Motion consistency without Correspondence
Measure motion consistency of two video segment is the core part in many computer vision applications. One example is view invariant human action recognition. The basic idea for view-invariant action recognition is to utilize the relationship between the optical flows (space-time gradient) in two views. There is a linear relationship between the pair of optical flows of two views. The interesting thing is that the fundamental matrix doesnot need to be explicitly calculated. The motion consistency measure can be estimated by the rank constraint of the observed matrix from corresponding optical flows. However, from our best knowledge, the state-of-the-art researchs inevitablely assume the correspondence be achieved. This is not true because the visual data is dynamic and the correspondence is difficult to estimate. Even worse, in the situation of multiple view environment, the oclussion often make the correspondence complex:
- Only part of data can find its correspondence in another. The selection of data whose correspondence is not trival;
- Because of the template scale variance, each data may not exact correspond to one data in another, but several data points approximately match one point in another;
The problem can be define mathmetically as follows
Given two data set. Ideally, if each data in one set corresponds to exact one data in another set, there is a linear relationship between them. However, now only part of two data set have correspondence as well as the associated linear relationship. But for the data in the collection that exists correspondence in another, the matching is approximately and several data points in one set can correspond to one data point in another set. It is related to the problem of matching of two point set with the difficulty of homology the 1-M (one-to-many) and M-1 (many-to-one) matching. Maximum Graph matching theory (bipartite graph) (related to spectral clustering) can be utilized for solving this problem.
Keyword: graph matching, spectral clustering, bipartite graph matching, pattern matching for point set
Given two data set. Ideally, if each data in one set corresponds to exact one data in another set, there is a linear relationship between them. However, now only part of two data set have correspondence as well as the associated linear relationship. But for the data in the collection that exists correspondence in another, the matching is approximately and several data points in one set can correspond to one data point in another set. It is related to the problem of matching of two point set with the difficulty of homology the 1-M (one-to-many) and M-1 (many-to-one) matching. Maximum Graph matching theory (bipartite graph) (related to spectral clustering) can be utilized for solving this problem.
Keyword: graph matching, spectral clustering, bipartite graph matching, pattern matching for point set
