13.3.5.1 Continuous Relaxation Theory

Ullman, S.,
Relaxation and Constrained Optimization by Local Processes,
CGIP(10), No. 2, June 1979, pp. 115-125.
WWW Version. BibRef 7906

Nagin, P.A., Hanson, A.R., Riseman, E.M.,
Variations in Relaxation Labeling Techniques,
CGIP(17), No. 1, September 1981, pp. 33-51.
WWW Version. BibRef 8109

Richards, J.A., Landgrebe, D.A., Swain, P.H.,
On the Accuracy of Pixel Relaxation,
SMC(11), 1981, pp. 303-309. BibRef 8100

Glazer, F.,
Multilevel Relaxation in Low-Level Computer Vision,
MIPA84(312-330). BibRef 8400

Kittler, J.V., and Illingworth, J.,
Relaxation Labelling Algorithms: A Review,
IVC(3), No. 4, November 1985, pp. 206-216.
WWW Version. Survey, Relaxation. Relaxation, Survey. BibRef 8511

Davis, L.S., and Rosenfeld, A.,
Cooperating Processes for Low-Level Vision: A Survey,
AI(17), No. 1-3, August 1981, pp. 245-263.
WWW Version. Survey, Relaxation. Relaxation, Survey. BibRef 8108

Haralick, R.M., Davis, L.S., Rosenfeld, A.[Azriel], and Milgram, D.L.[David L.],
Reduction Operations for Constraint Satisfaction,
IS(14), No. 3, April, 1978, pp. 199-219. BibRef 7804

Zhuang, X., Haralick, R.M., and Joo, H.,
A Simplex-Like Algorithm for the Relaxation Labeling Process,
PAMI(11), No. 12, December 1989, pp. 1316-1321.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 8912
Earlier: ICPR86(190-194). A new 1 iteration procedure. It is compared to the original RHZ relaxation and does perform better (but then everything does). BibRef

Haralick, R.M.[Robert M.],
Decision Making in Context,
PAMI(5), No. 4, July 1983, pp. 417-428. Bayes Networks. BibRef 8307
Earlier:
Contextual decision making with degrees of belief,
ICPR92(II:105-111).
IEEE DOI Reference 9208Discusses relaxation and how it gets around the problems of the usual Bayesian decision theoretic models. BibRef

Haralick, R.M.[Robert M.],
An Interpretation for Probabilistic Relaxation,
CVGIP(22), No. 3, June 1983, pp. 388-395.
WWW Version. Each iteration is a new computation of the conditional probability for the new context. Therefore iterations need to continue only until all the context has been considered. How to determine this is still an open question. BibRef 8306

Krishnamurthy, E.V., Narayanan, K.A.,
Relaxation: Application to the Matrix Reconstruction Problem,
CGIP(15), No. 3, March 1981, pp. 288-295.
WWW Version. BibRef 8103

Lloyd, S.A.,
An Optimization Approach to Relaxation Labeling Algorithms,
IVC(1), No. 2, May 1983, pp. 85-91.
WWW Version. BibRef 8305

Kalayeh, H.M., and Landgrebe, D.A.,
Adaptive Relaxation Labeling,
PAMI(6), No. 3, May, 1984, pp. 369-372. The problems with the constant compatibility coefficients. The fix is to estimate the compatibility coefficients based on small neighborhoods. BibRef 8405

Fekete, G., Eklundh, J.O., and Rosenfeld, A.,
Relaxation: Evaluation and Applications,
PAMI(3), No. 4, July 1981, pp. 459-469. BibRef 8107

Eklundh, J.O., and Rosenfeld, A.,
Some Relaxation Experiments Using Triples of Pixels,
SMC(10), 1980, pp. 150-153. BibRef 8000

Eklundh, J.O., and Rosenfeld, A.,
Convergence Properties of Relaxation,
UMD-TR-701, October 1978. BibRef 7810

Elfving, T., and Eklundh, J.O.,
Some Properties of Stochastic Labeling Procedures,
CGIP(20), No. 2, October 1982, pp. 158-170.
WWW Version. A particular model of relaxation processes is formulated and used to analyze the basic methods. Some mention of optimizing methods. BibRef 8210

