Fast and Memory Efficient GPU-based Rendering of Tensor Data (original) (raw)

Visualization of tensor fields using superquadric glyphs

Magnetic Resonance in Medicine, 2004

The spatially varying tensor fields that arise in magnetic resonance imaging are difficult to visualize due to the multivariate nature of the data. To improve the understanding of myocardial structure and function a family of objects called glyphs, derived from superquadric parametric functions, are used to create informative and intuitive visualizations of the tensor fields. The superquadric glyphs are used to visualize both diffusion and strain tensors obtained in canine myocardium. The eigensystem of each tensor defines the glyph shape and orientation. Superquadric functions provide a continuum of shapes across four distinct eigensystems (i , sorted eigenvalues), 1 ‫؍‬ 2 ‫؍‬ 3 (spherical), 1 < 2 ‫؍‬ 3 (oblate), 1 > 2 ‫؍‬ 3 (prolate), and 1 > 2 > 3 (cuboid). The superquadric glyphs are especially useful for identifying regions of anisotropic structure and function. Diffusion tensor renderings exhibit fiber angle trends and orthotropy (three distinct eigenvalues). Visualization of strain tensors with superquadric glyphs compactly exhibits radial thickening gradients, circumferential and longitudinal shortening, and torsion combined. The orthotropic nature of many biologic tissues and their DTMRI and strain data require visualization strategies that clearly exhibit the anisotropy of the data if it is to be interpreted properly. Superquadric glyphs improve the ability to distinguish fiber orientation and tissue orthotropy compared to ellipsoids.

Towards a High-quality Visualization of Higher-order Reynold’s Glyphs for Diffusion Tensor Imaging

Mathematics and Visualization, 2012

Recent developments in magnetic resonance imaging (MRI) have shown that displaying second-order tensor information reconstructed from diffusion-weighted MRI does not display the full structure information acquired by the scanner. Therefore, higher-order methods have been developed. Besides the visualization of derived structures such as fiber tracts or tractography (directly related to stream lines in fluid flow data sets), an extension of Reynold's glyph for second-order tensor fields is widely used to display local information. At the same time, fourth-order data becomes increasingly important in engineering as novel models focus on the change in materials under repeated application of stresses. Due to the complex structure of the glyph, a proper discrete geometrical approximation, e.g., a tessellation using triangles or quadrilaterals, requires the generation of many such primitives and, therefore, is not suitable for interactive exploration. It has previously been shown that those glyphs defined in spherical harmonic coordinates can be rendered using hardware acceleration. We show how tensor data can be rendered efficiently using a similar algorithm and demonstrate and discuss the use of alternative high-accuracy rendering algorithms.

The Tensor Splats Rendering Technique

2004

A new visualization technique for the visualization of symmetric positive definite tensor fields of rank two is introduced. It is based on a splatting technique that is build from tiny transparent glyph primitives which are capable to incorporate the full directional information content of a tensor. The result is an information-rich image that allows to read off the preferred directions in a tensor field. It is useful for analyzing slices or volumes of a three-dimensional tensor field and can be overlayed with standard volume rendering or color mapping. The application of the rendering technique is demonstrated on general relativistic data and the diffusion tensor field of a human brain. CR Categories: I.3.3 [Computer Graphics]: Picture/Image generation—Viewing algorithms; I.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism—Color, shading, shadowing, and texture; J.2.9 [Computer Applications]: Physical Sciences And Engineering—Physics

Superquadric Glyphs for Symmetric Second-Order Tensors

2010

Symmetric second-order tensor fields play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positive-definite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric second-order tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the tensor's quadratic form. We show that encoding arbitrary eigenvalue sign combinations requires design choices that differ fundamentally from those in previous work on traceless tensors (arising in the study of liquid crystals). Our method starts with a design of 2-D tensor glyphs guided by principles of symmetry and continuity, and creates 3-D glyphs that include the 2-D glyphs in their axis-aligned cross-sections. A key ingredient of our method is a novel way of mapping from the shape space of three-dimensional symmetric second-order tensors to the unit square. We apply our new glyphs to stress tensors from mechanics, geometry tensors and Hessians from image analysis, and rate-of-deformation tensors in computational fluid dynamics.

Interactive Multiscale Tensor Reconstruction for Multiresolution Volume Visualization

IEEE Transactions on Visualization and Computer Graphics, 2000

Large scale and structurally complex volume datasets from high-resolution 3D imaging devices or computational simulations pose a number of technical challenges for interactive visual analysis. In this paper, we present the first integration of a multiscale volume representation based on tensor approximation within a GPU-accelerated out-of-core multiresolution rendering framework. Specific contributions include (a) a hierarchical brick-tensor decomposition approach for pre-processing large volume data, (b) a GPU accelerated tensor reconstruction implementation exploiting CUDA capabilities, and (c) an effective tensor-specific quantization strategy for reducing data transfer bandwidth and out-of-core memory footprint. Our multiscale representation allows for the extraction, analysis and display of structural features at variable spatial scales, while adaptive level-of-detail rendering methods make it possible to interactively explore large datasets within a constrained memory footprint. The quality and performance of our prototype system is evaluated on large structurally complex datasets, including gigabyte-sized micro-tomographic volumes.

Tensor Splat Rendering Technique for Tensor Fields

A new visualization technique for the visualization of symmetric positive definite tensor fields of rank two is introduced. It is based on a splatting technique that is build from tiny transparent glyph primitives which are capable to incorporate the full directional information content of a tensor. The result is an information-rich image that allows to read off the preferred directions in a tensor field. It is useful for analyzing slices or volumes of a three-dimensional tensor field and can be overlayed with standard volume rendering or color mapping. The application of the rendering technique is demonstrated on general relativistic data and the diffusion tensor field of a human brain.

Physically based methods for tensor field visualization

IEEE Visualization 2004, 2004

The physical interpretation of mathematical features of tensor fields is highly application-specific. Existing visualization methods for tensor fields only cover a fraction of the broad application areas. We present a visualization method tailored specifically to the class of tensor field exhibiting properties similar to stress and strain tensors, which are commonly encountered in geomechanics. Our technique is a global method that represents the physical meaning of these tensor fields with their central features: regions of compression or expansion. The method is based on two steps: first, we define a positive definite metric, with the same topological structure as the tensor field; second, we visualize the resulting metric. The eigenvector fields are represented using a texture-based approach resembling line integral convolution (LIC) methods. The eigenvalues of the metric are encoded in free parameters of the texture definition. Our method supports an intuitive distinction between positive and negative eigenvalues. We have applied our method to synthetic and some standard data sets, and "real" data from Earth science and mechanical engineering application.