See also Gradient Descent.

*Barnard, S.T.*, and
*Thompson, W.B.*,

**Disparity Analysis of Images**,

*PAMI(2)*, No. 4, July 1980, pp. 333-340.
BibRef
**8007**

Earlier:
TR-79-1, CSD,
*Univ. of Minnesota*January 1979.
*Relaxation, Results*.
*Matching, Points*. Matching for motion. This program finds corresponding pairs of points
in a motion analysis system using the similarity of motion with
neighboring points. Feature points (such as corners) in both views
are used rather than the single view used in Moravec, and a
relaxation procedure finds the final global match between the two sets
of feature points. The initial assignments of possible matches for
the set of feature points is simply all the features with a similar
(nearby) position in the second image. Thus, small motions are
assumed. An iterative (relaxation based) procedure uses the
disparities of the nearby points to eliminate the unlikely assignments
from the set of possible assignments. These include points with
disparities different from the others in the neighborhood. The
formulation of the algorithm is very simple and thus it works for any
kind of disparity (such as from observer motion, multiple object
motions, or stereo) and it does not require any detailed camera
models. This provides a basic matching method to find disparity for a
moderate number of points (the feature points) that are generally
consistent with the other nearby points (i.e. smooth surfaces), but
allowing for edges or changes in the disparity field.

See also Lower-level Estimates and Interpretation of Visual Motion.
BibRef

*Barnard, S.T.*,

**The Image Correspondence Problem**,

*Ph.D.*Thesis (CS), U Minn, 1979.
The thesis version of his work.
BibRef
**7900**

*Kitchen, L.*,

**Relaxation Applied to Matching Quantitative Relational Structures**,

*SMC(10)*, February 1980, pp. 96-101.
*Fuzzy Logic*. Introduction of a new operator defined in terms of fuzzy logic with
some examples on synthetic structures. Experiments with the
operator on more general problems indicate that there may be
problems which are not indicated by the synthetic problems.
BibRef
**8002**

*Yamamoto, H.*,

**Some Experiments on LANDSAT Pixel Classification
Using Relaxation Operators**,

*CGIP(13)*, No. 1, May 1980, pp. 31-45.

Elsevier DOI
BibRef
**8005**

*Kirby, R.L.*,

**A Product Rule Relaxation Method**,

*CGIP(13)*, No. 2, June 1980, pp. 158-189.

Elsevier DOI
BibRef
**8006**

*Hwang, J.J.*, and
*Hall, E.L.*,

**Matching of Featured Objects Using
Relational Tables from Stereo Images**,

*CGIP(20)*, No. 1, September 1982, pp. 22-42.

Elsevier DOI
*Matching, Regions*. Features include regions, lines and vertices. The example is a
complex block-like UT. The structure is simply adjacencies. The
arrays are used to simplify the search for the matching subset.
They use precise knowledge of the camera locations to get search
lines in the second image.
BibRef
**8209**

*Hwang, J.J.*, and
*Hall, E.L.*,

**Scene Representation Using the Adjacency Matrix and
Sampled Shapes of Regions**,

*PRIP78*(250-261).
BibRef
**7800**

*Faugeras, O.D.*, and
*Price, K.E.*,

**Semantic Description of Aerial Images Using Stochastic Labeling**,

*PAMI(3)*, No. 6, November 1981, pp. 633-642.
BibRef
**8111**
*USC Computer Vision*
BibRef

And:
*ICPR80*(352-357).
BibRef

And:
*DARPA80*(89-94).
*Matching, Regions*.
*Relaxation, Results*.
The use of an optimization based relaxation method with structural
descriptions. This work uses a relaxation approach very similar to
that of (

See also Improving Consistency and Reducing Ambiguity in Stochastic Labeling: An Optimization Approach. ) for finding corresponding regions in two
images of the same scene and finding regions in the image
corresponding to elements in a model of the scene.
The relaxation matching procedure has two major steps: finding initial
potential matches and computing the updated match rating based on the
matches for the neighboring regions. These steps are combined by:
(1) Compute the match rating for each region in the model with all regions
in the image. Order these and keep only the best (15) matches.
(2)Compute the compatibility for each of these possible matches with the
current most likely match for all the neighboring (related in the
network) regions. (3) Update the match ratings so that compatible matches
improve and incompatible ones decrease. (4) If some match is very likely,
make the assignment permanent, and continue with the initialization
step. Otherwise continue with the compatibility computation step.
This procedure works by finding the most obvious match (e.g. largest
regions, and all other features match) and building around this one by
making assignments to regions related to the obvious match. This
matching system makes few assumptions about the types of scenes,
though assumptions can be used to improve the efficiency of the match,
and is applicable to a variety of tasks.

See also Symbolic Image Registration and Change Detection.
BibRef

*Price, K.E.*,

**Hierarchial Matching Using Relaxation**,

*CVGIP(34)*, No. 1, April 1986, pp. 66-75.

