A vectorized principal component approach for solving the data registration problem

• Type: Article in International Conference Proceedings Book
• Date: 2006

Authors

José A. Ramos (Author) Other; P. Lopes dos Santos (Author) FEUP; Erik I. Verriest (Author) Other

Conference proceedings International

Title: PROCEEDINGS OF THE 45TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-14

Pages: 1297-1302

45th IEEE Conference on Decision and Control

San Diego, CA, DEC 13-15, 2006

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 2 Citations

Scientific classification

FOS: Engineering and technology > Other engineering and technologies

Other information

Authenticus ID: P-007-KG0

DOI: 10.1109/cdc.2006.377400

Abstract (EN): 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 x m rotation matrix, a diagonal m x m scale matrix, and an m x 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 x 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 6