ELSEVIER Pattern Recognition Letters 18 (1997) 49- 53 Pattern, R.ecognition Lerters Shape alignment - Optimal initial point and pose estimation Jorge S. Marques a,*, Arnaldo J. Abrantes b a INESC, Technical University of Lisbon, R. Alves Redol 9, P-IO00 Lisboa, Portugal b INESC, Polytechnic Institute of Lisbon, Lisboa, Portugal Received 30 November 1995; revised 20 October 1996 Abstract This paper describes an algorithm for the optimal alignment of a pair of 2D shapes defined by point sequences. The proposed algorithm provides closed-form expressions for the estimation of the initial point, scale and pose parameters. © 1997 Elsevier Science B.V. Keywords: Shape alignment; Object representation; Pose estimation; Image analysis 1. Introduction 2D shape analysis plays a key role in many computer vision systems. Several models were pro- posed in the literature to represent the object bound- ary, including parametric models, active contours, differential equations and Fourier descriptors (e.g., Otterloo, 1991; Kass et al., 1987). One of the sim- plest ways to represent an object shape consists of forming a sequence of N boundary points, detected in the image according to some criterion (e.g., He and Kundu, 1991). Let x denote the sequence of detected points and a reference sequence adopted as a model. Several difficulties arise if one tries to compare both se- quences due to changes of the object attitude, scale, shape and initial point. Some of these difficulties have been extensively studied. The estimation of the object pose and scale from two sets of matched points is a well known problem which has been addressed by many re- * Corresponding author. E-mail: jsm@inesc.pt. searchers and which can be efficiently solved, e.g., by robust least squares techniques (e.g., Haralick et al., 1989). Shape deformation has also been ad- dressed by several authors, especially in the context of active contours (e.g., Kass et al., 1987). The estimation of the initial point is however a less studied problem. This task is often performed by complex optimization procedures followed in some cases by a manual correction. This paper describes a new algorithm for the optimal estimation of pose, scale and initial point parameters. The proposed algorithm is computation- ally efficient and allows a simple implementation. Experimental tests show that the proposed technique is able to align complex shapes and it is robust against shape deformations and changes of the initial point. 2. Problem formulation Let x i ~ E2, i = 0 ..... N- 1, be a sequence of N contour points detected in the image and orga- 0167-8655/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S01 67-8655(96)00 120- I