Presented by: Eugene (Austin) Stoudenmire 31 Jan 2007

Visualization of Anatomic Covariance Tensor FieldsGordon L. Kindlmann, David M. Weinstein, Agatha D. Lee, Arthur W. Toga, and Paul M. Thompson Presented by: Eugene (Austin) Stoudenmire 31 Jan 2007

Problem • Current methods of visualizing brain variability • Not sufficiently informative and interactive • Current methods involve computing • for each vertex of brain surface model • distribution of displacement vectors between individual brains and average brain • summarizing as covariance tensor • tensor – akin to vector field • And displaying as ellipsoid tensor glyphs • glyph – icon that maps features onto primitive • shape, size, orientation, appearance

Ellipsoidal Tensor Glyphs • But – feature values are hard to discern

We Care • Understanding anatomic variability of the brain is important • Visualization is an important component of understanding anatomic variability

Anatomic Variability Importance • Functional organization differs among people • measures are required to represent and visualize systematic patterns • Determine patterns of altered brain structure in diseases • based on databases of brain scans • Statistical info on anatomical variance to facilitate computer vision algorithms that automatically identify brain structures

Visualization Importance • Important component of understanding anatomic variability • Provide feedback for variability algorithm verification • Means of mucking with the data to form/refine hypotheses about variability

Approach • Map values onto superquadric glyphs • MRI brain scans of 40 subjects • Aligned and converted to 3D models • Interest: Deformation that would transform average onto each individual • Represented as 3D covariance tensor

Superquadric Glyphs

Ellipsoid Superquadric

Ellipsoid Superquadric Kindlmann, “Superquadric Tensor Glyphs”, Joint Eurographics – IEEE TCVG Symposium on Visualization 2004

Subject Mapping • MRI brain scans of 40 subjects • Aligned to standardized brain • Converted aligned brains to 3D models • Matched up major fissures • Interest: Minimum-energy 3D nonlinear elastic deformation that transforms the landmarks of average onto those of each individual • Represented at each point as 3D covariance tensor of the displacement vectors induced by the deformations from the average to all individuals

Tensor Creation • 3 x 3 covariance tensor T • Diagonalized • T = RR-1 • Where  = Diagonal matrix of eigenvalues R = Rotational matrix that transforms standard basis onto eigenvector basis

Tensor Creation • Tensor orientation – Eigenvectors • Tensor shape – Eigenvalues Kindlmann, “Superquadric Tensor Glyphs”, Joint Eurographics – IEEE TCVG Symposium on Visualization 2004

What Makes Superquadric So Good • Edges of superquadric tensor glyph • indicate eigenvalue differences • Eigenvalue differences • imply lack of rotational symmetry • Therefore need to emphasize glyph edges • which will emphasize eigenvalue differences

Space of Superquadratics

Tensor Creation • Create superquadric shape • Modify standard parameterization of sphere cos sin sin sin cos  ) ( 0 <=  <=2 p() = , 0 <=  <=  where x = sgn(x)|x| 

And More • Colormaps were used • To make large-scale patterns stand out • Depicted two tensor attributes simulataneously • Different map on mesh surface and glyph • Frobenius norm (overall variability) • Fractional anisotropy (extent to which variability extends more in some directions than others (e.g. not rotationally symmetrical)) • Skew (precise manner of difference from a sphere)

Evaluation • Back to the beginning, importance was • Understanding anatomic variability of the brain • Visualizing in order to understand anatomic variability • Comparative images were used for verification that the visualization was more discriminatory than elliptical tensors • These pictures, along with those of other references, appeared to more clearly differentiate among attribute values than did ellipsoid glyphs • No objective verification or validation • But • Their previous work referenced studies that did quantitatively measure an increased discrimination when superquadratic tensors were used.

Ellipsoid Superquadric Kindlmann, “Superquadric Tensor Glyphs”, Joint Eurographics – IEEE TCVG Symposium on Visualization 2004

Ellipsoid Superquadric Scientific Computing and Imaging Institute website

Alternative Methods • Spinor mentioned in another paper • Other methods from “Tensorlines: Advection-Diffusion based Propagation through Diffusion Tensor Fields”, David Weinstein, Gordon Kindlmann, Eric Lundberg • Brush strokes (stroke shape, color, texture) • Glyphs • Ellipsoids (one kind of glyph) • Stream-polygons (show info along a path) • Hyperstreamlines (show info along a path) • Other work of theirs did discuss ray-tracing the resulting superquadratic tensors with the caveat that it wouldn’t be real time

Conclusion • Computational efficiency – could be interactive, depending on problem size • Not designed to definitively depict attribute value • Certainly not designed as a physician’s diagnostic tool • Could be applicable to many other uses • Example calculation sure would have been helpful!

Next Steps • Other applications • Efficiency • Additional attributes (e.g. their colormapping scheme)

Question • What are the advantages of superquadric tensor fields (or are there any)

Question • Do the shapes really convey the info they are supposed to (i.e. differences)

Presented by: Eugene (Austin) Stoudenmire 31 Jan 2007