Section: New Results
Keywords : Shape recognition, cluster analysis, a contrario models.
Shape recognition in digital images
Participant : Frédéric Sur.
Shape recognition is the field of computer vision which addresses the problem of finding out whether a query shape lies or not in a shape database, up to a certain invariance. Most shape recognition methods simply sort shapes from the database along some (dis-)similarity measure to the query shape. Their Achilles' heel is the decision stage, which should aim at giving a clear-cut answer to the question: ``do these two shapes look alike?'' In  ,  , the proposed solution consists in bounding the number of false correspondences of the query shape among the database shapes, ensuring that the obtained matches are not likely to occur ``by chance''. As an application, one can decide with a parameterless method whether any two digital images share some shapes or not. In a paper submitted to VISAPP'06, we propose to apply the above a contrario methodology to shapes which are described by size functions, in order to design a perceptual matching algorithm.
A further step consists in grouping matching shapes that share the same respective positions in two corresponding images. In  , we intend to form spatially coherent groups of shapes. Each pair of matching shape elements indeed leads to a unique transformation (similarity or affine map.) 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 unit. As an application, the present theory on the choice of the right clusters is used to group shapes by detecting clusters in the transformation space.