Stochastic Geometry for Image Analysis

Chapter 7

Population Counting 1

In this chapter, we present a generic application that is about counting the number of individuals in a population. This population can consist of a set of cells, a plantation of trees, or even a colony of birds. The problem can be summarized as that of detecting a large number of objects in an image, presenting little variability in shape, other than possibly size. This kind of task, which recurs in many fields (e.g. medical, biology, and the study of biodiversity), can prove to be tedious and costly, in terms of the time it takes, when it is carried out manually by an expert. An automatic counting tool is therefore often highly appreciated by experts in different fields. Some techniques, other than marked point processes (MPPs), can be proposed to solve this problem. The Hough transform is a good candidate when the object is parameterized in a low-dimensional space. The tools resulting from mathematical morphology can also enable the problem to be solved, for example by defining openings with appropriate stuctural elements followed by a reconstruction procedure [SCH 93, SOI 03]. Nevertheless, these approaches prove limited when the populations are dense and contain adjacent objects. Indeed, the object being searched for in the Hough transform, or the structural element that defines the mathematical morphology, is no longer suited to the geometry of the connected set formed by adjacent objects. MPPs can make it possible, through the prior, to model ...