NDLI: A Vectorized Principal Component Approach for Solving the Data Registration Problem

Content Provider	IEEE Xplore Digital Library
Author	Ramos, J.A. dos Santos, P.L. Verriest, E.I.
Copyright Year	2006
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Indiana Univ., Indianapolis (Ramos, J.A.)
Abstract	The problem of estimating the motion and orientation parameters of a rigid object from two m - D point set patterns is of significant importance in medical imaging, electrocardiogram (ECG) alignment, and fingerprint matching. The rigid parameters can be defined by an m times m rotation matrix, a diagonal m times m scale matrix, and an m times 1 translation vector. All together, the total number of parameters to be found is m(m + 2). Several least squares based algorithms have recently appeared in the literature. These algorithms are all based on a singular value decomposition (SVD) of the m times m cross-covariance matrix between the two data sets. However, there are cases where the SVD based algorithms return a reflection matrix rather than a rotation matrix. Some authors have introduced a simple correction for guarding against such cases. Other types of algorithm are based on unit quaternions which guarantee obtaining a true rotation matrix. In this paper we introduce a principal component based registration algorithm which is solved in closed-form. By using matrix vectorization properties the problem can be cast as one of finding a rank-1 symmetric projection matrix. This is equivalent to solving a Sylvester equation with equality constraints. Once the solution is obtained, we apply the inverse vectorization operation to estimate the rotation and scale matrices, along with the translation vector. We apply the proposed algorithm to the alignment of ECG signals and compare the results to those obtained by the SVD and quaternion based algorithms
Starting Page	1297
Ending Page	1302
File Size	238202
Page Count	6
File Format	PDF
ISBN	1424401712
DOI	10.1109/CDC.2006.377400
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-12-13
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Matrix decomposition Symmetric matrices Electrocardiography Quaternions Motion estimation Biomedical imaging Fingerprint recognition Least squares methods Singular value decomposition Reflection
Content Type	Text
Resource Type	Article

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