J Math Imaging Vis DOI 10.1007/s10851-008-0071-8 High Angular Resolution Diffusion MRI Segmentation Using Region-Based Statistical Surface Evolution Maxime Descoteaux · Rachid Deriche © Springer Science+Business Media, LLC 2008 Abstract In this article we develop a new method to seg- ment high angular resolution diffusion imaging (HARDI) data. We first estimate the orientation distribution function (ODF) using a fast and robust spherical harmonic (SH) method. Then, we use a region-based statistical surface evo- lution on this image of ODFs to efficiently find coherent white matter fiber bundles. We show that our method is ap- propriate to propagate through regions of fiber crossings and we show that our results outperform state-of-the-art diffu- sion tensor (DT) imaging segmentation methods, inherently limited by the DT model. Results obtained on synthetic data, on a biological phantom, on real datasets and on all 13 sub- jects of a public NMR database show that our method is reproducible, automatic and brings a strong added value to diffusion MRI segmentation. Keywords Diffusion tensor imaging (DTI) · High angular resolution diffusion imaging (HARDI) · Q-ball imaging (QBI) · Orientation distribution function (ODF) · Region-based segmentation · Level set framework 1 Introduction We would like to segment white matter fiber bundles in which diffusion properties are similar and ultimately com- pare their features to those in other ROI in the same subject M. Descoteaux ( ) · R. Deriche Project Team Odyssée, INRIA/ENPC/ENS, INRIA Sophia Antipolis—Méditerranée, 2004 route des Lucioles, 06902 Sophia Antipolis, France e-mail: Maxime.Descoteaux@sophia.inria.fr R. Deriche e-mail: Rachid.Deriche@sophia.inria.fr or on multiple subjects. The goal is thus to find global co- herence that exists among white matter fiber tracts belong- ing to the same fiber bundle. Existing DTI-based segmen- tation techniques [17, 23, 25, 32, 37, 38, 40, 43] are inher- ently limited by the DT model and most often blocked in re- gions of fiber crossings where DTs are oblate and isotropic. This is why recent high angular resolution diffusion imaging (HARDI) techniques such as QBI [34] have been proposed to aid the inference of crossing, branching and kissing fiber configurations. New methods have thus started to appear to segment bundles from fields of ODFs [19, 24, 26]. In this paper, we answer the following three questions: (1) How can the segmentation problem be formulated and solved efficiently on a field of ODFs? (2) What is gained by the ODF with respect to the DT? (3) Is it possible to val- idate the segmentation results and make the segmentation automatic? To do so, we propose an efficient region-based level set approach using a regularized and robust spherical harmonics (SH) representation of the ODF [15]. We first show that a better local modeling of fiber crossings improves segmentation results globally. Then, we show that our ODF segmentation is more accurate than the state-of-the-art DTI segmentation based on the Euclidean and Riemannian dis- tances [25] in regions of complex fiber configurations from synthetic data, from a biological phantom and from real data. The ODF better captures statistics in crossing areas and is thus able to flow through complex fiber regions without leaking in the whole white matter. Finally, we show that our q-ball segmentation is reproducible by segmenting automat- ically the corpus callosum (CC) and the cortico spinal tract (CST) of the 13 subjects of a public NMR database [30]. The paper is organized as follows. Section 2 reviews the existing algorithms for segmentation of white matter fiber bundles from diffusion MRI data. Section 3.1 describes