Ross T. Whitaker

Partitioning 3D surface meshes using watershed segmentation

This paper describes a method for partitioning 3D surface meshes into useful segments. The proposed method generalizes morphological watersheds, an image segmentation technique, to 3D surfaces. This surface segmentation uses the total curvature of the surface as an indication of region boundaries. The surface is segmented into patches, where each patch has a relatively consistent curvature throughout, and is bounded by areas of higher, or drastically different, curvature. This algorithm has applications for a variety of important problems in visualization and geometrical modeling including 3D feature extraction, mesh reduction, texture mapping 3D surfaces, and computer aided design.

A Level-Set Approach to 3D Reconstruction from Range Data

This paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowledge about the application domain. The resulting optimization problem is solved by an incremental process of deformation. We represent a deformable surface as the level set of a discretely sampled scalar function of three dimensions, i.e., a volume. Such level-set models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume. The result is a voxel-based modeling technology that offers several advantages over conventional parametric models, including flexible topology, no need for reparameterization, concise descriptions of differential structure, and a natural scale space for hierarchical representations. This paper builds on previous work in both 3D reconstruction and level-set modeling. It presents a fundamental result in surface estimation from range data: an analytical characterization of the surface that maximizes the posterior probability. It also presents a novel computational technique for level-set modeling, called the sparse-field algorithm, which combines the advantages of a level-set approach with the computational efficiency and accuracy of a parametric representation. The sparse-field algorithm is more efficient than other approaches, and because it assigns the level set to a specific set of grid points, it positions the level-set model more accurately than the grid itself. These properties, computational efficiency and subcell accuracy, are essential when trying to reconstruct the shapes of 3D objects. Results are shown for the reconstruction objects from sets of noisy and overlapping range maps.

Particle-Based Simulation of Fluids

Due to our familiarity with how fluids move and interact, as well as their complexity, plausible animation of fluidsremains a challenging problem. We present a particle interaction method for simulating fluids. The underlyingequations of fluid motion are discretized using moving particles and their interactions. The method allows simulationand modeling of mixing fluids with different physical properties, fluid interactions with stationary objects, andfluids that exhibit significant interface breakup and fragmentation. The gridless computational method is suitedfor medium scale problems since computational elements exist only where needed. The method fits well into thecurrent user interaction paradigm and allows easy user control over the desired fluid motion.

Level set surface editing operators

We present a level set framework for implementing editing operators for surfaces. Level set models are deformable implicit surfaces where the deformation of the surface is controlled by a speed function in the level set partial differential equation. In this paper we define a collection of speed functions that produce a set of surface editing operators. The speed functions describe the velocity at each point on the evolving surface in the direction of the surface normal. All of the information needed to deform a surface is encapsulated in the speed function, providing a simple, unified computational framework. The user combines pre-defined building blocks to create the desired speed function. The surface editing operators are quickly computed and may be applied both regionally and globally. The level set framework offers several advantages. 1) By construction, self-intersection cannot occur, which guarantees the generation of physically-realizable, simple, closed surfaces. 2) Level set models easily change topological genus, and 3) are free of the edge connectivity and mesh quality problems associated with mesh models. We present five examples of surface editing operators: blending, smoothing, sharpening, openings/closings and embossing. We demonstrate their effectiveness on several scanned objects and scan-converted models.

Unsupervised, information-theoretic, adaptive image filtering for image restoration

Image restoration is an important and widely studied problem in computer vision and image processing. Various image filtering strategies have been effective, but invariably make strong assumptions about the properties of the signal and/or degradation. Hence, these methods lack the generality to be easily applied to new applications or diverse image collections. This paper describes a novel unsupervised, information-theoretic, adaptive filter (UINTA) that improves the predictability of pixel intensities from their neighborhoods by decreasing their joint entropy. In this way, UINTA automatically discovers the statistical properties of the signal and can thereby restore a wide spectrum of images. The paper describes the formulation to minimize the joint entropy measure and presents several important practical considerations in estimating neighborhood statistics. It presents a series of results on both real and synthetic data along with comparisons with state-of-the-art techniques, including novel applications to medical image processing.

