BACKGROUND AND OBJECTIVE: We focus on three-dimensional higher-order tensorial (HOT) images using Finsler geometry. In biomedical image analysis, these images are widely used, and they are based on the diffusion profiles inside the voxels. The diffusion information is stored in the so-called diffusion tensor D. Our objective is to present new methods revealing the architecture of neural fibers in presence of crossings and high curvatures. After tracking the fibers, we achieve direct 3D image segmentation to analyse the brain's white matter structures. METHODS: To deal with the construction of the underlying fibers, the inverse of the second-order diffusion tensor D, understood as the metric tensor D-1, is commonly used in DTI modality. For crossing and highly curved fibers, higher order tensors are more relevant, but it is challenging to find an analogue of such an inverse in the HOT case. We employ an innovative approach to metrics based on higher order tensors to track the fibers properly. We propose to feed the tracked fibers as the internal initial contours in an efficient version of 3D segmentation. RESULTS: We propose a brand-new approach to the inversion of a diffusion HOT, and an effective way of fiber tracking in the Finsler setting, based on innovative classification of the individual voxels. Thus, we can handle complex structures with high curvatures and crossings, even in the presence of noise. Based on our novel tractography approach, we also introduce a new segmentation method. We feed the detected fibers as the initial position of the contour surfaces to segment the image using a relevant active contour method (i.e., initiating the segmentation from inside the structures). CONCLUSIONS: This is a pilot work, enhancing methods for fiber tracking and segmentation. The implemented algorithms were successfully tested on both synthetic and real data. The new features make our algorithms robust and fast, and they allow distinguishing individual objects in complex structures, even under noise.

Department of Mathematics and Statistics Masaryk University Faculty of Science Kotlářská 2 Brno 611 37 Czech Republic

Department of Radiology and Nuclear Medicine St Olav's University Hospital Trondheim Norway; Department of Circulation and Medical Imaging NTNU Norwegian University of Science and Technology Trondheim Norway

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