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The iterative closet point (ICP) method is a dominant method for data registration that has attracted extensive attention. In this paper, a unified mathematical model of ICP based on Lie group representation is established. Under the framework, the registration problem is formulated into an optimization problem over a certain Lie group. In order to simplify the model and to reduce the dimension of parameter space, the translation part of geometric transformation is eliminated by calibrating the centers of two data sets under registration. As a result, a fast algorithm by solving an iterative linear system is designed for the optimization problem on Lie groups. Moreover, PCA and ICA methods are jointly applied to estimate the initial registration to achieve the global minimum. Finally, several illustrations and comparison experiments are presented to test the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

By minimizing the mean square reconstruction error, multisets mixture learning (MML) provides a general approach for object detection in image. To calculate each sample reconstruction error, as the object template is represented by a set of contour points, the MML needs to inefficiently enumerate the distances between the sample and all the contour points. In this paper, we develop the line segment approximation (LSA) algorithm to calculate the reconstruction error, which is shown theoretically and experimentally to be more efficient than the enumeration method. It is also experimentally illustrated that the MML based algorithm has a better noise resistance ability than the generalized Hough transform (GHT) based counterpart. [ABSTRACT FROM AUTHOR]