11,467 research outputs found
A Phase Field Model for Continuous Clustering on Vector Fields
A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.
Robust Feature Detection and Local Classification for Surfaces Based on Moment Analysis
The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.
Anomalous transport in Charney-Hasegawa-Mima flows
Transport properties of particles evolving in a system governed by the
Charney-Hasegawa-Mima equation are investigated. Transport is found to be
anomalous with a non linear evolution of the second moments with time. The
origin of this anomaly is traced back to the presence of chaotic jets within
the flow. All characteristic transport exponents have a similar value around
, which is also the one found for simple point vortex flows in the
literature, indicating some kind of universality. Moreover the law
linking the trapping time exponent within jets to the transport
exponent is confirmed and an accumulation towards zero of the spectrum of
finite time Lyapunov exponent is observed. The localization of a jet is
performed, and its structure is analyzed. It is clearly shown that despite a
regular coarse grained picture of the jet, motion within the jet appears as
chaotic but chaos is bounded on successive small scales.Comment: revised versio
Seismic Fault Preserving Diffusion
This paper focuses on the denoising and enhancing of 3-D reflection seismic
data. We propose a pre-processing step based on a non linear diffusion
filtering leading to a better detection of seismic faults. The non linear
diffusion approaches are based on the definition of a partial differential
equation that allows us to simplify the images without blurring relevant
details or discontinuities. Computing the structure tensor which provides
information on the local orientation of the geological layers, we propose to
drive the diffusion along these layers using a new approach called SFPD
(Seismic Fault Preserving Diffusion). In SFPD, the eigenvalues of the tensor
are fixed according to a confidence measure that takes into account the
regularity of the local seismic structure. Results on both synthesized and real
3-D blocks show the efficiency of the proposed approach.Comment: 10 page
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