Elsevier DOI
BibRef
**8604**
*USC Computer Vision*Discussion of the use of group level descriptions to aid relaxation.
BibRef

*Price, K.E.*,

**Relaxation Matching Techniques: A Comparison**,

*PAMI(7)*, No. 5, September 1985, pp. 617-623.
BibRef
**8509**
*USC Computer Vision*
BibRef

And:
*ICPR84*(987-989).
*Relaxation, Evaluation*.
Comparison of several relaxation methods, for accuracy and time.
BibRef

*Price, K.E.*,

**Symbolic Matching of Images and Scene Models**,

*DARPA82*(299-308).
BibRef
**8200**
*USC Computer Vision*
BibRef

And:
*CVWS82*(105-112).
Several discussions on relaxation techniques in one paper. The

See also Relaxation Matching Techniques: A Comparison. and

See also Hierarchial Matching Using Relaxation. supersede this one.
BibRef

*Price, K.E.*,

**Relaxation Matching Applied to Aerial Images**,

*DARPA81*(22-25).
BibRef
**8100**
*USC Computer Vision*Discussion of more recent results. Not much else.
BibRef

*Price, K.E.*,

**Symbolic Matching and Analysis with Substantial Changes in Orientation**,

*DARPA78*(93-99).
BibRef
**7800**
*USC Computer Vision*
BibRef

And:
*PRAI-78*(19-21).
BibRef

*Hummel, R.A.[Robert A.]*,

**A Design Method for Relaxation Labeling Applications**,

*AAAI-83*(168-171).
BibRef
**8300**

Earlier:
*NYU*CS Dept., TR 68, March 1983.
A discussion of how to set up a relaxation labeling system.
BibRef

*Ogawa, H.*,

**A Fuzzy Relaxation Technique For Partial Shape-Matching**,

*PRL(15)*, No. 4, April 1994, pp. 349-355.
BibRef
**9404**

*Qin, C.*,
*Luh, J.Y.S.*,

**Ambiguity Reduction by Relaxation Labeling**,

*PR(27)*, No. 1, January 1994, pp. 165-180.

Elsevier DOI
BibRef
**9401**

*Ranganath, H.S.[Heggere S.]*,
*Chipman, L.J.[Laure J.]*,

**Fuzzy Relaxation Approach for Inexact Scene Matching**,

*IVC(10)*, No. 9, November 1992, pp. 631-640.

Elsevier DOI
*Matching, Regions*.
BibRef
**9211**

*Cooper, P.R.[Paul R.]*,
*Swain, M.J.[Michael J.]*,

**Arc Consistency: Parallelism and Domain Dependence**,

*AI(58)*, No. 1-3, 1992, pp. 207-23.5

Elsevier DOI
BibRef
**9200**

*Cooper, P.R.[Paul R.]*,
*Swain, M.J.[Michael J.]*,

**Domain Dependence in Parallel Constraint Satisfaction**,

*IJCAI89*(54-59).
BibRef
**8900**

*Swain, M.J.[Michael J.]*,
*Cooper, P.R.[Paul R.]*,

**Parallel Hardware for Constraint Satisfaction**,

*AAAI-88*(682-686).
BibRef
**8800**

*Gold, S.[Steven]*,
*Rangarajan, A.[Anand]*,

**A Graduated Assignment Algorithm for Graph Matching**,

*PAMI(18)*, No. 4, April 1996, pp. 377-388.

IEEE DOI
BibRef
**9604**
*Yale*DCS/RR-1062, January 1995.
BibRef

And:

**Graph Matching by Graduated Assignment**,

*CVPR96*(239-244).

IEEE DOI Matching O(lm).
Similar to relaxation (annealing) approach. (But not quite).
Uses hand labeled features in the image for matching (multiple features
on an object). They note that relaxation labeling does poorly on
pure subgraph isomorphism (no attributed nodes), and does poorly
when noise is high for attributed graph matching. (Though the comparison
is with the most basic relaxation methodology.)
**9605**

BibRef

*Gold, S.[Steven]*,

**Matching and Learning Structural and Spatial Representation
with Neural Networks**,

*Ph.D.*Thesis, Yale, 1995.
BibRef
**9500**

*Gold, S.[Steven]*,
*Rangarajan, A.[Anand]*, and
*Mjolsness, E.*,

**Learning with Preknowledge:
Clustering with Point and Graph Matching Distance Measures**,

*NeurComp(8)*, 1966, pp. 787-804.
BibRef
**6600**

*Sitaraman, R.[Ramesh]*,
*Rosenfeld, A.[Azriel]*,

**Probabilistic Analysis of Two Stage Matching**,

*PR(22)*, No. 3, 1989, pp. 331-343.

Elsevier DOI
BibRef
**8900**

*Finch, A.M.[Andrew M.]*,
*Wilson, R.C.*,
*Hancock, E.R.[Edwin R.]*,

**Matching Delaunay Graphs**,

*PR(30)*, No. 1, January 1997, pp. 123-140.

Elsevier DOI
**9702**

BibRef

Earlier: A1, A3 only:
*CIAP95*(56-61).

Springer DOI
**9509**

BibRef

*Finch, A.M.[Andrew M.]*,
*Wilson, R.C.[Richard C.]*,
*Hancock, E.R.[Edwin R.]*,

**Matching delaunay triangulations by probabilistic relaxation**,

*CAIP95*(350-358).

Springer DOI
**9509**

BibRef

*Finch, A.M.*,
*Hancock, E.R.*,

**Matching Deformed Delaunay Triangulations**,

*SCV95*(31-36).

IEEE DOI Univ. of York.
Relaxation applied to matching graphs composed of triangles.
BibRef
**9500**

*Bhattacharya, P.*,

**Some Remarks on Fuzzy Graphs**,

*PRL(6)*, 1987, pp. 297-302.
BibRef
**8700**

*Pelillo, M.*,
*Fanelli, A.M.*,

**Autoassociative Learning in Relaxation Labeling Networks**,

*PRL(18)*, No. 1, January 1997, pp. 3-12.
**9704**

BibRef

Earlier:
*ICPR96*(IV: 105-110).

