A Variational Approach for Multi-Valued Velocity Field Estimation in Transparent Sequences

Abstract. We propose a variational approach for multi-valued velocity field estimation in transparent sequences. Starting from existing local motion estimators, we show a variational model for integrating in space and time these local estimations to obtain a robust estimation of the multi-valued velocity field. With this approach, we can indeed estimate some multi-valued velocity fields which are not necessarily piecewise constant on a layer: Each layer can evolve according to non-parametric optical flow. We show how our approach outperforms some existing approaches, and we illustrate its capabilities on several challenging synthetic/real sequences

Denoising of brain DW-MR data by single and multiple diffusion kernels Denoising of brain DW-MR data by single and multiple diffusion kernels

Las imágenes por resonancia magnética pesadas en difusión son ampliamente utilizadaspara el estudio de las estructuras cerebrales dentro de la materia blanca del cerebro. Sinembargo, recuperar las orientaciones de los axones puede ser susceptible a errores por elruido dentro de la señal. Una regularización espacial puede mejorar la estimación, perodebe ser realizada cuidadosamente dado que puede remover información espacial ó introducirfalsas orientaciones. En este trabajo se investigaron las ventajas de aplicar un filtroanisotrópico basado en simples y múltiples kerneles de orientación de manojos de axones.Para esto, hemos calculado kerneles locales de difusión basados en modelos de tensoresde difusión y multi tensores de difusión. Mostraremos los beneficios de nuestra propuestaen 3 tipos diferentes de imágenes obtenidas por resonancia magnética pesada en difusión:Datos sintéticos, imágenes humanas tomadas en vivo, y datos obtenidos de un fantasmasimulador de difusión.Diffusion Weighted Magnetic Resonance Imaging is widely used to study the structure ofthe fiber pathways of white matter in the brain. However, the recovered axon orientationscan be prone to error because of the low signal to noise ratio. Spatial regularization canreduce the error, but it must be done carefully so that real spatial information is not removedand false orientations are not introduced. In this paper we investigate the advantagesof applying an anisotropic filter based on single and multiple axon bundle orientation kernels.To this end, we compute local diffusion kernels based on Diffusion Tensor and multiDiffusion Tensor models. We show the benefits of our approach to three different types ofDW-MRI data: synthetic, in vivo human, and acquired from a diffusion phantom

Index Terms

Most optical flow algorithms provide flow fields as single valued functions of the image sequence domains. Only a very few of them attempt to recover multiple motion vectors at given location, which is necessary when some transparent layers are moving independently. In this report we introduce a novel framework for modeling multivalued motion fields, and propose an energy minimization formulation with smoothing terms and terms implementing velocity model competition. We illustrate the capabilities of this approach on synthetic and real sequences

Basis Functions for Estimating Intra–voxel Structure

Abstract — We present a new method for estimating and recovering the intra–voxel fiber paths, using Diffusion Weighted Magnetic Resonance Images (DW-MRI). The method recovers the intra–voxel information at voxels that contain fiber crossings or bifurcations by means of a combination of a known tensor basis functions (a “multi-tensor ” field). In contrast with the stateof-the art methods, our formulation requires a small number of DWMR images and the solution schema is simple. Another advantage is that the solution to our formulation is numerically stable when more than two fiber orientations are present within a voxel. Additionally, we apply a spatial regularization to the multi-tensor field being estimated in order to denoise the data. The regularization uses a generic piece-wise smooth prior on the fiber orientation. Several examples are presented to demonstrate the performance of the proposed algorithm on synthetic and real DW-MRI data. Index Terms — Multi-tensor MRI, Brain fiber tractography, Intra-voxel structure, DW–MRI, HARD DWI, DT–MRI