F. Alouges, "An energy decreasing algorithm for harmonic maps," in J.M. Coron et al., Editors, Nematics, Nato ASI Series, Kluwer Academic Publishers, Netherlands, pp. 1-13, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....chroma, and diffuse this unit vector with the harmonic maps flow (4. 11) The corresponding magnitude, representing the We re normalize at every discrete step of the numerical evolution to address deviations from the unit norm due to numerical errors [23] We could also extend the framework in [1] and apply it to our equations. brightness, is smoothed separately via scalar diffusion flows as those presented before (e.g. the intrinsic heat flow or the intrinsic anisotropic heat flow) That is, we have to regularize a map onto (the chroma) and another one onto (the brightness) 4.3.3 ....

F. Alouges, "An energy decreasing algorithm for harmonic maps," in J.M. Coron et al., Editors, Nematics, Nato ASI Series, Kluwer Academic Publishers, Netherlands, pp. 1-13, 1991.

....for directional data the same qualitative behavior that is well known and studied for scalar images. One of the advantages of directional diffusion is that, although advanced specialized numerical techniques to solve (5) and its corresponding gradient descent flow, have been developed, e.g. Alouges (1991), as a first approximation we can basically use the algorithms developed for isotropic and anisotropic diffusion without the unit norm constraint to implement (11) and (12) Cohen et al. 1987) Although, as stated before, these PDE s preserve the unit norm (that is, the solutions are vectors in S ....

Alouges, F. 1991. An energy decreasing algorithm for harmonic maps. In Nematics, J.M. Coron et al. (Eds.), Nato ASI Series, Kluwer Academic Publishers: Netherlands, pp. 1--13.

....on this approach will be reported elsewhere. singularities of the orientation diffusion flow. 5 Examples One of the advantages of directional diffusion is that, although advanced specialized numerical techniques to solve (5) and its corresponding gradientdescent flow, have been developed, e.g. [1], as a first approximation we can basically use the algorithms developed for isotropic and anisotropic diffusion without the unit norm constraint to implement (11) and (12) 10] Although these equations preserve the unit norm, numerical errors might violate the constraint. Therefore, between ....

F. Alouges, "An energy decreasing algorithm for harmonic maps," in J.M. Coron et al., Editors, Nematics, Nato ASI Series, Kluwer Academic Publishers, Netherlands, pp. 1-13, 1991.

....a number of examples for the chromaticity flows for (isotropic) and (anisotropic) We also combine this with median filtering and anisotropic diffusion for the brightness. Although specialized numerical techniques to solve (4) and its corresponding gradient descent flow, have been developed, e.g. [1], we can basically use the algorithms developed for isotropic and anisotropic diffusion without the unit norm constraint to implement (8) and (9) 12] Although these equations preserve the unit norm, numerical errors might violate the constraint. Therefore, between every two steps of the ....

F. Alouges, "An energy decreasing algorithm for harmonic maps," in Nematics, J. M. Coron et al., Eds. Norwell, MA: Kluwer, 1991, pp. 1--13.

.... and Kass [104] These works follow original ideas by Turing [96] who showed how reaction diffusion equations can be 2 We re normalize at every discrete step of the numerical evolution to address deviations from the unit norm due to numerical errors [23] We could also extend the framework in [1] and apply it to our equations. Solving PDE s on Implicit Surfaces 65 used to generate patterns. The basic idea in these models is to have a number of chemicals that diffuse at different rates and that react with each other. The pattern is then synthesized by assigning a brightness value to ....

F. Alouges, "An energy decreasing algorithm for harmonic maps," in J.M. Coron et al., Editors, Nematics, Nato ASI Series, Kluwer Academic Publishers, Netherlands, pp. 1-13, 1991.

.... steady state is achieved) To simulate anisotropic textures, instead of using additional chemicals as in [37] we use 2 We re normalize at every discrete step of the numerical evolution to address deviations from the unit norm due to numerical errors [8] We could also extend the framework in [1] and apply it to our equations. 3 Note that this is not the scheme proposed in [25] where the texture is created in the full 3D space. Here, the texture is created via reactiondiffusion flows intrinsic to the surface, just the implementation is on the embedding 3D space. 5 anisotropic ....

F. Alouges, "An energy decreasing algorithm for harmonic maps," in J.M. Coron et al., Editors, Nematics, Nato ASI Series, Kluwer Academic Publishers, Netherlands, pp. 1-13, 1991.

....D 1 and D 2 are two constants representing the diffusion rates and F and G are the functions that model the reaction. 3 We re normalize at every discrete step of the numerical evolution to address deviations from the unit norm due to numerical errors [17] We could also extend the framework in [1] and apply it to our equations. VARIATIONAL PROBLEMS AND PDE S ON IMPLICIT SURFACES 13 Introducing our framework, if u 1 and u 2 are defined on a surface S implicitly represented as the zero level set of we have u 1 t = F (u 1 ; u 2 ) D 1 1 k r k r Delta (Pr ru 1 k r k) 28) u ....

F. Alouges, "An energy decreasing algorithm for harmonic maps," in J.M. Coron et al., Editors, Nematics, Nato ASI Series, Kluwer Academic Publishers, Netherlands, pp. 1-13, 1991.

....A search direction is built up from these using the Fletcher Reeves conjugate gradient recurrence relations (see, for example, 11] A one dimensional search is then conducted in this direction but always remaining on the constraint set. The approach di#ers from other published approaches (e.g. [3, 6, 7, 15]) in this regard. Those schemes all perform a true line search, allowing the discrete director field to move o# of the constraint set, violating its pointwise unit length constraint, and then re normalizing all the vectors once the line search is terminated. In all of the situations in which ....

....field to move o# of the constraint set, violating its pointwise unit length constraint, and then re normalizing all the vectors once the line search is terminated. In all of the situations in which these other codes have been employed, this re normalization step was provably free energy reducing [3]. For our application below (and for others we envision) this is not the case. The structures and configurations we seek are also rather fragile, and so we feel that this greater fidelity to the constraints should enhance the robustness of the code. Some additional features have been added to the ....

F. Alouges. An energy-decreasing algorithm for harmonic map. In J.-M. Coron, J.-M. Ghidaglia, and F. Helein, editors, Nematics: Mathematical and Physical Aspects, volume 332 of NATO ASI Series. Series C: Mathematical and Physical Sciences, pages 1--13, Dordrecht / Boston / London, 1991. NATO, Kluwer Academic Publishers.

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F. Alouges, "An energy decreasing algorithm for harmonic maps," in J.M. Coron et al., Editors, Nematics, Nato ASI Series, Kluwer Academic Publishers, Netherlands, pp. 1-13, 1991.

No context found.

F. Alouges, "An energy decreasing algorithm for harmonic maps," in J.M. Coron et al., Editors, Nematics, Nato ASI Series, Kluwer Academic Publishers, Netherlands, pp. 1-13, 1991.

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