IEEE DOI
**9608**

(Univ. Ca Foscari Venezia, I)
BibRef

*Doa, K.H.[Kyeong-Hoon]*,
*Kima, Y.S.[Yong-Suk]*,
*Uama, T.U.[Tae-Uk]*,
*Ha, Y.H.[Yeong-Ho]*,

**Iterative Relaxational Stereo Matching Based on
Adaptive Support Between Disparities**,

*PR(31)*, No. 8, August 1998, pp. 1049-1059.

Elsevier DOI
**9807**

*Stereo, Matching*.
BibRef

*Skomorowski, M.[Marek]*,

**Use of random graph parsing for scene labelling by probabilistic
relaxation**,

*PRL(20)*, No. 8, August 1999, pp. 949-956.
BibRef
**9908**

*Torsello, A.[Andrea]*,
*Pelillo, M.[Marcello]*,

**Continuous-time relaxation labeling processes**,

*PR(33)*, No. 11, November 2000, pp. 1897-1908.

Elsevier DOI
**0011**

BibRef

*Medasani, S.*,
*Krishnapuram, R.*,
*Choi, Y.S.*,

**Graph Matching by Relaxation of Fuzzy Assignments**,

*Fuzzy(9)*, No. 1, 2001, pp. 173-182.
BibRef
**0100**

*Bengoetxea, E.[Endika]*,
*Larrañaga, P.[Pedro]*,
*Bloch, I.[Isabelle]*,
*Perchant, A.[Aymeric]*,
*Boeres, C.[Claudia]*,

**Inexact graph matching by means of estimation of distribution
algorithms**,

*PR(35)*, No. 12, December 2002, pp. 2867-2880.

Elsevier DOI
**0209**

BibRef

Earlier: A1, A2, A3, A4, Only:

**Estimation of Distribution Algorithms: A New Evolutionary Computation
Approach for Graph Matching Problems**,

*EMMCVPR01*(454-469).

Springer DOI
**0205**

BibRef

*Perchant, A.*,
*Bloch, I.*,

**Graph Fuzzy Homomorphism Interpreted as Fuzzy Association Graphs**,

*ICPR00*(Vol II: 1042-1045).

IEEE DOI
**0009**

BibRef

*Aldea, E.[Emanuel]*,
*Fouquier, G.[Geoffroy]*,
*Atif, J.[Jamal]*,
*Bloch, I.[Isabelle]*,

**Kernel Fusion for Image Classification Using Fuzzy Structural
Information**,

*ISVC07*(II: 307-317).

Springer DOI
**0711**

BibRef

*Aldea, E.[Emanuel]*,
*Atif, J.[Jamal]*,
*Bloch, I.[Isabelle]*,

**Image Classification Using Marginalized Kernels for Graphs**,

*GbRPR07*(103-113).

Springer DOI
**0706**

BibRef

*Fouquier, G.[Geoffroy]*,
*Atif, J.[Jamal]*,
*Bloch, I.[Isabelle]*,

**Local Reasoning in Fuzzy Attribute Graphs for Optimizing Sequential
Segmentation**,

*GbRPR07*(138-147).

Springer DOI
**0706**

BibRef

*Atif, J.[Jamal]*,
*Hudelot, C.*,
*Bloch, I.[Isabelle]*,

**Explanatory Reasoning for Image Understanding Using Formal Concept
Analysis and Description Logics**,

*SMCS(44)*, No. 5, May 2014, pp. 552-570.

IEEE DOI
**1405**

algebra
Algebraic erosion over the concept lattice of a background theory.

See also Mathematical morphology on hypergraphs, application to similarity and positive kernel.
BibRef

*Hudelot, C.[Céline]*,
*Atif, J.[Jamal]*,
*Bloch, I.[Isabelle]*,

**ALC(F): A New Description Logic for Spatial Reasoning in Images**,

*CVONT14*(370-384).

Springer DOI
**1504**

BibRef

*Cesar, Jr., R.M.[Roberto M.]*,
*Bengoetxea, E.[Endika]*,
*Bloch, I.[Isabelle]*,
*Larrañaga, P.[Pedro]*,

**Inexact graph matching for model-based recognition:
Evaluation and comparison of optimization algorithms**,

*PR(38)*, No. 11, November 2005, pp. 2099-2113.

Elsevier DOI
**0509**

BibRef

Earlier: A1, A2, A3, Only:

**Inexact graph matching using stochastic optimization techniques for
facial feature recognition**,

*ICPR02*(II: 465-468).

IEEE DOI
**0211**

BibRef

*Sminchisescu, C.[Cristian]*,
*Triggs, B.[Bill]*,

**Building Roadmaps of Minima and Transitions in Visual Models**,

*IJCV(61)*, No. 1, January 2005, pp. 81-101.

DOI Link
**0410**

BibRef

Earlier:

**Building Roadmaps of Local Minima of Visual Models**,

*ECCV02*(I: 566 ff.).

Springer DOI
**0205**

Avoiding local minima in searching techniques.
BibRef

*Richards, J.A.[John A.]*,
*Jia, X.P.[Xiu-Ping]*,

**A Dempster-Shafer Relaxation Approach to Context Classification**,

*GeoRS(45)*, No. 5, May 2007, pp. 1422-1431.

