SU‐F‐BRF‐08: Conformal Mapping‐Based 3D Surface Matching and Registration

Abstract

Purpose:Recently, non‐rigid 3D surface matching and registration has been used extensively in engineering and medicine. However, matching 3D surfaces undergoing non‐rigid deformation accurately is still a challenging mathematical problem. In this study, we present a novel algorithm to address this issue by introducing intrinsic symmetry to the registrationMethods:Our computational algorithm for symmetric conformal mapping is divided into three major steps: 1) Finding the symmetric plane; 2) Finding feature points; and 3) Performing cross registration. The key strategy is to preserve the symmetry during the conformal mapping, such that the image on the parameter domain is symmetric and the area distortion factor on the parameter image is also symmetric. Several novel algorithms were developed using different conformal geometric tools. One was based on solving Riemann‐Cauchy equation and the other one employed curvature flowResults:Our algorithm was implemented using generic C++ on Windows XP and used conjugate gradient search optimization for acceleration. The human face 3D surface images were acquired using a high speed 3D scanner based on the phase‐shifting method. The scanning speed was 30 frames/sec. The image resolution for each frame was 640 × 480. For 3D human face surfaces with different expressions, postures, and boundaries, our algorithms were able to produce consistent result on the texture pattern on the overlapping regionConclusion:We proposed a novel algorithm to improve the robustness of conformal geometric methods by incorporating the symmetric information into the mapping process. To objectively evaluate its performance, we compared it with most existing techniques. Experimental results indicated that our method outperformed all the others in terms of robustness. The technique has a great potential in real‐time patient monitoring and tracking in image‐guided radiation therapy