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In computer vision and pattern recognition, point set registration, also known as point matching, is the process of finding a spatial transformation that aligns two point sets. The purpose of finding such a transformation includes merging multiple data sets into a globally consistent model, and mapping a new measurement to a known data set to identify features or to estimate its pose. A point set may be raw data from 3D scanning or an array of rangefinders. For use in image processing and feature-based image registration, a point set may be a set of features obtained by feature extraction from an image, for example corner detection. Point set registration is used in optical character recognition〔 and aligning data from magnetic resonance imaging with computer aided tomography scans. == Overview of problem == The problem may be summarized as follows: Let be two finite size point sets in a finite-dimensional real vector space , which contain and points respectively. The problem is to find a transformation to be applied to the moving "model" point set such that the difference between and the static "scene" set is minimized. In other words, a mapping from to is desired which yields the best alignment between the transformed "model" set and the "scene" set. The mapping may consist of a rigid or non-rigid transformation. The transformation model may be written as where the transformed, registered model point set is: It is useful to define an optimization parameter : such that it is clear that the optimizing algorithm adjusts . Depending on the problem and number of dimensions, there may be more such parameters. The output of a point set registration algorithm is therefore the transformation parameter of model so that is optimally aligned to . In convergence, it is desired for the distance between the two point sets to reach a global minimum. This is difficult without exhausting all possible transformations, so a local minimum suffices. The distance function between a transformed model point set and the scene point set is given by some function . A simple approach is to take the square of the Euclidean distance for every pair of points: (m - s)^2|}} Minimizing such a function in rigid registration is equivalent to solving a least squares problem. However, this function is sensitive to outlier data and consequently algorithms based on this function tend to be less robust against noisy data. A more robust formulation of the cost function uses some ''robust function'' : (T(\mathcal), \mathcal) = \sum_ \sum_} Such a formulation is known as an ''M-estimator''. The robust function is chosen such that the local configuration of the point set is insensitive to distant points, hence making it robust against outliers and noise.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「point set registration」の詳細全文を読む スポンサード リンク
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