IEEE DOI
**0704**

BibRef

*Schellewald, C.[Christian]*,
*Roth, S.[Stefan]*,
*Schnorr, C.[Christoph]*,

**Evaluation of a convex relaxation to a quadratic assignment matching
approach for relational object views**,

*IVC(25)*, No. 8, 1 August 2007, pp. 1301-1314.

Elsevier DOI
**0706**

Quadratic assignment; Weighted graph matching; Combinatorial optimization;
Convex programming; Object recognition
BibRef

*Schellewald, C.[Christian]*,

**Conves Mathematical Programs for Relational Matching of Object Views**,

*Ph.D.*Thesis, Univ. of Mannhein, 2004.
**0905**

BibRef

*Werner, T.[Tomas]*,

**A Linear Programming Approach to Max-Sum Problem: A Review**,

*PAMI(29)*, No. 7, July 2007, pp. 1165-1179.

IEEE DOI
**0706**

*Constraint Satisfaction*. Maximization of a sum of binary functions.
Explore a formulation from early Russian paper.
BibRef

*Werner, T.[Tomas]*,

**Revisiting the Linear Programming Relaxation Approach to Gibbs Energy
Minimization and Weighted Constraint Satisfaction**,

*PAMI(32)*, No. 8, August 2010, pp. 1474-1488.

IEEE DOI
**1007**

E.g. Gibbs energy minimization, link to constraint programming.
BibRef

*Werner, T.[Tomas]*,

**High-arity interactions, polyhedral relaxations, and cutting plane
algorithm for soft constraint optimisation (MAP-MRF)**,

*CVPR08*(1-8).

IEEE DOI
**0806**

BibRef

*Werner, T.[Tomas]*,

**Combinatorial constraints on multiple projections of a set of points**,

*ICCV03*(1011-1016).

IEEE DOI
**0311**

BibRef

*Potetz, B.[Brian]*,
*Lee, T.S.[Tai Sing]*,

**Efficient belief propagation for higher-order cliques using linear
constraint nodes**,

*CVIU(112)*, No. 1, October 2008, pp. 39-54.

Elsevier DOI
**0810**

BibRef

Earlier: A1, Only:

**Efficient Belief Propagation for Vision Using Linear Constraint Nodes**,

*CVPR07*(1-8).

IEEE DOI
**0706**

Belief propagation; Higher-order cliques; Non-pairwise cliques; Factor
graphs; Continuous Markov random fields
BibRef

*Choi, Y.H.[Young-Hun]*,
*Jun, C.H.[Chi-Hyuck]*,

**A causal discovery algorithm using multiple regressions**,

*PRL(31)*, No. 13, 1 October 2010, pp. 1924-1934.

Elsevier DOI
**1003**

Causal discovery; Conditional independence test; Markov blanket;
Multiple regression
BibRef

*Bui, A.T.[Anh Tuan]*,
*Jun, C.H.[Chi-Hyuck]*,

**Learning Bayesian network structure using Markov blanket decomposition**,

*PRL(33)*, No. 16, 1 December 2012, pp. 2134-2140.

Elsevier DOI
**1210**

Causal structure learning; Conditional independence test; Directed
acyclic graph; Directed global Markov property; Moral graph; V
structure
BibRef

*Pock, T.[Thomas]*,
*Cremers, D.[Daniel]*,
*Bischof, H.[Horst]*,
*Chambolle, A.[Antonin]*,

**Global Solutions Of Variational Models With Convex Regularization**,

*SIIMS(3)*, No. 4, 2010, pp. 1122-1145.

WWW Link.

DOI Link
BibRef
**1000**

Earlier: A1, A4, A2, A3:

**A convex relaxation approach for computing minimal partitions**,

*CVPR09*(810-817).

IEEE DOI
**0906**

variational methods; calibrations; total variation; convex optimization
BibRef

*Chambolle, A.[Antonin]*,
*Cremers, D.[Daniel]*,
*Pock, T.[Thomas]*,

**A Convex Approach to Minimal Partitions**,

*SIIMS(5)*, No. 4, 2012, pp. 1113-1158.

DOI Link
**1211**

BibRef

*Pock, T.[Thomas]*,
*Chambolle, A.[Antonin]*,

**Diagonal preconditioning for first order primal-dual algorithms in
convex optimization**,

*ICCV11*(1762-1769).

IEEE DOI
**1201**

BibRef

*Goldluecke, B.[Bastian]*,
*Cremers, D.[Daniel]*,

**Introducing total curvature for image processing**,

*ICCV11*(1267-1274).

IEEE DOI
**1201**

Menger-Melnikov curvature of the Radon measure. For regularizer.
BibRef

*Goldluecke, B.[Bastian]*,
*Cremers, D.[Daniel]*,

**Convex Relaxation for Multilabel Problems with Product Label Spaces**,

*ECCV10*(V: 225-238).

Springer DOI
**1009**

BibRef

*Yang, Y.[Yang]*,
*Huang, Z.[Zi]*,
*Yang, Y.[Yi]*,
*Liu, J.J.[Jia-Jun]*,
*Shen, H.T.[Heng Tao]*,
*Luo, J.B.[Jie-Bo]*,

**Local image tagging via graph regularized joint group sparsity**,

*PR(46)*, No. 5, May 2013, pp. 1358-1368.

