D. Tschumperle and R. Deriche, "Regularization of Orthonormal Vector Sets Using Coupled PDES," Proc. IEEE Workshop Variational and Level Set Methods in Computer Vision, pp. 3-10, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the image domain. Recently, the TV restoration model (5) has been extended to data that live on general graphs (the so called digital TV ) COS01] and to non at data or image features (such as chromaticity, orientations of optical ows, and orthogonal frames) that live on Riemannian manifolds [CS01d, TSC, TD01]. Strong and Chan also have studied the scale dependency and edge preserving properties of the TV model in much more details [SC] 3.3. TV restoration: Computation and approximation. To computationally realize the TV restoration model (5) as rst proposed by Rudin, Osher, and Fatemi [RO94] one ....

D. Tschumperle and R. Deriche. Regularization of orthonormal vector sets using coupled PDE's. Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision, pages 3-10, 2001.

....issue of regularizing the data while preserving its structure has received some attention in the literature. Proposed methods include ones which smooth the original tensor field [16] or the principal eigenvector field[17, 18] Recent methods developed in the computer vision literature include [19, 20]. In this paper we introduce a geometric flow to reconstruct fibre tracts in diffusion tensor images. We assume that the images have first been suitably regularized. The key construction is to extend the vectors (locally) in the planes orthogonal to them and to then apply a flux maximizing flow ....

D. Tschumperle and R. Deriche, "Regularization of orthonormal vector sets using coupled pdes," in Proceedings of the IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2001, pp. 3--10.

....issue of regularizing the data while preserving its structure has received some attention in the literature. Proposed methods include ones which smooth the original tensor field [16] or the principal eigenvector field[17, 18] Recent methods developed in the computer vision literature include [19, 20]. In this paper we introduce a geometric flow to reconstruct fibre tracts in diffusion tensor images. We assume that the images have first been suitably regularized. The key construction is to extend the vectors (locally) in the planes orthogonal to them and to then apply a flux maximizing flow ....

D. Tschumperle and R. Deriche, "Regularization of orthonormal vector sets using coupled pdes," in Proceedings of the IEEE Workshop on Variational and Level Set Methods in Computer Vision, 2001, pp. 3--10.

....to detect discontinuities that are saddle points of the vector valued surface (Figure 2.11c) This may perturb regularization processes since certain sharp corners will be considered as quite homogeneous regions and will be probably smoothed. 3. # # , also denoted by is often chosen [25, 31, 140, 167, 175, 176] since it detects edges and corners in a good way, and is easy to compute (doesn t require an eigenvalue decomposition of G) trace(G) # # (2.21) Moreover, the norm has the property of giving preferences to certain corners (Figure 2.11d) This is very interesting for image ....

D. Tschumperle and R. Deriche. Regularization of orthonormal vector sets using coupled PDE's. In IEEE Workshop on Variational and Level Set Methods VLSM'01 pages 3--10, Vancouver/Canada.

.... directions and color images in the chromaticity brightness or HSV spaces (using the harmonic maps theory [27] the unitary norm total variation [6] or the geometric Beltrami framework [13] Other related works deal with images of probability vectors [19] orthonormal vector sets and rotations [30], or data on arbitrary manifolds [2] Such constrained minimization problems usually lead to sets of coupled vector PDE s where the constraints between data are expressed in the Euler Lagrange equations. In this article, we go one step further and study the constrained regularization of noisy ....

....on Fig.4c, but not the orthogonal angles. a) Synthetic orientation b) Regularization with an unconstrained PDE c) Regularization with a norm constrained PDE Figure 4. Classic PDE s fail to regularize U Following the idea of our previous regularization work acting on orthonormal vector sets [30], we propose to minimize this general functional with respect to u E(U) u ; u ; kru k; kru while preserving the spectral orthonormal constraints (4) is a free regularization functional (depending on the diffusion behaviour we desire) as for instance the one based ....

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D. Tschumperle and R. Deriche. Regularization of orthonormal vector sets using coupled PDE's. Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision, pages 3--10, July 2001.

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D. Tschumperle and R. Deriche, "Regularization of Orthonormal Vector Sets Using Coupled PDES," Proc. IEEE Workshop Variational and Level Set Methods in Computer Vision, pp. 3-10, 2001.

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D. Tschumperle and R. Deriche. Regularization of orthonormal vector sets using coupled pde's. Proceedings 1st IEEE Workshop on Variational and Level Set Methods in Computer Vision, 3-10, 2001.

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D. Tschumperle and R. Deriche, Regularization of Orthonormal Vector Sets Using Coupled PDE's, Proceedings 1st IEEE Workshop on Variational and Level Set Methods in Computer Vision, 3-10, 2001. 22

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D. Tschumperle and R. Deriche, "Regularization of orthonormal vector sets using coupled PDEs," IEEE Workshop on Variational and Level-Set Methods, Vancouver, Canada, July 2001.

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