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A statistical approach to identifying closed object boundaries in images

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Jeffrey D. Helterbrand ,
Noel Cressie  and
Jennifer L. Davidson
Jeffrey D. Helterbrand*
Affiliation:
Lilly Research Laboratories
Noel Cressie*
Affiliation:
Iowa State University
Jennifer L. Davidson*
Affiliation:
Iowa State University
*
* Postal address: Lilly Research Laboratories, A Division of Eli Lilly and Company, Indianapolis, IN 46285, USA.
** Postal address: Department of Statistics, Iowa State University, Ames, IA 50011, USA.
*** Postal address: Department of Electrical Engineering and Computer Engineering, Iowa State University, Ames, IA 50011, USA.
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Abstract

In this research, we present a statistical theory, and an algorithm, to identify one-pixel-wide closed object boundaries in gray-scale images. Closed-boundary identification is an important problem because boundaries of objects are major features in images. In spite of this, most statistical approaches to image restoration and texture identification place inappropriate stationary model assumptions on the image domain. One way to characterize the structural components present in images is to identify one-pixel-wide closed boundaries that delineate objects. By defining a prior probability model on the space of one-pixel-wide closed boundary configurations and appropriately specifying transition probability functions on this space, a Markov chain Monte Carlo algorithm is constructed that theoretically converges to a statistically optimal closed boundary estimate. Moreover, this approach ensures that any approximation to the statistically optimal boundary estimate will have the necessary property of closure.

Keywords

IMAGE ANALYSISBOUNDARY DETECTIONBAYESIAN METHODSMARKOV RANDOM FIELDSMARKOV CHAIN MONTE CARLO METHODS

MSC classification

Primary: 60G60: Random fields
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Advances in Applied Probability , Volume 26 , Issue 4 , December 1994 , pp. 831 - 854
Copyright
Copyright © Applied Probability Trust 1994 

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