Biomedical subjects

Gordon Kindlmann

Publications and source records attributed to Gordon Kindlmann.

3 recordsLinked to original sources

PubMed2006

Orthogonal tensor invariants and the analysis of diffusion tensor magnetic resonance images.

This paper outlines the mathematical development and application of two analytically orthogonal tensor invariants sets. Diffusion tensors can be mathematically decomposed into shape and orientation information, determined by the eigenvalues and eigenvectors, respectively. The developments herein orthogonally decompose the tensor shape using a set of three orthogonal invariants that characterize the magnitude of isotropy, the magnitude of anisotropy, and the mode of anisotropy. The mode of anisotropy is useful for resolving whether a region of anisotropy is linear anisotropic, orthotropic, or planar anisotropic. Both tensor trace and fractional anisotropy are members of an orthogonal invariant set, but they do not belong to the same set. It is proven that tensor trace and fractional anisotropy are not mutually orthogonal measures of the diffusive process. The results are applied to the analysis and visualization of diffusion tensor magnetic resonance images of the brain in a healthy volunteer. The theoretical developments provide a method for generating scalar maps of the diffusion tensor data, including novel fractional anisotropy maps that are color encoded for the mode of anisotropy and directionally encoded colormaps of only linearly anisotropic structures, rather than of high fractional anisotropy structures.

Anisotropy↗

PubMedDate not supplied

Reconstruction and visualization of planetary nebulae.

From our terrestrially confined viewpoint, the actual three-dimensional shape of distant astronomical objects is, in general, very challenging to determine. For one class of astronomical objects, however, spatial structure can be recovered from conventional 2D images alone. So-called planetary nebulae (PNe) exhibit pronounced symmetry characteristics that come about due to fundamental physical processes. Making use of this symmetry constraint, we present a technique to automatically recover the axisymmetric structure of many planetary nebulae from photographs. With GPU-based volume rendering driving a nonlinear optimization, we estimate the nebula's local emission density as a function of its radial and axial coordinates and we recover the orientation of the nebula relative to Earth. The optimization refines the nebula model and its orientation by minimizing the differences between the rendered image and the original astronomical image. The resulting model allows creating realistic 3D visualizations of these nebulae, for example, for planetarium shows and other educational purposes. In addition, the recovered spatial distribution of the emissive gas can help astrophysicists gain deeper insight into the formation processes of planetary nebulae.

Algorithms↗

PubMedDate not supplied

Diffusion tensor visualization with glyph packing.

A common goal of multivariate visualization is to enable data inspection at discrete points, while also illustrating larger-scale continuous structures. In diffusion tensor visualization, glyphs are typically used to meet the first goal, and methods such as texture synthesis or fiber tractography can address the second. We adapt particle systems originally developed for surface modeling and anisotropic mesh generation to enhance the utility of glyph-based tensor visualizations. By carefully distributing glyphs throughout the field (either on a slice, or in the volume) into a dense packing, using potential energy profiles shaped by the local tensor value, we remove undue visual emphasis of the regular sampling grid of the data, and the underlying continuous features become more apparent. The method is demonstrated on a DT-MRI scan of a patient with a brain tumor.

Algorithms↗