To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create "seams" or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT datasets seamlessly from one imaging space to another. Once the bijection has been achieved and tensors have been correctly relocated to the template space, we can appropriately reorient tensors in the template space using a warping method based on Procrustean estimation.

Methods for the analysis of brain morphology, including voxel-based morphology and surface-based morphometries, have been used to detect associations between brain structure and covariates of interest, such as diagnosis, severity of disease, age, IQ, and genotype. The statistical analysis of morphometric measures usually involves two statistical procedures: 1) invoking a statistical model at each voxel (or point) on the surface of the brain or brain subregion, followed by mapping test statistics (e.g., t test) or their associated p values at each of those voxels; 2) correction for the multiple statistical tests conducted across all voxels on the surface of the brain region under investigation. We propose the use of new statistical methods for each of these procedures. We first use a heteroscedastic linear model to test the associations between the morphological measures at each voxel on the surface of the specified subregion (e.g., cortical or subcortical surfaces) and the covariates of interest. Moreover, we develop a robust test procedure that is based on a resampling method, called wild bootstrapping. This procedure assesses the statistical significance of the associations between a measure of given brain structure and the covariates of interest. The value of this robust test procedure lies in its computationally simplicity and in its applicability to a wide range of imaging data, including data from both anatomical and functional magnetic resonance imaging (fMRI). Simulation studies demonstrate that this robust test procedure can accurately control the family-wise error rate. We demonstrate the application of this robust test procedure to the detection of statistically significant differences in the morphology of the hippocampus over time across gender groups in a large sample of healthy subjects.

In this paper, we introduce geometry-dependent lighting that allows lighting parameters to be defined independently and possibly discrepantly over an object or scene based on the local geometry. We present and discuss Light Collages, a lighting design system with geometry-dependent lights for effective feature-enhanced visualization. Our algorithm segments the objects into local surface patches and places lights that are locally consistent but globally discrepant to enhance the perception of shape. We use spherical harmonics for efficiently storing and computing light placement and assignment. We also outline a method to find the minimal number of light sources sufficient to illuminate an object well with our globally discrepant lighting approach.

We introduce Light Collages - a lighting design system for effective visualization based on principles of human perception. Artists and illustrators enhance perception of features with lighting that is locally consistent and globally inconsistent. Inspired by these techniques, we design the placement of light sources to convey a greater sense of realism and better perception of shape with globally inconsistent lighting. Our algorithm segments the objects into local surface patches and uses a number of perceptual heuristics, such as highlights, shadows, and silhouettes, to enhance the perception of shape. We show our results on scientific and sculptured datasets.

Subsurface scattering is important for photo-realistic rendering of translucent materials. We make approximations to the BSSRDF model and propose a simple lighting model to simulate the effects on translucent meshes. Our approximations are based on the observation that subsurface scattering is relatively local due to its exponential falloff.In the preprocessing stage we build subsurface scattering neighborhood information, which includes all the vertices within effective scattering range from each vertex. We then modify the traditional local illumination model into a run-time two-stage process. The first stage involves computation of reflection and transmission of light on surface vertices. The second stage bleeds in scattering effects from a vertex's neighborhood to generate the final result. We then merge the run-time two-stage process into a run-time single-stage process using precomputed integrals, and reduce the complexity of our run-time algorithm to O ( N ), where N is the number of vertices. The selection of the optimum set size for precomputed integrals is guided by a standard imagespace error-metric. Furthermore, we show how to compress the precomputed integrals using spherical harmonics. We compensate for the inadequacy of spherical harmonics for storing high frequency components by a reference points scheme to store high frequency components of the precomputed integrals explicitly. With this approach, we greatly reduce memory usage without loss of visual quality under a high-frequency lighting environment and achieve interactive frame rates for medium-sized scenes. Our model is able to capture the most important features of subsurface scattering: reflection and transmission due to multiple scattering.

We propose the idea of using variable-precision geometry transformations and lighting to accelerate 3D graphics rendering. Multiresolution approaches reduce the number of primitives to be rendered; our approach complements the multiresolution techniques as it reduces the precision of each graphics primitive. Our method relates the minimum number of bits of accuracy required in the input data to achieve a desired accuracy in the display output. We achieve speedup by taking advantage of (a) SIMD parallelism for arithmetic operations, now increasingly common on modern processors, and (b) spatial-temporal coherence in frame-to-frame transformations and lighting. We show the results of our method on datasets from several application domains including laser-scanned, procedural, and mechanical CAD datasets.