Foreground Estimation and Hidden Markov Models for Tracking
Håkan Ardö, Rikard Berthilsson, Kalle Åström · Lund University Publications (Lund University) · 2005
We will give a short introduction to foreground/background estimation and Hidden Markov for tracking. More information about the topics can be found in the papers listed at the end. 1 Foreground estimation The objective is to extract the foreground and consequently also the background from a sequence of images. Problems facing us includes for example • long execution time, • slowly varying lighting conditions, • rapidly varying lighting conditions, and • what should be considered background. The image sequence may come from a video camera with 352 × 288 resolution color images running 20 frames per second. Let It: R 2 → R 3, t = 0,... n−1 be a sequence of n color images. We use the notation It = (I 1 t, I 2 t, I 3 t) to denote the different color channels when needed. In order to compute a feature at each location we can use convolution f j t (x, y) = Ij t ∗ h(x, y) = I j t (x − a, y − b)h(a, b)dadb, where h: R 2 → R is the filter mask. This gives a filter response at every point (x, y) ∈ R 2 and the statistical properties of these can be used to classify background and foreground. 1.1 Pixel based foreground estimation The Stauffer–Grimson [15] estimator is obtained by letting h = δ0,0 be the Dirac measure at the origin in which case I j t ∗ δ0,0 = I j t, i.e. that is the estimator is based on the individual pixel data. A simple solution would be to define a probability function at each point (x, y) ∈ R. Note that for digital images there are only a finite set of points in the definition set giving a finite set of probability functions. Thus, for a gray level image we will need to define probability functions px,y(a) like for example px,y(a) = 1 √ e