Modelling occlusions using the Markov likelihood

Abstract

Previous chapters have explained how to perform statistical inferences about the presence or absence of target objects in a scene. The objective of this chapter is to perform the same inferences, even when parts of the targets may be occluded by unmodelled parts of the background. A typical example is shown in Figure 5.1, where the problem is to localise the coffee mugs in the two images. Is it possible to design a system which reports the presence of the unoccluded mugs, and in addition detects the occluded mug with an appropriate degree of confidence? Note that a heuristically based recognition system (relying, for example, on the number of a certain type of feature matches) might have difficulty even with the left-hand image, since the two targets might have very different scores. This problem is amplified in the right-hand image, where one mug is partially occluded: the heuristic scores of the two targets are very unlikely to reflect the actual relative probabilities that targets are present in those two configurations. In fact, the contour likelihood ratio of Chapter 3 deals satisfactorily with the left-hand image (as we shall see soon), but not with the right-hand one. The crucial problem is that all the generative models of Chapter 3 assume outputs on distinct measurement lines are independent. When many consecutive measurement lines are occluded by an unmodelled part of the “background”,¹ this independence assumption is violated badly, and unrealistic inferences are the result.