A unified framework for detecting groups and application to shape recognition

A unified a contrario detection method is proposed to solve three classical problems in clustering analysis. The first one is to evaluate the validity of a cluster candidate. The second problem is that meaningful clusters can contain or be contained in other meaningful clusters. A rule is needed to define locally optimal clusters by inclusion. The third problem is the definition of a correct merging rule between meaningful clusters, permitting to decide whether they should stay separate or unite. The motivation of this theory is shape recognition. Matching algorithms usually compute correspondences between more or less local features (called shape elements) between images to be compared. Each pair of matching shape elements leads to a unique transformation (similarity or affine map.) The present theory is used to group these shape elements into shapes by detecting clusters in the transformation space.