Regular algebraic curve segments (I) - Definitions and characteristics
In this paper (part one of a trilogy), we introduce the concept of a discriminating family of regular algebraic curves (real, nonsingular and connected). Several discriminating families are obtained which yield different characterizations of the Bernstein–Bezier (BB) bivariate polynomials over the plane triangle and the quadrilateral domain such that their zero contours are smooth and connected. These regular curve segments in BB basis can be smoothly joined together to form algebraic curve splines or A-splines. Algorithms for the efficient graphics display of these new A-spline families are also provided.

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: 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: 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: 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: Smart Remote Classroom: Creating a Revolutionary Real-Time Interactive Distance Learning System
abstract: Real-time interactive virtual classroom is an important type of distance learning. However currently available systems are insufficient in the support of large-scale user access, and neither can they accommodate accessing with heterogeneous devices and networks. Furthermore, these systems are usually desktop-based, which results that the teachers' experience is completely different from teaching in a real classroom. The Smart Remote Classroom project tackles these difficulties through the development of the following technologies: 1) A hybrid application-layer Multicast protocol called TORM and an Adaptive Content Delivery scheme called AMTM. Together they enable large-scale users to access a virtual classroom with different devices and networks at the same time. 2) A dedicated software called SameView, which take use of the proposed TORM and AMTM technology and provide a rich set of functions for teachers and students to efficiently carry out the real-time interactive distance learning. Moreover, SameView can record the whole process of a class into a compound multimedia document for later retrieval and review of the class. 3) An augmented classroom called Smart Classroom, where the user interface of the SameView for the teacher are distributed in and fused with the room space. Thus the teacher can instruct the remote students just like teaching face-to-face in a conventional classroom. All these technologies has been successfully integrated and demonstrated in the prototype system.

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: 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: Power domination in block graphs
abstract: The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known domination problem in graphs. In 2002, Haynes et al. considered the graph theoretical representation of this problem as a variation of the domination problem. They defined a set S to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The power domination number γp(G) of a graph G is the minimum cardinality of a power dominating set of G. This problem was proved NP-complete even when restricted to bipartite graphs and chordal graphs. In this paper, we present a linear time algorithm for solving the power domination problem in block graphs. As an application of the algorithm, we establish a sharp upper bound for power domination number in block graphs and characterize the extremal graphs.