Discrete Laplace-Beltrami Operator on Sphere and Optimal Spherical Triangulations
In this paper we first modify a widely used discrete Laplace-Beltrami operator proposed by Meyer et al over triangular surfaces, and then we show that the modified discrete operator has some convergence properties over the triangulated spheres. A sequence of spherical triangulations which is optimal in certain sense and leads to smaller truncation error of the discrete Laplace-Beltrami operator is constructed. Optimal hierarchical spherical triangulations are also given. Truncation error bounds of the discrete Laplace-Beltrami operator over the constructed triangulations are provided.

title: Automatic reconstruction of surfaces and scalar fields from 3D scans
abstract: We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of scanned point data. A possible application is the rapid computer model reconstruction of an existing part or prototype from a three dimensional (3D) points scan of its surface. Color, texture or some scalar material property of the physical part, define natural scalar fields over the surface of the CAD model. Our reconstruction algorithm does not impose any convexity or differentiability restrictions on the surface of the original physical part or the scalar field function, except that it assumes that there is a sufficient sampling of the input point data to unambiguously reconstruct the CAD model. Compared to earlier methods our algorithm has the advantages of simplicity, efficiency and uniformity (both CAD model and scalar field reconstruction). The simplicity and efficiency of our approach is based on several novel uses of appropriate sub-structures (alpha shapes) of a three-dimensional Delaunay Triangulation, its dual the three-dimensional Voronoi diagram, and dual uses of trivariate Bernstein-Bezier forms. The boundary of the CAD model is modeled using implicit cubic Bernstein-Bezier patches, while the scalar field is reconstructed with functional cubic Bernstein-Bezier patches.

title: Regular algebraic curve segments (II) - Interpolation and approximation
abstract: In this paper (part two of the trilogy) we introduce three classes of reduced form D -regular algebraic curve splines and use them for interpolation and approximation of various algebraic curves. Explicit formulas for interpolation and approximation are also given in some low degree cases.

title: Fast evaluation of the improved Loop's subdivision surfaces
abstract: For obtaining better curvature distributions of subdivision surfaces, various improvements for Loop's subdivision scheme (C. Loop, 1987) on triangular surface meshes have been made. A careful analysis shows that the fast evaluation technique of the subdivision surface proposed by Stam is no longer usable to these improved schemes. This paper describes a fast evaluating algorithm for improved Loop's subdivision surfaces. The algorithm is applicable to a vast class of subdivision schemes for triangular surface meshes. Using the proposed algorithm, one can evaluate the subdivision surface at any domain point for any set of input subdivision masks and a control mesh.

title: Hierarchical multiresolution reconstruction of shell surfaces
abstract: We present an adaptive, hierarchical Hh-multiresolution reconstruction algorithm to model shell surface objects from a matched pair of triangulated surfaces. Shell surfaces are an interval of contours of trivariate functions with prismatic support. In the H-direction, a hierarchical representation of the scaffold is constructed. For any adaptively extracted scaffold from the hierarchy, a sequence of functions in the h-direction (regularly subdivided mesh) is constructed so that their contours approximate the input shell to within a given error e. The shell surfaces can be made to capture sharp curve creases on the shell while being C1 smooth everywhere else. Using an interval of iso-contours of smooth trivariate spline functions, rather than a pair of inner and outer surface splines, one avoids the need for interference checks between the inner and outer surface boundaries.

title: Spline Approximations of Real Algebraic Surfaces
abstract: We use a combination of both symbolic and numerical techniques to construct several degree boundedG0andG1continuous, piecewise spline approximations of real implicit algebraic surfaces for both computer graphics and geometric modeling. These approximations are based upon an adaptive triangulation (aG0planar approximation) of the real components of the algebraic surface, and include both singular points and singular curves on the surface. A curvilinear wireframe is also constructed using minimum bending energy, parametric curves with additionally normals varying along them. The spline approximations over the triangulation or curvilinear wireframe could be one of several forms: either low degree, implicit algebraic splines (triangular A-patches) or multivariate functional B-splines (B-patches) or standardized rational Bernstein?Bezier patches (RBB), or triangular rational B-Splines. The adaptive triangulation is additionally useful for a rapid display and animation of the implicit surface.

title: Low voltage test in place of fast clock in DDSI delay test
abstract: By testing the CUT at lower supply voltages, the CUT slows down and thus slow, low-cost testers can be used to perform DDSI (defect detection within slack intervals) tests. Apart from this, because the delay fault size is known in a DDSI test, this information can be further used to diagnose the causing mechanism behind the delay faults. Experimental results are presented to investigate the potential of the method.

title: Three-dimensional animated face modeling from stereo video
abstract: 3D modeling of human face has been an active research topic in computer vision and computer graphics communities. In this paper we develop a face-modeling system from calibrated stereo video input. The stereo configuration is chosen according to the characteristics of the face structure. For data capturing the subject sits in front of the calibrated stereo video cameras and rotates his/her head from front view to side view. Then we can create his/her 3D face model with realistic texture mapped, which is ready for MPEG-4 compatible facial animation, by adapting a generic wireframe model to the input. In deciding 3D face geometry we utilize two kinds of 2D information. One is the correspondence between stereo pair; the other is self-occluded contour. After some 3D points in the specific face are obtained from both image clues in different frames, RBF (Radius Basis Function) data interpolation is performed to decide its shape. Afterwards texture image is generated from the face geometry and video. Experiments show that satisfactory results can be reached with our system.

title: 3D model based expression tracking in intrinsic expression space
abstract: A method of learning the intrinsic facial expression space for expression tracking is proposed. First, a partial 3D face model is constructed from a trinocular image and the expression space is parameterized using MPEG4 FAP. Then an algorithm of learning the intrinsic expression space from the parameterized FAP space is derived. The resulted intrinsic expression space reduces even to 5 dimensions. We will show that the obtained expression space is superior to the space obtained by PCA. Then the dynamical model is derived and trained on this intrinsic expression space. Finally, the learned tracker is developed in a particle-filter-style tracking framework. Experiments on both synthetic and real videos show that the learned tracker performs stably over a long sequence and the results are encouraging.

title: Error analysis of pure rotation-based self-calibration
abstract: Self-calibration using pure rotation is a well-known technique and has been shown to be a reliable means for recovering intrinsic camera parameters. However, in practice, it is virtually impossible to ensure that the camera motion for this type of self-calibration is a pure rotation. In this paper, we present an error analysis of recovered intrinsic camera parameters due to the presence of translation. We derived closed-form error expressions for a single pair of images with nondegenerate motion; for multiple rotations for which there are no closed-form solutions, analysis was done through repeated experiments. Among others, we show that translation-independent solutions do exist under certain practical conditions. Our analysis can be used to help choose the least error-prone approach (if multiple approaches exist) for a given set of conditions.

title: Subject-independent natural action recognition
abstract: A primitive-based dynamic Bayesian networks are proposed for subject-independent natural action recognition. Inferred by high-level knowledge, primitives are distinctive features that describe the context information and the motion information representing human action as well as pose. Dynamic Bayesian networks could fuse multi-information so that many kinds of weak information could function as strong information for inference. The experimental results show that primitive-based dynamic Bayesian networks not only increase the recognition rate but also improve the robustness.