Abstract
Streamsurfaces in diffusion tensor fields are used to represent structures with primarily planar diffusion. So far, however, no effort has been made on the visualization of the anisotropy of diffusion on them, although this information is very important to identify the problematic regions of these structures. We propose two methods to display this anisotropy information. The first one employs a set of merging ellipsoids, which simultaneously characterize the local tensor details — anisotropy — on them and portray the shape of the streamsurfaces. The weight between the streamsurfaces continuity and the discrete local tensors can be interactively adjusted by changing some given parameters. The second one generates a dense LIC (line integral convolution) texture of the two tangent eigenvector fields along the streamsurfaces firstly, and then blends in some color mapping indicating the anisotropy information. For high speed and high quality of texture images, we confine both the generation and the advection of the LIC texture in the image space. Merging ellipsoids method reveals the entire anisotropy information at discrete points by exploiting the geometric attribute of ellipsoids, and thus suits for local and detailed examination of the anisotropy; the texture-based method gives a global representation of the anisotropy on the whole streamsurfaces with texture and color attributes. To reveal the anisotropy information more efficiently, we integrate the two methods and use them at two different levels of details.
Similar content being viewed by others
References
B Cabral, L C Leedom. Imaging vector fields using line integral convolution, SIGGRAPH’93, 1993, 263–270.
C F Westin, S Peled, H Gubjartsson, et al. Geometrical diffusion measures for MRI from tensor basis analysis, Proc Int Soc Magnetic Resonance Med (ISMRM), 1997.
C Pierpaoli, P J Basser. Toward a quantitative assessment of diffusion anisotropy, Magnetic Resonance Med, 1996, 36: 893–906.
D Stalling. LIC on surfaces, SIGGRAPH’97, 1997, 51–64.
D Stalling, H C Hege. Fast and resolution independent line integral convolution, SIGGRAPH’95, 1995, 249–256.
E Hsu. Generalized line integral convolution rendering of diffusion tensor fields, Proc ISMRM, 2001, pp790.
G Turk. Re-tiling polygonal surfaces, SIGGRAPH’92, 1992, 55–64.
J J van Wijk. Spot noise-texture synthesis for data visualization, SIGGRAPH’91, 1991, 309–318.
J J van Wijk. Image based flow visualization, IEEE Trans Graph, 2002, 21(3): 745–754.
J J van Wijk. Image based flow visualization for curved surfaces, Proc IEEE Vis 2003, 2003, 123–130.
J Palacios, E Zhang. Interactive visualization of rotational symmetry fields on surfaces, IEEE Trans Vis Comput Graph, 2011, 17(7): 947–955.
M Brill, H Hagen, H C Rodrian, et al. Streamball techniques for flow visualization, Proc Conf Vis’94, 1994, 225–231.
P J Basser, J Mattiello, D Lebihan. Estimation of the effective self-diffusion tensor from the NMR Spin-Echo, J Magnetic Resonance B, 1994, 103(3): 247–254.
R S Laramee, B Jobard, H Hauser. Image space based visualization of unsteady flow on surfaces, Proc IEEE Vis 2003, 2003, 131–138.
R Sondershaus, S Gumhold. Meshing of diffusion surfaces for point-based tensor field visualization, Proc 12th Int Meshing Roundtable, 2003, 177–188.
S Eichelbaum. Image space tensor field visualization using a LIC-like method, Diploma Thesis, University of Leipzig, 2009.
S Zhang, C Demiralp, D Laidlaw. Visualizing diffusion tensor MR images using streamtubes and streamsurfaces, IEEE Trans Vis Comput Graph, 2003, 9(4): 454–462.
W Chen, S Zhang, S Correia, et al. Visualizing diffusion tensor imaging data with merging ellipsoids, 2009 IEEE Pac Vis Symp, 2009, 145–151.
W E Lorenson, H E Cline. Marching cubes: a high resolution 3D surface construction algorithm, Comput Graph, 1987, 21(3): 163–169.
W J Song, J Z Cui, Z L Ye. Visualizing 3-D symmetric tensor fields using a type of surface icons, IEEE CAD/Graphics’09, 2009, 627–631.
Y Xu, R Z Hu, C Gotsman, et al. Blue noise sampling of surfaces, Comput Graph, 2012, 36(4): 232–240.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (61070233) and the Natural Science Foundation of Shaanxi Province, China (2011JM1006).
Rights and permissions
About this article
Cite this article
Song, Wj., Chen, W., Chen, Hd. et al. Visualizing diffusion tensor fields on streamsurfaces with merging ellipsoids and LIC texture. Appl. Math. J. Chin. Univ. 29, 399–409 (2014). https://doi.org/10.1007/s11766-014-3234-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11766-014-3234-y