4. Models of Shot Activity

4. Models of Shot Activity

Given a sequence of images, various features can be used to obtain an estimate of the amount of activity in the underlying scene. In our work we have considered two metrics that can be derived from low-level image measurements: the colour histogram distance and the tangent distance [12,13] between successive images in the sequence. Since space is limited and the histogram distances have been widely used as a similarity measure for object recognition [16], content-based retrieval [17], and temporal video segmentation [18], we restrict our attention to them in this chapter. In particular we will rely on the well established L₁ norm of the histogram difference,

where a and b are histograms of successive frames.

Statistical modelling of the histogram distance features requires the identification of the various states through which the video may progress. For simplicity, we restrict ourselves to a video model composed of two states: "regular frames" (S = 0) and "shot transitions" (S = 1). The fundamental principles are however applicable to more complex models. As illustrated by Figure 3.3, for regular frames the distribution is asymmetric about the mean, always positive and concentrated near zero. This suggests that a mixture of Erlang distributions is an appropriate model for this state, a suggestion that is confirmed by the fit to the empirical density obtained with the expectation-maximization (EM) algorithm, also depicted in the figure. On the other hand, for shot transitions the fit obtained with a simple Gaussian model is sufficient to achieve a reasonable approximation to the empirical density. In both cases, a uniform mixture component is introduced to account for the tails of the distributions [13].

Figure 3.3: Left— Conditional activity histogram for regular frames, and best fit by a mixture with three Erlang and a uniform component. Right— Conditional activity histogram for shot transitions, and best fit by a mixture with a Gaussian and a uniform component ( 2000 IEEE).