Geometric surface smoothing via anisotropic diffusion of normals

This paper introduces a method for smoothing complex, noisy surfaces, while preserving (and enhancing) sharp, geometric features. It has two main advantages over previous approaches to feature preserving surface smoothing. First is the use of level set surface models, which allows us to process very complex shapes of arbitrary and changing topology. This generality makes it well suited for processing surfaces that are derived directly from measured data. The second advantage is that the proposed method derives from a well-founded formulation, which is a natural generalization of anisotropic diffusion, as used in image processing. This formulation is based on the proposition that the generalization of image filtering entails filtering the normals of the surface, rather than processing the positions of points on a mesh.

Microstructural connectivity of the arcuate fasciculus in adolescents with high-functioning autism.

The arcuate fasciculus is a white matter fiber bundle of great importance in language. In this study, diffusion tensor imaging (DTI) was used to infer white matter integrity in the arcuate fasciculi of a group of subjects with high-functioning autism and a control group matched for age, handedness, IQ, and head size. The arcuate fasciculus for each subject was automatically extracted from the imaging data using a new volumetric DTI segmentation algorithm. The results showed a significant increase in mean diffusivity (MD) in the autism group, due mostly to an increase in the radial diffusivity (RD). A test of the lateralization of DTI measurements showed that both MD and fractional anisotropy (FA) were less lateralized in the autism group. These results suggest that white matter microstructure in the arcuate fasciculus is affected in autism and that the language specialization apparent in the left arcuate of healthy subjects is not as evident in autism, which may be related to poorer language functioning.

Calibration requirements and procedures for a monitor-based augmented reality system

Augmented reality entails the use of models and their associated renderings to supplement information in a real scene. In order for this information to be relevant or meaningful, the models must be positioned and displayed in such a way that they blend into the real world in terms of alignments, perspectives, illuminations, etc. For practical reasons the information necessary to obtain this realistic blending cannot be known a priori, and cannot be hard wired into a system. Instead a number of calibration procedures are necessary so that the location and parameters of each of the system components are known. We identify the calibration steps necessary to build a computer model of the real world and then, using the monitor based augmented reality system developed at ECRC (GRASP) as an example, we describe each of the calibration processes. These processes determine the internal parameters of our imaging devices (scan converter, frame grabber, and video camera), as well as the geometric transformations that relate all of the physical objects of the system to a known world coordinate system. >

Rician noise removal in diffusion tensor MRI

Rician noise introduces a bias into MRI measurements that can have a significant impact on the shapes and orientations of tensors in diffusion tensor magnetic resonance images. This is less of a problem in structural MRI, because this bias is signal dependent and it does not seriously impair tissue identification or clinical diagnoses. However, diffusion imaging is used extensively for quantitative evaluations, and the tensors used in those evaluations are biased in ways that depend on orientation and signal levels. This paper presents a strategy for filtering diffusion tensor magnetic resonance images that addresses these issues. The method is a maximum a posteriori estimation technique that operates directly on the diffusion weighted images and accounts for the biases introduced by Rician noise. We account for Rician noise through a data likelihood term that is combined with a spatial smoothing prior. The method compares favorably with several other approaches from the literature, including methods that filter diffusion weighted imagery and those that operate directly on the diffusion tensors.

Gaze-directed volume rendering

We direct our gaze at an object by rotating our eyes or head until the objects projection falls on the fovea, a small region of enhanced spatial acuity near the center of the retina. In this paper, we explore methods for encorporating gaze direction into rendering algorithms. This approach permits generation of images exhibiting continuously varying resolution, and allows these images to be displayed on conventional television monitors. Specifically, we describe a ray tracer for volume data in which the number of rays cast per unit area on the image plane and the number of samples drawn per unit length along each ray are functions of local retinal acuity. We also describe an implementation using 2D and 3D mip maps, an eye tracker, and the Pixel-Planes 5 massively parallel raster display system. Pending completion of Pixel-Planes 5 in the spring of 1990, we have written a simulator on a Stellar graphics supercomputer. Preliminary results indicate that while users are aware of the variable-resolution structure of the image, the high-resolution sweet spot follows their gaze well and promises to be useful in practice.