A statistical approach to identifying closed object boundaries in images

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.

[1]  J. Doob.  Stochastic processes , 1953 .

[2]  J. M. Hammersley,et al.  Markov fields on finite graphs and lattices , 1971 .

[3]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[4]  J. Laurie Snell,et al.  Markov Random Fields and Their Applications , 1980 .

[5]  J. Kittler,et al.  Statistical Image Processing , 1983 .

[6]  Azriel Rosenfeld,et al.  Compact Region Extraction Using Weighted Pixel Linking in a Pyramid , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Azriel Rosenfeld,et al.  Multiresolution image processing and analysis , 1984 .

[8]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Donald Geman,et al.  Application of the Gibbs distribution to image segmentation , 1984, ICASSP.

[10]  J. Besag.  On the Statistical Analysis of Dirty Pictures , 1986 .

[11]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[12]  Edward J. Delp,et al.  A cost minimization approach to edge detection using simulated annealing , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[13]  D. M. Keenan,et al.  Towards automated image understanding , 1989 .

[14]  Robert J. Schalkoff,et al.  Digital Image Processing and Computer Vision , 1989 .

[15]  B. Ripley,et al.  Using spatial models as priors in astronomical image analysis , 1989 .

[16]  Joseph Shou-Pyng Shu.  One-pixel-wide edge detection , 1989, Pattern Recognit..

[17]  R. Cristi,et al.  Markov and recursive least squares methods for the estimation of data with discontinuities , 1990, IEEE Trans. Acoust. Speech Signal Process..

[18]  W. Qian,et al.  Parameter estimation for hidden Gibbs chains , 1990 .

[19]  Donald Geman,et al.  Boundary Detection by Constrained Optimization , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  A. L. Sutherland,et al.  Finding spiral structures in images of galaxies , 1990, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[21]  N. Cressie,et al.  Statistics for Spatial Data. , 1992 .

[22]  W. Qian,et al.  Estimation of parameters in hidden Markov models , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[23]  J. Besag,et al.  Bayesian image restoration, with two applications in spatial statistics , 1991 .

[24]  Federico Girosi,et al.  Parallel and Deterministic Algorithms from MRFs: Surface Reconstruction , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  U. Grenander,et al.  Comparing sweep strategies for stochastic relaxation , 1991 .

[26]  A. Raftery,et al.  Ice Floe Identification in Satellite Images Using Mathematical Morphology and Clustering about Principal Curves , 1992 .

[27]  Edward J. Delp,et al.  A Cost Minimization Approach to Edge Detection Using Simulated Annealing , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Jeffrey Donald Helterbrand,et al.  Spatial dependence models and image analysis , 1993 .

[29]  Jeffrey D. Helterbrand.  One-pixel-wide closed boundary identification , 1996, IEEE Trans. Image Process..

[30]  D.,et al.  ICE FLOE IDENTIFICATION IN SATELLITE IMAGES USING MATHEMATICAL MORPHOLOGY AND CLUSTERING ABOUT PRINCIPAL CURVES , .