Elsevier DOI
**1302**

Local image tagging; Group sparse coding; Graph regularization; Tag
propagation
BibRef

*Ortiz-Bayliss, J.C.[José Carlos]*,
*Terashima-Marín, H.[Hugo]*,
*Conant-Pablos, S.E.[Santiago Enrique]*,

**Learning vector quantization for variable ordering in constraint
satisfaction problems**,

*PRL(34)*, No. 4, 1 March 2013, pp. 423-432.

Elsevier DOI
**1302**

Constraint satisfaction; Hyper-heuristics; Learning vector
quantization; Variable and value ordering
BibRef

*Zach, C.[Christopher]*,
*Hane, C.[Christian]*,
*Pollefeys, M.[Marc]*,

**What Is Optimized in Convex Relaxations for Multilabel Problems:
Connecting Discrete and Continuously Inspired MAP Inference**,

*PAMI(36)*, No. 1, 2014, pp. 157-170.

IEEE DOI
**1312**

BibRef

Earlier:

**What is optimized in tight convex relaxations for multi-label problems?**,

*CVPR12*(1664-1671).

IEEE DOI
**1208**

Markov random fields
BibRef

*Liu, Z.Y.[Zhi-Yong]*,
*Qiao, H.[Hong]*,
*Yang, X.[Xu]*,
*Hoi, S.C.H.[Steven C. H.]*,

**Graph Matching by Simplified Convex-Concave Relaxation Procedure**,

*IJCV(109)*, No. 3, September 2014, pp. 169-186.

Springer DOI
**1408**

BibRef

*Yang, X.[Xu]*,
*Qiao, H.[Hong]*,
*Liu, Z.Y.[Zhi-Yong]*,

**Feature correspondence based on directed structural model matching**,

*IVC(33)*, No. 1, 2015, pp. 57-67.

Elsevier DOI
**1412**

Feature correspondence
BibRef

*Yang, X.[Xu]*,
*Qiao, H.[Hong]*,
*Liu, Z.Y.[Zhi-Yong]*,

**Outlier robust point correspondence based on GNCCP**,

*PRL(55)*, No. 1, 2015, pp. 8-14.

Elsevier DOI
**1503**

Feature correspondence
BibRef

*Yang, X.[Xu]*,
*Liu, Z.Y.[Zhi-Yong]*,
*Qiao, H.[Hong]*,

**A Continuation Method for Graph Matching Based Feature Correspondence**,

*PAMI(42)*, No. 8, August 2020, pp. 1809-1822.

IEEE DOI
**2007**

Optimization, Task analysis, Linear programming,
Image processing, Pattern matching, Smoothing methods,
combinatorial optimization
BibRef

*Yang, X.[Xu]*,
*Liu, Z.Y.[Zhi-Yong]*,

**Adaptive Graph Matching**,

*Cyber(48)*, No. 5, May 2018, pp. 1432-1445.

IEEE DOI
**1804**

Adaptation models, Control systems, Cybernetics,
Linear programming, Manganese, Optimization, Pattern recognition,
regularization method
BibRef

*Yan, J.*,
*Wang, J.*,
*Zha, H.*,
*Yang, X.*,
*Chu, S.*,

**Consistency-Driven Alternating Optimization for Multigraph Matching:
A Unified Approach**,

*IP(24)*, No. 3, March 2015, pp. 994-1009.

IEEE DOI
**1502**

BibRef

*Åström, F.[Freddie]*,
*Petra, S.[Stefania]*,
*Schmitzer, B.[Bernhard]*,
*Schnörr, C.[Christoph]*,

**Image Labeling by Assignment**,

*JMIV(58)*, No. 2, June 2017, pp. 211-238.

Springer DOI
**1704**

BibRef

Earlier:

**A Geometric Approach to Image Labeling**,

*ECCV16*(V: 139-154).

Springer DOI
**1611**

BibRef

And:

**The Assignment Manifold: A Smooth Model for Image Labeling**,

*DIFF-CV16*(963-971)

IEEE DOI
**1612**

BibRef

*Zern, A.[Artjom]*,
*Zisler, M.[Matthias]*,
*Petra, S.[Stefania]*,
*Schnörr, C.[Christoph]*,

**Unsupervised Assignment Flow: Label Learning on Feature Manifolds by
Spatially Regularized Geometric Assignment**,

*JMIV(62)*, No. 6-7, July 2020, pp. 982-1006.

Springer DOI
**2007**

BibRef

Earlier: A2, A1, A3, A4:

**Unsupervised Labeling by Geometric and Spatially Regularized
Self-assignment**,

*SSVM19*(432-444).

Springer DOI
**1909**

BibRef

*Zisler, M.[Matthias]*,
*Zern, A.[Artjom]*,
*Petra, S.[Stefania]*,
*Schnörr, C.[Christoph]*,

**Self-Assignment Flows for Unsupervised Data Labeling on Graphs**,

*SIIMS(13)*, No. 3, 2020, pp. 1113-1156.

DOI Link
**2010**

BibRef

*Zern, A.[Artjom]*,
*Zisler, M.[Matthias]*,
*Åström, F.[Freddie]*,
*Petra, S.[Stefania]*,
*Schnörr, C.[Christoph]*,

**Unsupervised Label Learning on Manifolds by Spatially Regularized
Geometric Assignment**,

*GCPR18*(698-713).

