Merge-and-simplify operation for compact combinatorial pyramid definition

International audienceImage pyramids are employed for years in digital image processing. They permit to store and use different scales/levels of details of an image. To represent all the topological information of the different levels, combinatorial pyramids have proved having many interests. But, when using an explicit representation, one drawback of this structure is the memory space required to store such a pyramid. In this paper, this drawback is solved by defining a compact version of combinatorial pyramids. This definition is based on the definition of a new operation, called "merge-and-simplify", which simultaneously merges regions and simplifies their boundaries. Our experiments show that the memory space of our solution is much smaller than the one of the original version. Moreover, the computation time of our solution is faster, because there are less levels in our pyramid than in the original one

Receptive fields within the Combinatorial Pyramid framework

A hierarchical structure is a stack of successively reduced image representations. Each basic element of a hierarchical structure is the father of a set of elements in the level below. The transitive closure of this father-child relationship associates to each element of the hierarchy a set of basic elements in the base level image representation. Such a set, called a receptive field, defines the embedding of one element of the hierarchy on the original image. Using the father-child relationship, global properties of a receptive field may be computed in O(log(m)) parallel processing steps where m is the diameter of the receptive field. Combinatorial pyramids are defined as a stack of successively reduced combinatorial maps, each combinatorial map being defined by two permutations acting on a set of half edges named darts. The basic element of a combinatorial pyramid is thus the dart. This paper defines the receptive field of each dart within a combinatorial pyramid and study the main properties of these sets