By John MacCormick
A vital challenge in desktop imaginative and prescient is to trace items as they flow and distort in a video series. Stochastic algorithms -- specifically, particle filters and the Condensation set of rules -- have dramatically greater the state-of-the-art for such visible monitoring difficulties lately. This e-book provides a unified framework for visible monitoring utilizing particle filters, together with the hot means of partitioned sampling that could alleviate the "curse of dimensionality" suffered by means of average particle filters. The e-book additionally introduces the concept of contour chance: a suite of versions for assessing item form, color and movement, that are derived from the statistical houses of photo gains. as a result of their statistical nature, contour likelihoods are perfect for use in stochastic algorithms. A unifying subject matter of the publication is using facts and chance, which allow the ultimate output of the algorithms offered to be interpreted because the computer's "belief" in regards to the nation of the realm. The booklet should be of use and curiosity to scholars, researchers and practitioners in desktop imaginative and prescient, and assumes merely an trouble-free wisdom of likelihood theory.
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Extra info for Stochastic Algorithms for Visual Tracking: Probabilistic Modelling and Stochastic Algorithms for Visual Localisation and Tracking
Example text
1998). Finally, the field of computer vision - with its intractable likelihood functions and often complex configuration spaces - has seen an explosion of interest in particle filters since Isard and Blake first introduced the Condensation algorithm in 1996. nd Hogg (1998). This· book presents two more' advances: a probabilistic exclusion principle (Chapter 6) which builds on the discrete-continuous formulation of Condensation (Isard and Blake, 1998c) and partitioned sampling (Chapter 7) which makes Condensation feasible for multiple targets and extended configuration spaces.
In this case it is a rather routine calculation. Wh~n c = 0, all n features are. distributed uniformly on [O,L] so Prob(z' ~ y) = (1":' 2y/L)n. Thus the cdf C(y) = Prob(z'::; y) = 1-(1-2y/L)n, and differentiating gives the result. The case c = 1, n = 0 has zero probability since a target boundary is present and we have assumed a non-detection probability of zero. \Vhen c = 1 and n = 1, Zl is distributed as Q by assumption so we are done. That leaves the case c = 1,n ~ 2. In this case, Prob(z' ~ y) = (1- 2y/L)n-l (1- J~yQ(yl)dyl).
1997) and Doucet (1998); Geweke (1989) calls this quantity the relative numerical efficiency. The reason for this terminology will be clear after the following definition. d. random variables with distribution p(x). The nth MOilte Carlo estimator of ¢' is M~n) = .!. n t ¢'(i'i). i=i An equivalent definition would be to let S be the standard Monte Carlo set for p, define M = ¢' x S, and take M~n) to be the nth estimator of ¢' using Mas defined above. By elementary probability theory, EM~n) = E¢" and var(M~n) = var(¢')/n.