Springer DOI
**1905**

BibRef

*Hühnerbein, R.[Ruben]*,
*Savarino, F.[Fabrizio]*,
*Åström, F.[Freddie]*,
*Schnörr, C.[Christoph]*,

**Image Labeling Based on Graphical Models Using Wasserstein Messages
and Geometric Assignment**,

*SIIMS(11)*, No. 2, 2018, pp. 1317-1362.

DOI Link
**1807**

BibRef

*Hühnerbein, R.[Ruben]*,
*Savarino, F.[Fabrizio]*,
*Petra, S.[Stefania]*,
*Schnörr, C.[Christoph]*,

**Learning Adaptive Regularization for Image Labeling Using Geometric
Assignment**,

*SSVM19*(393-405).

Springer DOI
**1909**

BibRef

*Åström, F.[Freddie]*,
*Hühnerbein, R.[Ruben]*,
*Savarino, F.[Fabrizio]*,
*Recknagel, J.[Judit]*,
*Schnörr, C.[Christoph]*,

**MAP Image Labeling Using Wasserstein Messages and Geometric Assignment**,

*SSVM17*(373-385).

Springer DOI
**1706**

BibRef

*Savarino, F.[Fabrizio]*,
*Schnörr, C.[Christoph]*,

**A Variational Perspective on the Assignment Flow**,

*SSVM19*(547-558).

Springer DOI
**1909**

BibRef

*Savarino, F.[Fabrizio]*,
*Hühnerbein, R.[Ruben]*,
*Åström, F.[Freddie]*,
*Recknagel, J.[Judit]*,
*Schnörr, C.[Christoph]*,

**Numerical Integration of Riemannian Gradient Flows for Image Labeling**,

*SSVM17*(361-372).

Springer DOI
**1706**

BibRef

*Sitenko, D.[Dmitrij]*,
*Boll, B.[Bastian]*,
*Schnorr, C.[Christoph]*,

**A Nonlocal Graph-PDE and Higher-Order Geometric Integration for Image
Labeling**,

*SIIMS(16)*, No. 1, 2023, pp. 501-567.

DOI Link
**2305**

See also Image Labeling by Assignment.
BibRef

*Boll, B.[Bastian]*,
*Schwarz, J.[Jonathan]*,
*Gonzalez-Alvarado, D.[Daniel]*,
*Sitenko, D.[Dmitrij]*,
*Petra, S.[Stefania]*,
*Schnörr, C.[Christoph]*,

**Modeling Large-scale Joint Distributions and Inference by Randomized
Assignment**,

*SSVM23*(730-742).

Springer DOI
**2307**

BibRef

*Schwarz, J.[Jonathan]*,
*Boll, B.[Bastian]*,
*Gonzalez-Alvarado, D.[Daniel]*,
*Sitenko, D.[Dmitrij]*,
*Gärttner, M.[Martin]*,
*Albers, P.[Peter]*,
*Schnörr, C.[Christoph]*,

**Quantum State Assignment Flows**,

*SSVM23*(743-756).

Springer DOI
**2307**

BibRef

*Lin, G.F.[Guang-Feng]*,
*Liao, K.Y.[Kai-Yang]*,
*Sun, B.Y.[Bang-Yong]*,
*Chen, Y.J.[Ya-Jun]*,
*Zhao, F.[Fan]*,

**Dynamic graph fusion label propagation for semi-supervised
multi-modality classification**,

*PR(68)*, No. 1, 2017, pp. 14-23.

Elsevier DOI
**1704**

Dynamic graph fusion
BibRef

*Pruša, D.[Daniel]*,
*Werner, T.[Tomáš]*,

**LP Relaxation of the Potts Labeling Problem Is as Hard as Any Linear
Program**,

*PAMI(39)*, No. 7, July 2017, pp. 1469-1475.

IEEE DOI
**1706**

BibRef

Earlier:

**How Hard Is the LP Relaxation of the Potts Min-Sum Labeling Problem?**,

*EMMCVPR15*(57-70).

Springer DOI
**1504**

Approximation algorithms, Computational modeling, Cost function,
Graphical models, Labeling, Measurement, Minimization, MAP inference,
Markov random field, Potts model, discrete energy minimization,
graphical model, linear programming relaxation,
uniform metric labeling problem, valued constraint satisfaction.
BibRef

*Bergmann, R.[Ronny]*,
*Fitschen, J.H.[Jan Henrik]*,
*Persch, J.[Johannes]*,
*Steidl, G.[Gabriele]*,

**Iterative Multiplicative Filters for Data Labeling**,

*IJCV(123)*, No. 3, July 2017, pp. 435-453.

Springer DOI
**1706**

for the supervised partitioning of data
Derived from:

See also Image Labeling by Assignment.
BibRef

*Magri, L.[Luca]*,
*Fusiello, A.[Andrea]*,

**Multiple structure recovery via robust preference analysis**,

*IVC(67)*, No. 1, 2017, pp. 1-15.

Elsevier DOI
**1710**

BibRef

Earlier:

**Multiple Models Fitting as a Set Coverage Problem**,

*CVPR16*(3318-3326)

IEEE DOI
**1612**

BibRef

Earlier:

**Robust Multiple Model Fitting with Preference Analysis and Low-rank
Approximation**,

*BMVC15*(xx-yy).

DOI Link
**1601**

BibRef

And:

**Fitting Multiple Models via Density Analysis in Tanimoto Space**,

*CIAP15*(I:73-84).

Springer DOI
**1511**

BibRef

And:

**Scale Estimation in Multiple Models Fitting via Consensus Clustering**,

*CAIP15*(II:13-25).

