Variational versus Markov random field methods for image segmentation

Sanjeev R. Kulkarni; S. K. Mitter

doi:10.1117/12.179231

30 June 1994 Variational versus Markov random field methods for image segmentation

Sanjeev R. Kulkarni, S. K. Mitter

Proceedings Volume 2304, Neural and Stochastic Methods in Image and Signal Processing III; (1994) https://doi.org/10.1117/12.179231
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

Variational and Markov random field (MRF) methods have been proposed for a number of tasks in image processing and early vision. Continuous (variational) formulations have the advantages of being more amenable to analysis and more easily incorporating geometric constraints and invariants. However, discrete (MRF) formulations have computational advantages and are typically used in implementing such methods. Certain commonly used MRF models for image segmentation do not properly approximate a standard continuous formulation in the sense that the discrete solutions may not converge to a solution of the continuous problem as the lattice spacing tends to zero. We propose several modifications of the MRF formulations for which we prove convergence in the continuum limit. Although these MRF models require complex neighborhood structures, we discuss results that indicate that for MRF models with bounded number of states, the difficulties are inherent and cannot be avoided in any scheme with the desired convergence properties.

Citation Download Citation

Sanjeev R. Kulkarni and S. K. Mitter "Variational versus Markov random field methods for image segmentation", Proc. SPIE 2304, Neural and Stochastic Methods in Image and Signal Processing III, (30 June 1994); https://doi.org/10.1117/12.179231

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