Other Theories, Discussion

In this chapter, we review and discuss precursory and alternative theories. We start in the first section with Lindenbaum et al. Their papers contain a theory of shape detection whose setting is essentially the same as the one developed in this book. The Bienenstock et al. compositional model discussed in Sections 15.2 and 15.5 is an ambitious theory attempting to build directly a grammar of visual primitives. A nice illustration of these compositional approaches is the work of Zhu et al. described in Section 15.2. Section 15.3 discusses the link among meaningful events, hypothesis testing, and Signal Detection Theory. It also shows that the Number of False Alarms (NFA) can be put in a classical statistical framework where multiple testing is involved. In Section 15.4 the Arias-Castro et al. geometric detection theory is addressed. This theory is very close in spirit to the tools in this book and are actually partly inspired from it. It gives complementary information on asymptotic geometric detection thresholds and hints on how to speed up detection algorithm. Section 15.5 discusses the Bayesian theory according to which the probability of the image interpretation given the observation must be maximized. An extension of this theory, the Minimum Description Length, is also invoked in the compositional model. In both cases, a probability is maximized. In contrast, meaningful events were obtained by minimizing an a-contrario probability. This point is discussed and the complementarity of both approaches are indicated.