Springer DOI
**1511**

BibRef

And:

**T-Linkage:
A Continuous Relaxation of J-Linkage for Multi-model Fitting**,

*CVPR14*(3954-3961)

IEEE DOI
**1409**

Multi-model fitting
BibRef

*Magri, L.[Luca]*,
*Fusiello, A.[Andrea]*,

**Multiple structure recovery with maximum coverage**,

*MVA(29)*, No. 1, January 2018, pp. 159-173.

WWW Link.
**1801**

BibRef

*Zoidi, O.[Olga]*,
*Tefas, A.*,
*Nikolaidis, N.[Nikos]*,
*Pitas, I.[Ioannis]*,

**Positive and Negative Label Propagations**,

*CirSysVideo(28)*, No. 2, February 2018, pp. 342-355.

IEEE DOI
**1802**

BibRef

Earlier: A1, A3, A4, Only:

**Label propagation on data with multiple representations through
multi-graph locality preserving projections**,

*ICIP14*(1505-1509)

IEEE DOI
**1502**

Cost function, Face recognition, Laplace equations, Manifolds,
Semisupervised learning, Training, Action recognition,
label propagation (LP).
Accuracy
BibRef

*Uzun, A.O.[Arif Orhun]*,
*Usta, T.[Tugba]*,
*Dündar, E.B.[Enes Burak]*,
*Korkmaz, E.E.[Emin Erkan]*,

**A solution to the classification problem with cellular automata**,

*PRL(116)*, 2018, pp. 114-120.

Elsevier DOI
**1812**

Classification, Cellular automata, Heat Transfer, Big Data
BibRef

*Nassif, R.*,
*Vlaski, S.*,
*Richard, C.*,
*Sayed, A.H.*,

**A Regularization Framework for Learning Over Multitask Graphs**,

*SPLetters(26)*, No. 2, February 2019, pp. 297-301.

IEEE DOI
**1902**

approximation theory, gradient methods, graph theory,
inference mechanisms, learning (artificial intelligence),
distributed implementation
BibRef

*Ji, W.[Wei]*,
*Li, X.[Xi]*,
*Wei, L.[Lina]*,
*Wu, F.[Fei]*,
*Zhuang, Y.T.[Yue-Ting]*,

**Context-Aware Graph Label Propagation Network for Saliency Detection**,

*IP(29)*, 2020, pp. 8177-8186.

IEEE DOI
**2008**

saliency detection, superpixel pooling, graph neural network
BibRef

*Hoang, T.*,
*Do, T.*,
*Nguyen, T.V.*,
*Cheung, N.*,

**Unsupervised Deep Cross-modality Spectral Hashing**,

*IP(29)*, 2020, pp. 8391-8406.

IEEE DOI
**2008**

Binary codes, Semantics, Optimization, Correlation, Sparse matrices,
Task analysis, Training data, Cross-modal retrieval,
constraint optimization
BibRef

*Lim, K.L.[Kart-Leong]*,
*Jiang, X.D.[Xu-Dong]*,

**Variational posterior approximation using stochastic gradient ascent
with adaptive stepsize**,

*PR(112)*, 2021, pp. 107783.

Elsevier DOI
**2102**

Dirichlet process mixture, Stochastic gradient ascent,
Fisher information, Scalable algorithm
BibRef

IEEE DOI

BibRef

*Strecke, M.[Michael]*,
*Goldluecke, B.[Bastian]*,

**Sublabel-Accurate Convex Relaxation with Total Generalized Variation
Regularization**,

*GCPR18*(263-277).

Springer DOI
**1905**

BibRef

*Lê-Huu, D.K.*,
*Paragios, N.*,

**Continuous Relaxation of MAP Inference: A Nonconvex Perspective**,

*CVPR18*(5533-5541)

IEEE DOI
**1812**

Convex functions, Markov processes, Optimization, Indexes.
BibRef

*Dong, J.X.[Jiang-Xin]*,
*Liu, R.S.[Ri-Sheng]*,
*Tang, K.W.[Ke-Wei]*,
*Wang, Y.Y.[Yi-Yang]*,
*Zhang, X.D.[Xin-Dong]*,
*Su, Z.X.[Zhi-Xun]*,

**Sparse Gradient Pursuit for Robust Visual Analysis**,

*ACCV16*(I: 369-384).

Springer DOI
**1704**

BibRef

*Li, D.[Dong]*,
*Hung, W.C.[Wei-Chih]*,
*Huang, J.B.[Jia-Bin]*,
*Wang, S.J.[Sheng-Jin]*,
*Ahuja, N.[Narendra]*,
*Yang, M.H.[Ming-Hsuan]*,

**Unsupervised Visual Representation Learning by Graph-Based Consistent
Constraints**,

*ECCV16*(IV: 678-694).