Kuschel, S.A., and Page, C.V.,
Augmented Relaxation Labeling and Dynamic Relaxation Labeling,
PAMI(4), No. 6, November 1982, pp. 676-683. BibRef 8211
Earlier: PRIP81(441-448). Augmentation to give nonhomogeneous neighborhood. The value of a point is broadcast to a specific neighborhood (depending on its likely assignment) rather than to all neighbors. BibRef

Wong, A.K.C.[Andrew K. C.], Chiu, D.K.Y.[David K. Y.],
An event-covering method for effective probabilistic inference,
PR(20), No. 2, 1987, pp. 245-255.
WWW Version. 0309 BibRef
Earlier:
A Probabilistic Inference System,
ICPR84(303-306). BibRef

Chan, K.C.C., Wong, A.K.C.,
PIS: a probabilistic inference system,
ICPR88(I: 360-364).
IEEE DOI Reference 8811 BibRef

Jamison, J.S., and Schalkoff, R.J.,
Image Labeling: A Neural Network Approach,
IVC(6), No. 4, November 1988, pp. 203-214.
WWW Version. BibRef 8811

Duncan, J.S., and Frei, W.,
Relaxation Labeling Using Continuous Label Sets,
PRL(9), No. 1, January 1989, pp. 27-37. BibRef 8901

Soo, V.W., Huang, K.,
On Evidential Relaxation Labeling: A Scheme Toward Knowledge-Based Vision,
JISE(9), No. 2, 1993, pp. 153-175. BibRef 9300

Fogel, D.B.,
An Introduction to Simulated Evolutionary Optimization,
TNN(5), No. 1, 1994, pp. 3-14. Problems with hill-climbing in local optimization. BibRef 9400

Sastry, P.S., Thathachar, M.A.L.,
Analysis of Stochastic Automata Algorithm for Relaxation Labelling,
PAMI(16), No. 5, May 1994, pp. 538-543.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9405

Qi, X.F., and Palmieri, F.,
Theoretical Analysis of Evolutionary Algorithms with an Infinite Population in Continuous Space: Basic Properties of Selection and Mutation,
TNN(5), 1994, pp. 102-119. BibRef 9400
And:
Theoretical Analysis of Evolutionary Algorithms with an Infinite Population in Continuous Space: Analysis of the Diversification Role of Crossover,
TNN(5), 1994, pp. 120-129. Genetic Algorithms. BibRef

Snyder, W., Han, Y.S., Bilbro, G.L., Whitaker, R.T., Pizer, S.,
Image Relaxation: Restoration and Feature-Extraction,
PAMI(17), No. 6, June 1995, pp. 620-624.
IEEE Abstract. IEEE Top Reference.
WWW Version. Image Restoration. Equivalence with Graduated Nonconvexity, Variable Conductance Diffusion, Anisotropic Diffusion and Biased Anisotropic Diffusion, Mean Field Annealing and Image Relaxation. BibRef 9506

Pelillo, M., Abbattista, F., Maffione, A.,
An Evolutionary Approach to Training Relaxation Labeling Processes,
PRL(16), No. 10, October 1995, pp. 1069-1078. BibRef 9510

Chen, Q., Luh, J.Y.S.,
Relaxation Labeling Algorithm for Information Integration and its Convergence,
PR(28), No. 11, November 1995, pp. 1705-1722.
WWW Version. BibRef 9511

Cucka, P., Rosenfeld, A.,
Evidence Based Pattern-Matching Relaxation,
PR(26), No. 9, September 1993, pp. 1417-1427.
WWW Version. BibRef 9309

Pelillo, M.[Marcello],
The Dynamics of Nonlinear Relaxation Labeling Processes,
JMIV(7), No. 4, October 1997, pp. 309-323.
WWW Version. 9710 BibRef
Earlier:
Nonlinear relaxation labeling as growth transformation,
ICPR94(B:201-206).
IEEE DOI Reference 9410 BibRef

Pelillo, M.[Marcello], Refice, M.,
An optimization algorithm for determining the compatibility coefficients of relaxation labeling processes,
ICPR92(II:145-148).
IEEE DOI Reference 9208 BibRef

Fu, A.M.N., Yan, H.,
A New Probabilistic Relaxation Method Based on Probability Space Partition,
PR(30), No. 11, November 1997, pp. 1905-1917.
WWW Version. 9801 BibRef

