Atlas-Based Segmentation of Brain Tumor Images Using a Markov Random Field-Based Tumor Growth Model and Non-Rigid Registration Stefan Bauer, Christof Seiler, Thibaut Bardyn, Philippe Buechler and Mauricio Reyes Abstract— We propose a new and clinically oriented ap- proach to perform atlas-based segmentation of brain tumor images. A mesh-free method is used to model tumor-induced soft tissue deformations in a healthy brain atlas image with subsequent registration of the modified atlas to a pathologic patient image. The atlas is seeded with a tumor position prior and tumor growth simulating the tumor mass effect is performed with the aim of improving the registration accuracy in case of patients with space-occupying lesions. We perform tests on 2D axial slices of five different patient data sets and show that the approach gives good results for the segmentation of white matter, grey matter, cerebrospinal fluid and the tumor. I. INTRODUCTION Accurate automatic segmentation of important brain struc- tures from Magnetic Resonance Imaging (MRI) is of major interest for surgical planning procedures as well as for phys- iological and biomechanical modeling. Atlas-based segmen- tation of different tissue types like grey matter (GM), white matter (WM) and cerebrospinal fluid (CSF) is an established way to classify different tissues in MR images of healthy humans [1]. The different atlas tissue labels are propagated to the patient image through warping with a deformation field obtained by non-rigid registration techniques. However, this strategy fails in case of brain tumor images because of the missing tumor prior in the atlas. Several groups [2], [3], [4] suggest to circumvent this problem by introducing a tumor seed into the atlas and grow the tumor to its approximate shape using different methods. Cuadra et al. [2] use a model of lesion growth which does not consider any mechanical tissue properties, while Mohamed et al. [3] use a finite element method (FEM) model to calculate tissue displacements induced by the tumor mass effect according to the mechanical properties of the surrounding tissues. After introducing a tumor prior into the atlas, this modified atlas image is warped to the patient image using non-rigid registration algorithms, thus implicitly performing segmentation. A good overview of the state of the art was collected by Angelini et al. in [5]. It is clearly desirable to incorporate mechanical tissue properties into models of tumor-induced deformations. FEM- based methods offer this capability, however they suffer from the need of transforming the data into a mesh. Au- tomatic mesh generation is a challenging and error-prone task, while semi-automatic mesh generation is tedious and time-consuming. Additionally, large-scale deformations of the mesh are difficult to handle. Therefore, a completely S. Bauer, C. Seiler, T. Bardyn, P. Buechler and M. Reyes are with the Institute of Surgical Technology and Biomechanics, University of Bern, Switzerland; e-mail: stefan.bauer@istb.unibe.ch image-processing based method, which does not require any meshing would greatly simplify this task. Such an approach is suggested in [4], but it suffers from difficult parameterization and for reasons of computation speed it runs on a subsampled version of the input image only, which hinders its clinical usability. Our aim is to develop a simple tool to segment brain tissues based on previous segmentation of the tumor areas. While tumor segmentation can be done manually or using (semi)-automatic methods with reasonable effort, the seg- mentation of brain tissues is a time-consuming and tedious task. However, tissue segmentation is necessary in order to be able to apply more sophisticated models to simulate and predict patient-specific tumor progression. The tool should be sufficiently simple and generally applicable to be used by clinicians without expert knowledge in model parameteriza- tion on a daily basis. II. MATERIALS & METHODS We show the application of a clinically-oriented, mesh- free method for modeling soft-tissue deformations to tumor- induced deformation and segmentation of pathologic brain images. It is based on finite differences in a local neighbor- hood of each voxel using Markov Random Fields (MRF). The work was initially proposed in [6] and validated against an FEM-based deformation method with good results on a number of synthetic cases. In this work it was adopted to account for deformations in pathological brain images and is briefly described in the next section. A. Hierarchical Displacement Model The general idea outlined by Seiler et al. in [6] is to minimize an energy function U total = U prior + U observation (1) where U prior represents the biomechanical information of the brain tissues and U observation introduces boundary condi- tions. These energies are minimized in cliques of a neighbor- hood system surrounding a center voxel. Local tissue char- acteristics are based on Young’s modulus. Four exemplary cliques of one center voxel t are shown in Fig. 1. Fig. 1. Four different cliques belonging to the center voxel t in 2D.