1026 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 20, NO. 10, OCTOBER 2001 A Joint Physics-Based Statistical Deformable Model for Multimodal Brain Image Analysis Christophoros Nikou, Associate Member, IEEE, Gloria Bueno, Fabrice Heitz*, and Jean-Paul Armspach Abstract—A probabilistic deformable model for the represen- tation of multiple brain structures is described. The statistically learned deformable model represents the relative location of different anatomical surfaces in brain magnetic resonance images (MRIs) and accommodates their significant variability across different individuals. The surfaces of each anatomical structure are parameterized by the amplitudes of the vibration modes of a deformable spherical mesh. For a given MRI in the training set, a vector containing the largest vibration modes describing the different deformable surfaces is created. This random vector is statistically constrained by retaining the most significant variation modes of its Karhunen–Loève expansion on the training population. By these means, the conjunction of surfaces are deformed according to the anatomical variability observed in the training set. Two applications of the joint probabilistic deformable model are presented: isolation of the brain from MRI using the probabilistic constraints embedded in the model and deformable model-based registration of three-dimensional multimodal (mag- netic resonance/single photon emission computed tomography) brain images without removing nonbrain structures. The multi- object deformable model may be considered as a first step toward the development of a general purpose probabilistic anatomical atlas of the brain. Index Terms—Brain isolation, image registration, magnetic res- onance imaging (MRI), physically based deformable model, single photon emission computed tomography (SPECT), statistical shape models. Manuscript received September 16, 1999; revised July 31, 2001. This work was supported by the “Groupement d’Intérêt Scientifique-Sciences de la Cog- nition” (CNRS, CEA, INRIA, MENESR). The work of C. Nikou was supported by the Commission of the European Communities, DG XII, in the framework of the Training and Mobility of Researchers (TMR) Program under Contract ERBFMIBCT960701. The Associate Editor responsible for coordinating the re- view of this paper and recommending its publication was J. Duncan. Asterisk indicates corresponding author. C. Nikou was with the Université Louis Pasteur (Strasbourg I), Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection, CNRS UPRES-A 7005 and the Institut de Physique Biologique, Faculté de Médecine, CNRS-UPRES-A 7004. He is now with the Aristotle University of Thessa- loniki, Department of Informatics, Artificial Intelligence and Information Analysis Laboratory, 54006 Thessaloniki, Greece. G. Bueno was with the Université Louis Pasteur (Strasbourg I), Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection, CNRS UPRES-A 7005 and the Institut de Physique Biologique, Faculté de Médecine, CNRS-UPRES-A 7004. She is now with the Centro de Estudios e Investiga- ciones Tecnicas (CEIT) de Gipuzkoa, Paseo de Manuel Lardizabal 15, 20018 San Sebastian, Spain. *F. Heitz is with the Université Louis Pasteur (Strasbourg I), Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection, CNRS UPRES-A 7005, 4. Bd. Sébastien Brant, 67400 Illkirch, France (e-mail: Fabrice.Heitz@ensps.u-strasbg.fr). J.-P. Armspach is with the Université Louis Pasteur (Strasbourg I) Institut de Physique Biologique, Faculté de Médecine, CNRS-UPRES-A 7004, 67085 Strasbourg, France. Publisher Item Identifier S 0278-0062(01)09308-9. I. INTRODUCTION I N MEDICAL image analysis, deformable models offer a powerful approach to accommodate the significant variability of biological structures over time and across dif- ferent individuals [1]. A survey on deformable models as a promising computer-assisted medical image analysis technique has recently been presented in [2]. Deformable models have principally been used to describe and characterize pathological shape deformations [3], [4], to register single modal images [5], [6], to label and segment different anatomical structures [7]–[9], or to track temporal structure deformations [10]. We present a three-dimensional (3-D) statistical deformable model (SDM) carrying information on multiple anatomical structures for multimodal brain image processing. The anatom- ical structures taken into consideration are head (skull and scalp), brain, ventricles, and cerebellum. Our goal is to describe the spatial relations between these anatomical structures as well as the biological shape variations observed over a representative population of individuals. In the proposed approach, the surfaces of the anatomical structures of interest are first extracted from a training set of 3-D magnetic resonance imaging (MRI). To this end, a 24-patient training set is aligned in the same reference coordinate system and segmented using semi-automatic segmentation algorithms. Each segmented surface is parameterized by the amplitudes of the vibration modes of a physically based deformable model [10], [11] and a joint model is constructed for the different anatomical structures. The joint model is statistically constrained by a Karhunen–Loève (KL) decomposition of the vibration mode parameters. By these means, the spatial relation between the different structures, as well as the anatomical variability observed in the training set are compactly described by a limited number of parameters. The resulting joint SDM may be considered as a first step toward the development of a general purpose probabilistic atlas of the brain, for various applications in medical image analysis (segmentation, labeling, registration, and pathology characterization). Two preliminary applications of the probabilistic deformable model are presented in this paper. • The isolation of the brain [intracranial cavity (ICC)] from MRI using the probabilistic constraints embedded in the joint deformable model. • The deformable model-based rigid registration of 3-D multimodal (MR/SPECT) brain images by optimizing an energy function relying on the chamfer distance between 0278–0062/01$10.00 © 2001 IEEE