ORIGINAL ARTICLE Y.-Z. Chang (*) Department of Mechanical Engineering, Chang Gung University, Tao-Yuan 33302, Taiwan e-mail: zen@mail.cgu.edu.tw Z.-R. Tsai Department of Computer Science and Information Engineering Asia University, Taichung, Taiwan S.-T. Lee Medical Augmented Reality Research and Development Center Chang Gung Memorial Hospital, Linkou Branch, Tao-Yuan., Taiwan This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008 Artif Life Robotics (2008) 13:242–245 © ISAROB 2008 DOI 10.1007/s10015-008-0532-6 Yau-Zen Chang · Zhi-Ren Tsai · Shih-Tseng Lee 3D registration of human face using evolutionary computation and Kriging interpolation 1 Introduction Registration of 3D geometric data coming from multimodal images is essential for exploiting the complementary infor- mation between them. In medical imaging, the data can be obtained from computer tomography (CT), laser range finder, or magnetic resonance imaging (MRI), and the information can be used in image-guided procedures, such as positioning for frameless neurosurgery. The Iterative Closest Point algorithm (ICP), together with the K-D search method (K-D tree), has become a popular registration scheme. Approximate K-D tree search algorithm (AK-D tree) was proposed by excluding the backtracking in K-D tree, which improves runtime effi- ciency with the sacrifice of reducing the correspondence accuracy. However, these conventional schemes are extremely sensitive to initial trial pose and requires multi- ple trials to find a reliable solution. Besides, the scheme demands huge computing power when large data set is involved in either reference image or template image, which is not uncommon in medical applications. We thus pro- pose a scheme that is both consistent in each run and fast enough to extend the applicability of 3D registration in intra-operative applications. To illustrate the validity and applicability of the pro- posed approach, a problem composed of 174 635 points computer tomography (CT) reference image and a 11 280 points template image, derived from a laser range finder, is provided. 2 The proposed method The proposed registration scheme is composed of a coarse transformation stage and a fine-tuning stage. 2.1 The coarse transformation stage In the first stage, fuzzy c-mean (FCM) is used to reduce the data amount of template 3D image, and evolutionary Abstract This paper proposes a fast and robust 3D human face geometric data registration strategy dedicated for image-guided medical applications. The registration scheme is composed of a coarse transformation stage and a fine- tuning stage. In the first stage, fuzzy c-mean is used to reduce the data amount of template 3D image, and evolu- tionary computation is implemented to find optimal initial pose for the Iterative Closest Point plus k-dimensional (K- D) tree scheme. In the second stage, the huge reference image data are replaced by a Kriging model. The time-con- suming search for corresponding points in evaluating the degree of misalignment is substituted by projecting the points in the template image onto the model. To illustrate the validity and applicability of the proposed approach, a problem composed of 174 635 points reference image and an 11 280 points template image is demonstrated. Compu- tational results show that our approach accelerates the reg- istration process from 1361.28 seconds to 432.85 seconds when compared with the conventional ICP plus K-D tree scheme, while the average misalignment reduces from 11.35 mm to 2.33 mm. Key words Human face registration · Evolutionary com- putation · Kriging model · Iterative closest point · Image- guided therapy Received and accepted: July 18, 2008