Stochastic Geometry for Image Analysis

Chapter 6

How to Set Up a Point Process? 1

In this chapter, we present a bibliographical synthesis of modeling using marked point processes in image analysis. We present the various problems that need to be resolved to develop a marked point process, using the framework of a concrete application, and also consider the solutions that have been proposed by various authors. The following sections will describe, in detail, several examples of large-scale applications in image analysis, as approached by using marked point process modeling.

Any simulation using a marked point process is characterized by various factors, described in this chapter, which are:

– choice of objects;

– choice of a priori constraints;

– choice of the data term;

– choice of an optimization algorithm (and the reference measure).

6.1. From disks to polygons, via a discussion of segments

Evidently, the choice of object is, first and foremost, influenced by the geometry of the objects being detected. Indeed, one of the major advantages of marked point processes, which can be considered to be a generalization of Markov random fields, is that they are able to apply strong geometric constraints on the solution. Nevertheless, the size of the configuration space is crucial for optimization, as we will see later. It is therefore desirable to restrict the dimension of the objects. In some cases, a model based on disks, leading to a faster optimization than a model based on ellipses, results in a minimal loss of geometric ...