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Optimal closed boundary identification in gray-scale imagery

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Abstract

Identification of closed boundary contours is an important problem in image analysis because boundaries delineate the structural components, or objects, present in a scene. Most filter-based edge-detection methods do not have a mechanism to identify a group of edge sites that defines a complete closed object boundary. In this paper, we construct a suitable parameter space of one-pixel-wide closed boundaries for gray-scale images that reduces the complexity of the boundary identification problem. An algorithm based on stochastic processes and Bayesian methods is presented to identify an optimal boundary from this space. By defining a prior probability model and appropriately specifying transition probability functions on the space, a Markov chain Monte Carlo algorithm is constructed that theoretically converges to a statistically optimal closed boundary estimate. Moreover, this approach ensures that implementation via computer will result in a final boundary estimate that has the necessary property of closure which previous stochastic approaches have been unable to achieve.

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Author information

Authors and Affiliations

  1. Statistical and Mathematical Sciences Division, Lilly Research Laboratories, Lilly Corporate Center, 46285, Indianapolis, IN, USA

    Jeffrey D. Helterbrand

  2. Department of Electrical and Computer Engineering, Iowa State University, 50011, Ames, IA, USA

    Jennifer L. Davidson

  3. Department of Statistics, Iowa State University, 50011, Ames, IA, USA

    Noel Cressie

Authors
  1. Jeffrey D. Helterbrand
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  2. Jennifer L. Davidson
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  3. Noel Cressie
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Helterbrand, J.D., Davidson, J.L. & Cressie, N. Optimal closed boundary identification in gray-scale imagery. J Math Imaging Vis 5, 179–205 (1995). https://doi.org/10.1007/BF01248371

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