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L. Hérault, R. Horaud, "FigureGround Discrimination: A Combinatorial Optimization Approach," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 9, pp. 899914, September, 1993.  
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@article{ 10.1109/34.232076, author = {L. Hérault and R. Horaud}, title = {FigureGround Discrimination: A Combinatorial Optimization Approach}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {15}, number = {9}, issn = {01628828}, year = {1993}, pages = {899914}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.232076}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  FigureGround Discrimination: A Combinatorial Optimization Approach IS  9 SN  01628828 SP899 EP914 EPD  899914 A1  L. Hérault, A1  R. Horaud, PY  1993 KW  combinatorial optimization; figureground discrimination; shape; cocircularity; smoothness; proximity; contrast; image element interactions; cost function; interacting spin system; mean field annealing; mean field approximation theory; microcanonical annealing; deterministic approximation; stochastic methods; simulated annealing; combinatorial mathematics; image processing; simulated annealing VL  15 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
The figureground discrimination problem is considered from a combinatorial optimization perspective. A mathematical model encoding the figureground discrimination problem that makes explicit a definition of shape based on cocircularity, smoothness, proximity, and contrast is presented. This model consists of building a cost function on the basis of image element interactions. This cost function fits the constraints of an interacting spin system that, in turn, is a well suited physical model that solves hard combinatorial optimization problems. Two combinatorial optimization methods for solving the figureground problem, namely mean field annealing, which combines mean field approximation theory and annealing, and microcanonical annealing, are discussed. Mean field annealing may be viewed as a deterministic approximation of stochastic methods such as simulated annealing. The theoretical bases of these methods are described, and the computational models are derived. The efficiencies of mean field annealing, simulated annealing, and microcanonical annealing algorithms are compared. Within the framework of such a comparison, the figureground problem may be viewed as a benchmark.
[1] S. T. Barnard, "Stochastic stereo matching over scale,"Int. J. Comput. Vision, vol. 3, no. 1, pp. 1732, May 1989.
[2] A. Blake, "Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 1, pp. 212, Jan. 1989.
[3] A. Blake and A. Zisserman,Visual Reconstruction. Cambridge, MA: MIT Press, 1987.
[4] M. Brady and H. Asada, "Smoothed local symmetries and their implementation,"Int. J. Robotics Res., vol. 3, no. 3, pp. 3661, 1984.
[5] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI8, pp. 679697, 1986.
[6] P. Carnevali, L. Coletti, and S. Patarnello, "Image processing by simulated annealing,"IBM J. Res. Development, vol. 29, no. 6, pp. 569579, Nov. 1985.
[7] M. Creutz, "Microcanonical Monte carlo simulation,"Phys. Rev. Lett., vol. 50, no. 19, pp. 14111414, May 1983.
[8] R. Deriche, "Using Canny's criteria to derive a recursively implemented optimal edge detector,"Int. J. Comput. Vision, vol. 1, no. 2, pp. 167187, 1987.
[9] D. Geiger and F. Girosi, "Parallel and deterministic algorithms from mrf's: Surface reconstruction,"IEEE Trans. Patt. Anal. Machine Intell., vol. 13, no. 5, pp. 410412, May 1991.
[10] D. Geiger and A. Yuille, "A common framework for image segmentation,"Int. J. Comput. Vision, 1990, to be published.
[11] S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and bayesian restoration of images,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI6, pp. 721741, 1984.
[12] D. Gutfinger and J. Sklansky, "Robust classifiers by mixed adaptation,"IEEE Trans. Patt. Anal. Machine Intell., vol. 13, no. 6, pp. 552567, June 1991.
[13] L. Hérault and J. J. Niez, "Neural networks and graph Kpartitioning,"Complex Syst., vol. 3, no. 6, pp. 531576, Dec. 1989.
[14] L. Hérault and J. J. Niez, "Neural networks and combinatorial optimization: A study of NPcomplete graph problems," inNeural Networks: Advances and Applications(E. Gelembe, Ed.). Amsterdam: North Holland, 1991, pp. 165213.
[15] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models,"Int. J. Comput. Vision, vol. 1, no. 4, pp. 321331, Jan. 1988.
[16] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing,"Sci., vol. 220, pp. 671680, 1983.
[17] W. Kohler,Gestalt Psychology. New York: Meridian, 1980.
[18] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, "Equations of state calculations by fast computing machines,"J. Chem. Phys., vol. 21, pp. 10871092, 1953.
[19] H. Orland, "Mean field theory for optimization problems,"J. Phys.Lett., vol. 46, no. 17, pp. L763L770, Sept. 1985.
[20] P. Parent and S. W. Zucker, "Trace inference, curvature consistency, and curve detection,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 8, pp. 823839, Aug. 1989.
[21] C. Peterson, "A new method for mapping optimization problems onto neural networks,"Int. J. Neural Syst., vol. 1, no. 1, pp. 322, 1989.
[22] C. Peterson, "Track finding with neural networks,"Nuclear Instrum. Methods Phys. Res., vol. A279, pp. 537545, 1989.
[23] C. Peterson and J. R. Anderson, "A mean field learning algorithm for neural networks,"Complex Syst., vol. 1, pp. 9951019, 1987.
[24] F. Reif,Fundamental of Statistical and Thermal Physics. New York: McGrawHill, 1965.
[25] T. J. Sejnowski and G. E. Hinton, "Separating figure from ground with a Boltzmann machine," inVision, Brain, and Cooperative Computation(M. Arbib and A. Hanson, Eds.). Cambridge, MA: MIT Press, 1988, pp. 703724.
[26] A. Sha'ashua and S. Ullman, "Structural saliency: The detection of globally salient structures using a locally connected network," inProc. Second Int. Conf. Comput. Vision(Tarpon Springs, FL), 1988, pp. 321327.
[27] H. E. Stanley,Introduction to Phases Transitions and Critical Phenomena. Oxford, UK: Oxford University Press, 1971.
[28] D. E. Van den Bout and T. K. Miller, "Graph partitioning using annealed neural networks," inProc. Int. Joint Conf. Neural Networks(Washington DC), June 1989, pp. 521528.
[29] J. Zerubia and R. Chellappa, "Mean field approximation using compound GaussMarkov random field for edge detection and image restoration," inProc. ICASSP(Alburquerque, NM), 1990, pp. 21932196, Apr. 1990.