Relaxation Labeling for Contour Point Matching under Affine Transformations

2013 ◽  
Vol 380-384 ◽  
pp. 3449-3452
Author(s):  
Wei Wang ◽  
Yong Mei Jiang ◽  
Bo Li Xiong ◽  
Gang Yao Kuang
Keyword(s):  
Affine Transformations ◽  
Point Matching ◽  
Matching Criterion ◽  
Relaxation Labeling ◽  
Contour Point ◽  
Soft Matching ◽  
Matching Probability

A matching between two sets of points under affine transformations has attracted more and more attention. Many algorithms devote to extracting the descriptor for the point from the configuration, and the descriptor based point matching is achieved ignoring the pairwise geometric relations. In this paper, taking advantage of the inlier correspondences in matched configurations, we formalize a soft matching criterion which emerges from a matching probability matrix, followed by a relaxation labeling process to refine the match. The proposed approach has been implemented and gives encouraging results under rotation, scaling, shearing and noise.

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

1996 ◽  
Vol 8 (4) ◽  
pp. 787-804 ◽  
Author(s):  
Steven Gold ◽  
Anand Rangarajan ◽  
Eric Mjolsness
Keyword(s):  
Optimization Problem ◽  
Distance Measure ◽  
Graph Matching ◽  
Optimization Techniques ◽  
Distance Measures ◽  
Deterministic Annealing ◽  
Weighted Graphs ◽  
Affine Transformations ◽  
Learning Problem ◽  
Point Matching

Prior knowledge constraints are imposed upon a learning problem in the form of distance measures. Prototypical 2D point sets and graphs are learned by clustering with point-matching and graph-matching distance measures. The point-matching distance measure is approximately invariant under affine transformations—translation, rotation, scale, and shear—and permutations. It operates between noisy images with missing and spurious points. The graph-matching distance measure operates on weighted graphs and is invariant under permutations. Learning is formulated as an optimization problem. Large objectives so formulated (∼ million variables) are efficiently minimized using a combination of optimization techniques—softassign, algebraic transformations, clocked objectives, and deterministic annealing.

Relaxation labeling for non-rigid point matching under neighbor preserving

2013 ◽  
Vol 20 (11) ◽  
pp. 3077-3084 ◽  
Author(s):  
Xing-wei Yan ◽  
Wei Wang ◽  
Jian Zhao ◽  
Jie-min Hu ◽  
Jun Zhang ◽  
...  
Keyword(s):  
Point Matching ◽  
Relaxation Labeling

The Standard Metric

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Affine Transformation ◽  
Convex Sets ◽  
Finite Dimension ◽  
Affine Subspace ◽  
Affine Transformations ◽  
Real Vector ◽  
Euclidean Metric ◽  
Affine Hyperplane ◽  
Tits Building ◽  
Convex Closure

This chapter presents some results about groups generated by reflections and the standard metric on a Bruhat-Tits building. It begins with definitions relating to an affine subspace, an affine hyperplane, an affine span, an affine map, and an affine transformation. It then considers a notation stating that the convex closure of a subset a of X is the intersection of all convex sets containing a and another notation that denotes by AGL(X) the group of all affine transformations of X and by Trans(X) the set of all translations of X. It also describes Euclidean spaces and assumes that the real vector space X is of finite dimension n and that d is a Euclidean metric on X. Finally, it discusses Euclidean representations and the standard metric.

Sign in / Sign up

Export Citation Format

Share Document