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In this paper, we focus on techniques for vector-valued image regularization, based on variational methods and PDEs. Starting from the study of PDE-based formalisms previously proposed in the literature for the regularization of scalar and vector-valued data, we propose a unifying expression that gathers the majority of these previous frameworks into a(More)
1 We address the problem of vector-valued image regu-larization with variational methods and PDE's. From the study of existing formalisms, we propose a unifying framework based on a very local interpretation of the regulariza-tion processes. The resulting equations are then specialized into new regularization PDE's and corresponding numerical schemes that(More)
We are interested in PDE's (Partial Differential Equations) in order to smooth multi-valued images in an anisotropic manner. Starting from a review of existing anisotropic regularization schemes based on diffusion PDE's, we point out the pros and cons of the different equations proposed in the literature. Then, we introduce a new tensor-driven PDE,(More)
This paper deals with the problem of regularizing noisy fields of diffusion tensors, considered as symmetric and semi-positive definite Ò ¢ Ò matrices (as for instance 2D structure tensors or DT-MRI medical images). We first propose a simple anisotropic PDE-based scheme that acts directly on the matrix coefficients and preserve the semi-positive constraint(More)
Nonlinear partial differential equations (PDE) are now widely used to regularize images. They allow to eliminate noise and ar-tifacts while preserving large global features, such as object contours. In this context, we propose a geometric framework to design PDE flows acting on constrained datasets. We focus our interest on flows of matrix-valued functions(More)
We are interested in regularizing fields of orthonormal vector sets, using constraint-preserving anisotropic diffusion PDE's. Each point of such a field is defined by multiple orthogonal and unitary vectors and can indeed represent a lot of interesting orientation features such as direction vectors or orthogonal matrices (among other examples). We first(More)
We address three crucial issues encountered in DT-MRI (Diffusion Tensor Magnetic Resonance Imaging) : diffusion tensor Estimation, Regularization and fiber bundle Vi-sualization. We first review related algorithms existing in the literature and propose then alternative variational formalisms that lead to new and improved schemes, thanks to the preservation(More)
Recent advances in diffusion magnetic resonance image (dMRI) modeling have led to the development of several state of the art methods for reconstructing the diffusion signal. These methods allow for distinct features to be computed, which in turn reflect properties of fibrous tissue in the brain and in other organs. A practical consideration is that to(More)
We present a robust method to retrieve neuronal fibers in human brain white matter from High-Angular Resolution MRI (HARDI datasets). Contrary to classical fiber-tracking techniques done on the traditional 2nd-order tensor model (DTI) which may lead to truncated or biased estimated diffusion directions in case of fiber crossing configurations, we propose(More)
We design a family of non-local image smoothing algorithms which approximate the application of diffusion PDE's on a specific Eu-clidean space of image patches. We first map a noisy image onto this high-dimensional space and estimate its geometric structure thanks to a straightforward extension of the structure tensor field. The tensors spectral elements(More)