A common framework for image segmentation

We attempt to unify several approaches to image segmentation in early vision under a common framework. The Bayesian approach is very attractive since: (i) it enables the assumptions used to be explicitly stated in the probability distributions, and (ii) it can be extended to deal with most other problems in early vision. Here, we consider the Markov random field formalism, a special case of the Bayesian approach, in which the probability distributions are specified by an energy function.We show that: (i) our discrete formulations for the energy function is closely related to the continuous formulation; (ii) by using the mean field (MF) theory approach, introduced by Geiger and Girosi [1991], several previous attempts to solve these energy functions are effectively equivalent; (iii) by varying the parameters of the energy functions we can obtain connections to nonlinear diffusion and minimal description length approaches to image segmentation; and (iv) simple modifications to the energy can give a direct relation to robust statistics or can encourage hysteresis and nonmaximum suppression.

[1]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[2]  R. E. Graham,et al.  Snow removal-A noise-stripping process for picture signals , 1962, IRE Trans. Inf. Theory.

[3]  E. Wasserstrom.  Numerical Solutions by the Continuation Method , 1973 .

[4]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[5]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[6]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[7]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[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]  Andrew P. Witkin,et al.  Scale-space filtering: A new approach to multi-scale description , 1984, ICASSP.

[10]  José L. Marroquín,et al.  Probabilistic solution of inverse problems , 1985 .

[11]  T. Poggio,et al.  Fingerprints theorems for zero crossings , 1985 .

[12]  W. Eric L. Grimson,et al.  Discontinuity detection for visual surface reconstruction , 1985, Comput. Vis. Graph. Image Process..

[13]  Demetri Terzopoulos,et al.  Regularization of Inverse Visual Problems Involving Discontinuities , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  C Koch,et al.  Analog "neuronal" networks in early vision. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[15]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[17]  Stuart Geman,et al.  Statistical methods for tomographic image reconstruction , 1987 .

[18]  Tomaso A. Poggio,et al.  An Optimal Scale for Edge Detection , 1988, IJCAI.

[19]  Tomaso Poggio,et al.  Probabilistic Solution of Ill-Posed Problems in Computational Vision , 1987 .

[20]  Richard Durbin,et al.  An analogue approach to the travelling salesman problem using an elastic net method , 1987, Nature.

[21]  T. Poggio,et al.  Visual Integration and Detection of Discontinuities: The Key Role of Intensity Edges , 1987 .

[22]  Max Mintz,et al.  Robust fusion of location information , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[23]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[24]  David Lee,et al.  One-Dimensional Regularization with Discontinuities , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  G. Parisi,et al.  Statistical Field Theory , 1988 .

[26]  Decision Systems.,et al.  Variational problems in SBV , 1988 .

[27]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  Tomaso A. Poggio,et al.  Extensions of a Theory of Networks for Approximation and Learning , 1990, NIPS.

[29]  M. Sarrafzadeh.  Department of electrical engineering and computer science , 1990, SIGD.

[30]  Federico Girosi,et al.  Parallel and deterministic algorithms from MRFs: surface reconstruction and integration , 1990, ECCV.

[31]  Niklas K Nordstrom,et al.  Variational Edge Detection , 1990 .

[32]  Kenneth Charles Keeler.  Map representations and optimal encoding for image segmentation , 1990 .

[33]  Yvan G. Leclerc,et al.  Constructing simple stable descriptions for image partitioning , 1989, International Journal of Computer Vision.

[34]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[35]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[36]  A. Yuille,et al.  Energy functions for early vision and analog networks , 1989, Biological Cybernetics.