Spline Approximations of Real Algebraic Surfaces
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: 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: 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: 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: Nurbs Approximation of A-Splines and A-Patches
abstract: Given A-spline curves and A-patch surfaces that are implicitly defined on triangles and tetrahedra, we determine their NURBS representations. We provide a trimmed NURBS form for A-spline curves and a parametric tensor-product NURBS form for A-patch surfaces. We concentrate on cubic A-patches, providing a C1-continuous surface that interpolates a given triangulation together with surface normals at the vertices. In many cases we can generate cubic trimming curves that are rationally parametrizable on the triangular faces of the tetrahedra; for the remaining faces we resort to using quadratic curves, which are always rationally parametrizable, to approximate the cubic trimming curves.

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: A Speaker Tracking Algorithm Based on Audio and Visual Information Fusion Using Particle Filter
abstract: Object tracking by sensor fusion has become an active research area in recent years, but how to fuse various information in an efficient and robust way is still an open problem. This paper presents a new algorithm for tracking speaker based on audio and visual information fusion using particle filter. A closed-loop architecture with reliability of each individual tracker is adopted, and a new method for data fusion and reliability adjustment is proposed. Experiments show the new algorithm is efficient in fusing information and robust to noise.

title: Efficient Algorithms for Determining 3-D Bi-Plane Imaging Geometry
abstract: Biplane projection imaging is one of the primary methods for imaging and visualizing the cardiovascular system in medicine. A key problem in such a technique is to determine the imaging geometry (i.e., the relative rotation and translation) of two projections so that the 3-D structure can be accurately reconstructed. Based on interesting observations and efficient geometric techniques, we present in this paper new algorithmic solutions for this problem. Comparing with existing optimization-based approaches, our techniques yield better accuracy and have bounded execution time, thus is more suitable for on-line applications. Our techniques can easily detect outliers to further improve the accuracy.

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: Hidden Markov Model Based Events Detection in Soccer Video
abstract: This paper presents an algorithm developed based on hidden Markov model for cues fusion and event inference in soccer video. Four events, shoot, foul, offside and normal playing, are defined to be detected. The states of the events are employed to model the observations of the five cues, which are extracted from the shot sequences directly. The experimental results show the algorithm is effective and robust in inferring events from roughly extracted cues.