A point set registration problem is a task using two shapes, each consisting of a set of points, to estimate the relationship of individual points between the two shapes. Here, a “shape” is like a human body or face, which is similar to another body or face but exhibits morphological diversity. Taking the face as an example: the center position of the pupil of an eye varies depending on individuals but can be thought to have a correspondence with that of another person. Such a correspondence can be estimated by gradually deforming one shape to be superimposable on the other. Estimation of the correspondence of a point on one shape to a point on another is the point set registration problem. Since the number of points of one shape could be millions, estimation of correspondence is calculated by a computer. Nonetheless, up to now, even when the fastest conventional method was used, it took a lot of time for calculation for registration of ca. 100,000 points. Thus, algorithms that could find a solution far faster without affecting accuracy have been sought. Furthermore, preliminary registration before automated estimation was a prerequisite for the conventional calculation method, so algorithms that do not need preliminary registration are desirable.
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