Stoddart, A.J., Petrou, M.[Maria], Kittler, J.V.,
On the Foundations of Probabilistic Relaxation with Product Support,
JMIV(9), No. 1, July 1998, pp. 29-48.
WWW Version. 9807 BibRef
Earlier:
Probabilistic Relaxation as an Optimiser,
BMVC95(613-622).
PDF Version. 9509 BibRef

Stoddart, A.J., Petrou, M., Kittler, J.V.,
A New Algorithm for Probabilistic Relaxation Based on the Baum Eagon Theorem,
CAIP95(674-679).
Springer DOI Reference 9509 BibRef

Arathorn, D.W.,
Recognition under transformation using ordering property of superpositions,
EL(37), 2001, 164-166.
WWW Version. Map-Seeking Circuit Algorithm BibRef 0100

Jacobson, M.W., Fessler, J.A.,
An Expanded Theoretical Treatment of Iteration-Dependent Majorize-Minimize Algorithms,
IP(16), No. 10, October 2007, pp. 2411-2422.
IEEE DOI Reference 0711Iterative process (relaxation), first majorize one, then minimize another. BibRef

Chen, X., Li, Y.,
A Modified PSO Structure Resulting in High Exploration Ability With Convergence Guaranteed,
SMC-B(37), No. 5, October 2007, pp. 1271-1289.
IEEE DOI Reference 0711Particle swarm optimization. Simulate swarm of insects. BibRef

Harker, S.R., Vogel, C.R., Gedeon, T.,
Analysis of Constrained Optimization Variants of the Map-Seeking Circuit Algorithm,
JMIV(29), No. 1, Septmeber 2007, pp. 49-62.
Springer DOI Reference 0709Efficiently solve the combinatorial problem of correspondence maximization. See also Recognition under transformation using ordering property of superpositions. BibRef

Gedeon, T.[Tomáš], Arathorn, D.[David],
Convergence of Map Seeking Circuits,
JMIV(29), No. 2-3, November 2007, pp. 235-248.
Springer DOI Reference 0712 BibRef

Wang, H.F.[Hong-Fang], Hancock, E.R.[Edwin R.],
Probabilistic relaxation labelling using the Fokker-Planck equation,
PR(41), No. 11, November 2008, pp. 3393-3411.
WWW Version. 0808 BibRef
Earlier:
Probabilistic Relaxation Labeling by Fokker-Planck Diffusion on a Graph,
GbRPR07(204-214).
Springer DOI Reference 0706 BibRef
And:
Kernelised Relaxation Labelling using Fokker-Planck Diffusion,
CIAP07(29-34).
IEEE DOI Reference 0709 BibRef
Earlier:
Probabilistic Relaxation using the Heat Equation,
ICPR06(II: 666-669).
WWW Version. 0609Data clustering; Feature correspondence matching; Scene labelling; Relaxation labelling; Graph theory; Diffusion process; Fokker-Planck equation BibRef

Petrou, M., Mirmehdi, M., and Coors, M.,
Multilevel Probabilistic Relaxation,
BMVC97(60-69).
HTML Version. Segmentation technique. BibRef 9700

Draper, B.A.,
Modelling Object Recognition as a Markov Decision Process,
ICPR96(IV: 95-99).
IEEE DOI Reference 9608Colorado State.
WWW Version. BibRef

Poole, I.,
Optimal probabilistic relaxation labeling,
BMVC90(xx-yy).
PDF Version. 9009 BibRef

Bozma, H.I., and Duncan, J.S.,
Admissibility of Constraint Functions in Relaxation Labeling,
ICCV88(328-332).
IEEE Abstract. IEEE Top Reference. Conditions on the constraint functions in a relaxation process that is solving an optimization problem. BibRef 8800

Zhang, D., Liu, J., Wan, F.,
Multiresolution Relaxation: Experiments and Evaluations,
ICPR88(II: 712-714).
IEEE DOI Reference
IEEE Top Reference. BibRef 8800

Thompson, W.B., Mutch, K.M., Kearney, J.K., Madarasz, R.L.,
Relaxation Labeling Using Staged Updating,
PRIP81(449-451). BibRef 8100

Chapter on Matching and Recognition Using Volumes, High Level Vision Techniques, Invariants continues in
Boltzmann Machine, Simulated Annealing, and Related Topics .