Grouping Spatially Coherent Meaningful Matches

This chapter is about forming coherent groups of matching shape elements. This grouping, sometimes called generalized Hough transform, is crucial for virtually all shape recognition algorithms. It will be used for the main shape identification method treated in this book, namely the LLD, the MSER method in Chap. 9 and the SIFT method in Chap. 11. Each pair of matching shape elements leads to a unique transformation (similarity or affine map). A natural way to group these shape elements into larger shapes is to find clusters in the transformation space. The theory in the previous chapter is immediately applicable. The main problem addressed here is the correct definition and computation of the background model π. This background model is a probability distribution on the set of similarities, or on the set of affine transformations. In order to have accurate shape clusters, π must be built from empirical measurements on observable shape matching transformations. As in Chap. 5, the main issue is to compute accurately a density function in high dimension (4 or 6) with relatively few samples. The found solution is analogous: determine the marginal variables for which an independence assumption is sound. Then the density functions of these marginal laws can be accurately estimated on the data and yield an accurate background model.