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In this paper, we address the problem of segmenting data defined on a manifold into a set of regions with uniform properties. In particular, we propose a numerical method when the manifold is represented by a triangular mesh. Based on recent image segmentation models, our method minimizes a convex energy and then enjoys significant favorable properties: it is robust to initialization and avoid the problem of the existence of local minima present in many variational models. The contributions of this paper are threefold: firstly we adapt the convex image labeling model to manifolds; in particular the total variation formulation. Secondly we show how to implement the proposed method on triangular meshes, and finally we show how to use and combine the method in other computer vision problems, such as 3D reconstruction. We demonstrate the efficiency of our method by testing it on various data.

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Spinal cord (SC) atrophy is an important contributor to the development of disability in many neurological disorders including multiple sclerosis (MS). To assess the spinal cord atrophy in clinical trials and clinical practice, largely automated methods are needed due to the sheer amount of data. Moreover, using these methods in longitudinal trials requires them to deliver highly reliable measurements, enabling comparisons of multiple data sets of the same subject over time. We present a method for SC volumetry using 3D MRI data providing volume measurements for SC sections of fixed length and location. The segmentation combines a continuous max flow approach with SC surface reconstruction that locates the SC boundary based on image voxel intensities. Two cutting planes perpendicular to the SC centerline are determined based on predefined distances to an anatomical landmark, and the cervical SC volume (CSCV) is then calculated in-between these boundaries. The development of the method focused on its application in MRI follow-up studies; the method provides a high scan-rescan reliability, which was tested on healthy subject data. Scan-rescan reliability coefficients of variation (COV) were below 1 %, intra- and interrater COV were even lower (0.1-0.2 %). To show the applicability in longitudinal trials, 3-year follow-up data of 48 patients with a progressive course of MS were assessed. In this cohort, CSCV loss was the only significant predictor of disability progression (p = 0.02). We are, therefore, confident that our method provides a reliable tool for SC volumetry in longitudinal clinical trials.

In this paper we address the problem of segmentation in image sequences using region-based active contours and level set methods. We propose a novel method for variational segmentation of image sequences containing nonrigid, moving objects. The method is based on the classical Chan-Vese model augmented with a novel frame-to-frame interaction term, which allow us to update the segmentation result from one image frame to the next using the previous segmentation result as a shape prior. The interaction term is constructed to be pose-invariant and to allow moderate deformations in shape. It is expected to handle the appearance of occlusions which otherwise can make segmentation fail. The performance of the model is illustrated with experiments on synthetic and real image sequences.