other exemplar digitized images—a variety of alternative specifications is considered.

From the perspective of areas such as computer vision or image processing, our problem definitions identify an important gap in the fundamental theory of image formation and image processing—how to determine, even in the absence of noise, if a digitized image of a scene could contain an image of a given pattern. This is done using carefulaxiomatization.

Such a “digitized-based” approach may lead toward building on the theory of string-matching algorithms (in one, or higher, dimensions) for the benefit of algorithmic pattern matching in image processing.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Polytechnic University, 333 Jay Street, 11201, NY, Brooklyn, USA

    G. M. Landau

  2. Institute for Advanced Computer Studies and Electrical Engineering Department, University of Maryland College Park, 20742, MD, USA

    U. Vishkin

  3. Department of Computer Science, School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    U. Vishkin

Authors
  1. G. M. Landau
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  2. U. Vishkin
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Additional information

Communicated by Alberto Apostolico.

This paper is the journal version of [LV2].

Partially supported by NSF Grants CCR-8908286 and CCR-9305873 and the New York State Science and Technology Foundation, Center for Advanced Technology in Telecommunications, Polytechnic University, Brooklyn, NY, USA.

Partially supported by NSF Grants CCR-8906949 and CCR-9111348.

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Landau, G.M., Vishkin, U. Pattern matching in a digitized image. Algorithmica 12, 375–408 (1994). https://doi.org/10.1007/BF01185433

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  • DOI: https://doi.org/10.1007/BF01185433

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