Discrete Laplace-Beltrami operators and their convergence
The convergence property of the discrete Laplace-Beltrami operators is the foundation of convergence analysis of the numerical simulation process of some geometric partial differential equations which involve the operator. In this paper we propose several simple discretization schemes of Laplace-Beltrami operators over triangulated surfaces. Convergence results for these discrete Laplace-Beltrami operators are established under various conditions. Numerical results that support the theoretical analysis are given. Application examples of the proposed discrete Laplace-Beltrami operators in surface processing and modelling are also presented.

title: Smooth Shell Construction with Mixed Prism Fat Surfaces
abstract: Several naturally occurring as well as manufactured objects have shell like structures, that is their boundaries consist of surfaces with thickness. In an earlier paper, we have provided a reconstruction algorithm for such shell structures using smooth fat surfaces within three-sided prisms. In this paper, we extend the approach to a scaffolding consisting of three and four-sided prisms. Within each prism the constructed function is converted to a spline representation. In addition to the adaptive feature of our earlier scheme, the new scheme has the following extensions: (a) four sided fat patches are employed; (b) the size of individual fat patches are bigger; (c) fairing techniques are combined to obtain nicely shaped fat surfaces.

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: 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: 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: Directional smoothing of triangular meshes
abstract: In this paper, we propose a so-called directional smoothing method based mean curvature flow. The selection of the diffusion direction is based on the descent of some energy functional. We show that the directional diffusion flow is volume-preserving. Based on the local directional diffusion flow, we present a feature-preserving smoothing method. Finally, we provide a series of examples to graphically demonstrate the quality of our results.

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: Delay Defect Characterization Using Low Voltage Test
abstract: For nanometer designs, many subtle defects lead to excessive delays in signal paths that cause reliability concerns. Traditional test-based diagnosis methods can only identify the failing nodes without the capability to tell the defect nature behind the observed delay faults. This differentiation is important for gathering accurate defect statistics for process improvement during yield ramp-up. In this paper we presented an effective delay defect analysis methodology that can quickly categorize the delay defects into either transistor related defects or resistive interconnect defects. The new delay defect/failure characterization method is based on low voltage test and delay defect detection in slack interval (DDSI) method. Experimental results were presented to validate the effectiveness of the new method. Practical considerations were also addressed for adoption of the methodology.

title: VISATRAM: a real-time vision system for automatic traffic monitoring
abstract: This paper presents a novel approach to automatic traffic monitoring using 2D spatio-temporal images. A TV camera is mounted above a highway to monitor the traffic through two slice windows, and a panoramic view image and an epipolar plane image are formed for each lane. Our real-time vision system for automatic traffic monitoring, VISATRAM, is an inexpensive system with a PC486 and a frame grabber. The system cannot only count vehicles and estimate their speeds but also classify them using 3D measurements. The system has been tested with real road images under various light conditions, including shadows in daytime and lights at night.

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.

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.