2011
DOI: 10.1109/tvcg.2010.107
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Coherent Structures of Characteristic Curves in Symmetric Second Order Tensor Fields

Abstract: This paper generalizes the concept of Lagrangian coherent structures, which is known for its potential to visualize coherent regions in vector fields and to distinguish them from each other. In particular, we extend the concept of the flow map to generic mappings of coordinates. As the major application of this generalization, we present a semiglobal method for visualizing coherent structures in symmetric second order tensor fields. We demonstrate the usefulness by examples from DT-MRI, uncovering anatomical s… Show more

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Cited by 9 publications
(7 citation statements)
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“…One solution might be to allow effective surface structure detection by adding a “cap” at the end of a tube to allow the perception of surfaces and provide a clear view of those broken fibers, for example, depicting the tensor field with glyphs or volume rendering methods [22]. We may alter the data-rendering method to increase visual legibility, especially since the rendering method will alter the perceived structure, for example by applying flow maps [16] or showing topological structures [30, 39]. One possibility is to study the tradeoffs between display characteristics and more advanced depth-enhancement techniques, e.g., adding halos and providing better color design [19].…”
Section: Discussionmentioning
confidence: 99%
“…One solution might be to allow effective surface structure detection by adding a “cap” at the end of a tube to allow the perception of surfaces and provide a clear view of those broken fibers, for example, depicting the tensor field with glyphs or volume rendering methods [22]. We may alter the data-rendering method to increase visual legibility, especially since the rendering method will alter the perceived structure, for example by applying flow maps [16] or showing topological structures [30, 39]. One possibility is to study the tradeoffs between display characteristics and more advanced depth-enhancement techniques, e.g., adding halos and providing better color design [19].…”
Section: Discussionmentioning
confidence: 99%
“… Visualizations of diffusion tensor medical images with (a) glyphs [ 63 ], (b) hybrid voxel-based and tractography method [ 64 ], and (c, d) tractography methods [ 61 , 62 ]. Different uncertainty-aware glyph encodings are shown in (a), from left to right: ellipsoids, superquadrics, and fourth-order homogeneous polynomial [ 63 ].…”
Section: Fundamental Medical Image Visualization Techniquesmentioning
confidence: 99%
“…Different uncertainty-aware glyph encodings are shown in (a), from left to right: ellipsoids, superquadrics, and fourth-order homogeneous polynomial [ 63 ]. A combined rendering of voxel-based visualization of characteristic curves along with extracted tractography is shown in (b) [ 64 ]. For tractography visualizations, extracted fiber tracts of the brain are visualized as tubes with shadows with (c) ray tracing [ 62 ] and are combined into the context of volume rendering of scalar MRI with unified volume and surface occlusion shading [ 61 ] (d).…”
Section: Fundamental Medical Image Visualization Techniquesmentioning
confidence: 99%
“…As topological features may be boundary induced, a direct application of tensor field topology to brain data is challenging due to the brain's complex surface. There, topological features on derived values instead of the tensor data directly show promising results [Sch11, THBG12, HVSW11].…”
Section: State Of the Art – Tensor Fieldsmentioning
confidence: 99%