We compare a variety of triangle shape measures using concepts such as smoothness and convexity. We show that one of these measures, the elongation measure, lends itself to an intuitive geometric interpretation.

The Double Insertion, Nonuniform, Stationary subdivision surface (DINUS) generalizes both the nonuniform, bicubic spline surface and the Catmull-Clark subdivision surface. DINUS allows arbitrary knot intervals on the edges, allows incorporation of special features, and provides limit point as well as limit normal rules. It is the first subdivision scheme that gives the user all this flexibility and at the same time all essential limit information, which is important for applications in modeling and adaptive rendering. DINUS is also amenable to analysis techniques for stationary schemes. We implemented DINUS as an Autodesk Maya plugin to show several modeling and rendering examples.

We present a novel GPU-based algorithm for high-quality rendering of bivariate spline surfaces. An essential difference to the known methods for rendering graph surfaces is that we use quartic smooth splines on triangulations rather than triangular meshes. Our rendering approach is direct in the sense that since we do not use an intermediate tessellation but rather compute ray-surface intersections (by solving quartic equations numerically) as well as surface normals (by using Bernstein-Bézier techniques) for Phong illumination on the GPU. Inaccurate shading and artifacts appearing for triangular tesselated surfaces are completely avoided. Level of detail is automatic since all computations are done on a per fragment basis. We compare three different (quasi-) interpolating schemes for uniformly sampled gridded data, which differ in the smoothness and the approximation properties of the splines. The results show that our hardware based renderer leads to visualizations (including texturing, multiple light sources, environment mapping, etc.) of highest quality.

This paper presents a fully automated 3D face authentication (verification) and recognition (identification) method and recent results from our work in this area. The major contributions of our paper are: (a) the method can handle data with different facial expressions including hair, upper body, clothing, etc. and (b) development of weighted features for discrimination. The input to our system is a triangular mesh and it outputs a matching % against a gallery. Our method includes both surface and curve based features that are automatically extracted from a given face data. The test set for authentication consisted of 117 different people with 421 scans including different facial expressions. Our study shows equal error rate (EER) at 0.065% for normal faces and 1.13% in faces with expressions. We report verification rates of 100% in normal faces and 93.12% in faces with expressions at 0.1% FAR. For identification, our experiment shows 100% rate in normal faces and 95.6% in faces with expressions. From our experiment we conclude that combining feature points, profile curve, and partial face surface matching gives better authentication and recognition rate than any single matching method.

This paper presents a shape-based approach in extracting thin structures, such as lines and sheets, from three-dimensional (3D) biomedical images. Of particular interest is the capability to recover cellular structures, such as microtubule spindle fibers and plasma membranes, from laser scanning confocal microscopic (LSCM) data. Hessian-based shape methods are reviewed. A synthesized linear structure is used to evaluate the sensitivity of the multiscale filtering approach in extracting closely positioned fibers. We find that the multiscale approach tends to fuse lines together, which makes it unsuitable for visualizing mouse egg spindle fibers. Single-scale Gaussian filters, balanced between sensitivity and noise resistance, are adopted instead. In addition, through an ellipsoidal Gaussian model, the eigenvalues of the Hessian matrix are quantitatively associated with the standard deviations of the Gaussian model. Existing shape filters are simplified and applied to LSCM data. A significant improvement in extracting closely positioned thin lines is demonstrated by the resultant images. Further, the direct association of shape models and eigenvalues makes the processed images more understandable qualitatively and quantitatively.

In this paper, we present a deformable surface geometric model for segmenting targets from volumetric data. This model deforms under external forces only, and changes its geometry and topology by using improved geometric constraints. External forces are calculated by using the sum of inflation forces, whose contributions take place on internal regions of objects, and the gradient forces, which play a key role when the surface is near the boundary of objects. A new set of geometric constraints is proposed which includes constraints on vertices, edges and faces. Once a constraint is broken, the corresponding topological transformation will occur to keep the geometric and topological integrity of the surface unaltered. We demonstrate that our model can efficiently segment complex anatomic structures from medical 3D images, and achieve the requirements of accuracy and geometry for image segmentation.

The concentration edge -detection and Gegenbauer image-reconstruction methods were previously shown to improve the quality of segmentation in magnetic resonance imaging. In this study, these methods are utilized as a pre-processing step to the Weibull E-SD field segmentation. It is demonstrated that the combination of the concentration edge detection and Gegenbauer reconstruction method improves the accuracy of segmentation for the simulated test data and real magnetic resonance images used in this study.

We present a method for extracting feature curves called crest lines from a triangulated surface. Then, we calculate the geodesic Voronoi diagram of crest lines to segment the surface into several regions. Afterward, barycentric surface flattening using theory from graph embeddings is implemented and, using the Geodesic Voronoi diagram, we develop a faster surface flattening algorithm.

Hierarchical B-splines have been widely used for shape modeling since their discovery by Forsey and Bartels. In this paper, we present an application of this concept, in the form of free-form deformation, to image registration by matching two images at increasing levels of detail. Results using MRI brain data are presented that demonstrate high degrees of matching while unnecessary distortions are avoided. We compare our results with the nonlinear ICP (Iterative Closest Point) algorithm (used for landmark-based registration) and optical flow (used for intensity-based registration).

This paper presents a coarse-grain approach for segmentation of objects with gray levels appearing in volume data. The input data is on a 3D structured grid of vertices v(i. j. k), each associated with a scalar value. In this paper, we consider a voxel as a /spl kappa/ /spl times/ /spl kappa/ /spl times/ /spl kappa/ cube and each voxel is assigned two values: expectancy and standard deviation (E-SD). We use the Weibull noise index to estimate the noise in a voxel and to obtain more precise E-SD values for each voxel. We plot the frequency of voxels which have the same E-SD, then 3D segmentation based on the Weibull E-SD field is presented. Our test bed includes synthetic data as well as real volume data from a confocal laser scanning microscope (CLSM). Analysis of these data all show distinct and defining regions in their E-SD fields. Under the guide of the E-SD field, we can efficiently segment the objects embedded in real and simulated 3D data.

Given a three dimensional (3D) array of function values F/sub i,j,k/ on a rectilinear grid, the marching cubes (MC) method is the most common technique used for computing a surface triangulation T approximating a contour (isosurface) F(x, y, z)=T. We describe the construction of a C/sup 0/ continuous surface consisting of rational quadratic surface patches interpolating the triangles in T. We determine the Bezier control points of a single rational quadratic surface patch based on the coordinates of the vertices of the underlying triangle and the gradients and Hessians associated with the vertices.

In this paper the construction of curvature continuous, planar curves (open or closed) that consist of conic segments, represented in the rational Bézier form, is discussed, and an iterative procedure to compute their offset curves is outlined.