Convergence Analysis of Discrete Differential Geometry Operators over Surfaces
In this paper, we study the convergence property of several discrete schemes of the surface normal. We show that the arithmetic mean, area-weighted averaging, and angle-weighted averaging schemes have quadratic convergence rate for a special triangulation scenario of the surfaces. By constructing a counterexample, we also show that it is impossible to find a discrete scheme of normals that has quadratic convergence rate over any triangulated surface and hence give a negative answer for the open question raised by D.S.Meek and D.J. Walton. Moreover, we point out that one cannot build a discrete scheme for Gaussian curvature, mean curvature and Laplace-Beltrami operator that converges over any triangulated surface.

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: 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: 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: A probabilistic dynamic contour model for accurate and robust lip tracking
abstract: In this paper a new condensation style contour tracking method called probabilistic dynamic contour (PDC) is proposed for lip tracking: a novel mixture dynamic model is designed to represent shape more compactly and to tolerate larger motions between frames, a measurement model is designed to include multiple visual cues. The proposed PDC tracker has the advantage that it is conceptually general but effectively suitable for lip tracking with the designed dynamic and measurement model. The new tracker improves the traditional condensation style tracker in three aspects: Firstly, the dynamic model is partially derived from the image sequence, so the tracker does not need to learn the dynamics in advance. Secondly, the measurement model is easy to be updated during tracking, which avoids modeling the foreground object in prior. Thirdly, to improve the tracker's speed, a compact representation of shape and a noise model are proposed to reduce the samples required to represent the posterior distribution. An experiment on lip contour tracking shows that the proposed method tracks contours robustly as well as accurately compared to the existing tracking method.

title: Statistical modeling and conceptualization of natural images
abstract: Multi-level annotation of images is a promising solution to enable semantic image retrieval by using various keywords at different semantic levels. In this paper, we propose a multi-level approach to interpret and annotate the semantics of natural images by using both the dominant image components and the relevant semantic image concepts. In contrast to the well-known image-based and region-based approaches, we use the concept-sensitive salient objects as the dominant image components to achieve automatic image annotation at the content level. By using the concept-sensitive salient objects for image content representation and feature extraction, a novel image classification technique is developed to achieve automatic image annotation at the concept level. To detect the concept-sensitive salient objects automatically, a set of detection functions are learned from the labeled image regions by using support vector machine (SVM) classifiers with an automatic scheme for searching the optimal model parameters. To generate the semantic image concepts, the finite mixture models are used to approximate the class distributions of the relevant concept-sensitive salient objects. An adaptive EM algorithm has been proposed to determine the optimal model structure and model parameters simultaneously. In addition, a large number of unlabeled samples have been integrated with a limited number of labeled samples to achieve more effective classifier training and knowledge discovery. We have also demonstrated that our algorithms are very effective to enable multi-level interpretation and annotation of natural images.

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: 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: Acyclic domination on bipartite permutation graphs
abstract: For a graph G = (V, E), a subset S ⊆ V is called an acyclic dominating set of G if every vertex in V - S is adjacent to at least one vertex in S and the subgraph induced by S contains no cycles. In this paper, we present a linear time algorithm for transforming a minimum dominating set in a bipartite permutation graph into a minimum acyclic dominating set. Chao et al. gave a linear time algorithm to find a minimum dominating set of a permutation graph. Thus, we show that the acyclic domination problem is linear time solvable for bipartite permutation graphs.