Springer DOI
**1611**

BibRef

*Kim, K.I.[Kwang In]*,
*Tompkin, J.[James]*,
*Pfister, H.[Hanspeter]*,
*Theobalt, C.[Christian]*,

**Context-Guided Diffusion for Label Propagation on Graphs**,

*ICCV15*(2776-2784)

IEEE DOI
**1602**

Anisotropic magnetoresistance
BibRef

*Souiai, M.[Mohamed]*,
*Oswald, M.R.[Martin R.]*,
*Keef, Y.[Youngwook]*,
*Kim, J.[Junmo]*,
*Pollefeys, M.[Marc]*,
*Cremers, D.[Daniel]*,

**Entropy Minimization for Convex Relaxation Approaches**,

*ICCV15*(1778-1786)

IEEE DOI
**1602**

Computer vision
BibRef

*Zhang, Z.[Zhao]*,
*Li, F.Z.[Fan-Zhang]*,
*Zhao, M.B.[Ming-Bo]*,

**Transformed Neighborhood Propagation**,

*ICPR14*(3792-3797)

IEEE DOI
**1412**

Control charts
BibRef

*Oswald, M.R.[Martin R.]*,
*Cremers, D.[Daniel]*,

**Surface Normal Integration for Convex Space-time Multi-view
Reconstruction**,

*BMVC14*(xx-yy).

HTML Version.
**1410**

BibRef

Earlier:

**A Convex Relaxation Approach to Space Time Multi-view 3D
Reconstruction**,

*4DMOD13*(291-298)

IEEE DOI
**1403**

image reconstruction
BibRef

*Stuhmer, J.[Jan]*,
*Schroder, P.[Peter]*,
*Cremers, D.[Daniel]*,

**Tree Shape Priors with Connectivity Constraints Using Convex
Relaxation on General Graphs**,

*ICCV13*(2336-2343)

IEEE DOI
**1403**

Medical Imaging; Optimization; Segmentation
BibRef

*Wang, B.[Bo]*,
*Tsotsos, J.K.[John K.]*,

**Dynamic Label Propagation for Semi-supervised Multi-class Multi-label
Classification**,

*PR(52)*, No. 1, 2016, pp. 75-84.

Elsevier DOI
**1601**

Dynamic label propagation
BibRef

Earlier:
Add A2:
*Tu, Z.W.[Zhuo-Wen]*,
*ICCV13*(425-432)

IEEE DOI
**1403**

Dynamic Label Propagation; Multi-class; Multi-label
BibRef

*Ebert, S.[Sandra]*,
*Fritz, M.[Mario]*,
*Schiele, B.[Bernt]*,

**Pick Your Neighborhood:
Improving Labels and Neighborhood Structure for Label Propagation**,

*DAGM11*(152-162).

Springer DOI
**1109**

propogate labels on graph in learning.
BibRef

*Kasprzak, W.[Wlodzimierz]*,
*Czajka, L.[Lukasz]*,
*Wilkowski, A.[Artur]*,

**A Constraint Satisfaction Framework with Bayesian Inference for
Model-Based Object Recognition**,

*ICCVG10*(II: 1-8).

Springer DOI
**1009**

BibRef

*Pawan Kumar, M.*,
*Torr, P.H.S.*,

**Fast Memory-Efficient Generalized Belief Propagation**,

*ECCV06*(IV: 451-463).

Springer DOI
**0608**

BibRef

*Coito, F.J.[Fernando J.]*,
*Lemos, J.M.[João M.]*,

**Adaptive Optimization with Constraints:
Convergence and Oscillatory Behaviour**,

*IbPRIA05*(II:19).

Springer DOI
**0509**

BibRef

*Yuille, A.L.[Alan L.]*,

**A Double-Loop Algorithm to Minimize the Bethe Free Energy**,

*EMMCVPR01*(3-18).

Springer DOI
**0205**

BibRef

Earlier:

**A Double-Loop Algorithm to Minimize the Bethe and Kikuchi Free Energies**,

*SCTV01*(xx-yy).
**0106**

BibRef

*Yedidia, J.*,
*Freeman, W.T.*,
*Weiss, Y.*,

**Bethe free energy, Kikuchi approximations, and belief propagation
algorithms**,

*SCTV01*(xx-yy).
**0106**

Stable points of belief propagation algorithms for graphs
with loops correspond to extrema of the Bethe free energy.
BibRef

*Haddon, J.*,
*Boyce, J.*,

**Spatio-Temporal Relaxation Labelling Applied to Segmented
Infrared Image Sequences**,

*ICPR96*(II: 171-175).

IEEE DOI
**9608**

(Defence Res. Agency, UK)
BibRef

*Horiuchi, T.*,
*Yamamoto, K.*,
*Yamada, H.*,

**Robust Relaxation Method for Structural Matching Under Uncertainty**,

*ICPR96*(II: 176-180).

IEEE DOI
**9608**

(Univ. of Tsukuba, J)
BibRef

*Shao, Z.*,
*Kittler, J.V.*,

**Fuzzy Non-Iterative ARG Labeling with Multiple Interpretations**,

*ICPR96*(II: 181-185).

IEEE DOI
**9608**

(Univ. of Surrey, UK)
BibRef

*Hatef, M.*,
*Kittler, J.V.*,

**Combining symbolic with numeric attributes in multi-class object
recognition problems**,

*ICIP95*(III: 364-367).

IEEE DOI
**9510**

BibRef

*Choate, J.A.*,
*Gennert, M.A.*,

**Multiscale relaxation labeling of fractal images**,

*CVPR93*(674-675).

IEEE DOI
**0403**

BibRef

*McLean, C.R.*,
*Dyer, C.R.*,

**An Analog Relaxation Processor**,

*ICPR80*(58-60).
BibRef
**8000**

Chapter on Matching and Recognition Using Volumes, High Level Vision Techniques, Invariants continues in

Continuous Relaxation Theory, Constraint Satisfaction .

Last update:Feb 29, 2024 at 09:13:14