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Condensation algorithm : ウィキペディア英語版
Condensation algorithm
The condensation algorithm (Conditional Density Propagation) is a computer vision algorithm. The principal application is to detect and track the contour of objects moving in a cluttered environment. Object tracking is one of the more basic and difficult aspects of computer vision and is generally a prerequisite to object recognition. Being able to identify which pixels in an image make up the contour of an object is a non-trivial problem. Condensation is a probabilistic algorithm that attempts to solve this problem.
The algorithm itself is described in detail by Isard and Blake in a publication in the International Journal of Computer Vision in 1998. One of the most interesting facets of the algorithm is that it does not compute on every pixel of the image. Rather, pixels to process are chosen at random, and only a subset of the pixels end up being processed. Multiple hypotheses about what is moving are supported naturally by the probabilistic nature of the approach. The evaluation functions come largely from previous work in the area and include many standard statistical approaches. The original part of this work is the application of particle filter estimation techniques.
The algorithm’s creation was inspired by the inability of Kalman filtering to perform object tracking well in the presence of significant background clutter. The presence of clutter tends to produce probability distributions for the object state which are multi-modal and therefore poorly modeled by the Kalman filter. The Condensation Algorithm in its most general form requires no assumptions about the probability distributions of the object or measurements.
==Algorithm Overview==

The Condensation algorithm seeks to solve the problem of estimating the conformation of an object described by a
vector
\mathbf at time t, given observations \mathbf of the detected features in the images up to and including the current time. The Condensation Algorithm outputs an estimate to the state
conditional probability density
p(\mathbf|\mathbf) by applying a nonlinear filter based on factored sampling and can be thought of as a development of a Monte-Carlo method.〔 p(\mathbf|\mathbf) is a representation of the probability of possible conformations for the objects based on previous conformations and measurements. The condensation algorithm is a generative model since it models the joint distribution of the object and the observer.
The conditional density of the object at the current time p(\mathbf|\mathbf) is estimated as a weighted, time-indexed sample set \ with weights \pi_t^. N is a parameter determining the number of sample sets chosen. A realization of p(\mathbf|\mathbf) is obtained by sampling with replacement from the set s_t with probability equal to the corresponding element of \pi_t.〔
The assumptions that object dynamics form a temporal Markov chain and that observations are
independent
of each other and the dynamics facilitate the implementation of the Condensation Algorithm. The first assumption allows the dynamics of the object to be entirely determined by the conditional density p(\mathbf|\mathbf|\mathbf{x_{t-1}}) must also be selected for the algorithm, and generally includes both deterministic and stochastic dynamics.
The algorithm can be summarized by initialization at time t = 0 and three steps at each time t:

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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