Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
In this paper, we study the convergence property of a well known discretized scheme for approximating Gaussian curvature, derived from Gauss-Bonnet theorem, over triangulated surface. Suppose the triangulation is obtained from a sampling of a smooth parametric surface, we show theoretically that the approximation has quadratic convergence rate if the surface sampling satisfies the so-called parallelogram criterion. Numerical results which justify the theoretical analysis are also presented.

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: 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: 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: 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: 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: 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: Learning object intrinsic structure for robust visual tracking
abstract: In this paper, a novel method to learn the intrinsic object structure for robust visual tracking is proposed. The basic assumption is that the parameterized object state lies on a low dimensional manifold and can be learned from training data. Based on this assumption, firstly we derived the dimensionality reduction and density estimation algorithm for unsupervised learning of object intrinsic representation, the obtained non-rigid part of object state reduces even to 2 dimensions. Secondly the dynamical model is derived and trained based on this intrinsic representation. Thirdly the learned intrinsic object structure is integrated into a particle-filter style tracker. We will show that this intrinsic object representation has some interesting properties and based on which the newly derived dynamical model makes particle-filter style tracker more robust and reliable. Experiments show that the learned tracker performs much better than existing trackers on the tracking of complex non-rigid motions such as fish twisting with self-occlusion and large inter-frame lip motion. The proposed method also has the potential to solve other type of tracking problems.

title: Delay Test Scan Flip-Flop: DFT for High Coverage Delay Testing
abstract: Scan based delay testing is currently mostly implemented using launch-on-capture (LOC) delay tests. Launch-on-shift (LOS) tests are generally more effective, achieving higher fault coverage with significantly fewer test vectors, but require a fast scan enable, which is not supported by most designs. The paper presents low cost solution for implementing LOS tests by adding a small amount of logic (six transistors) in each flip-flop to align the slow scan enable signal to the clock edge. The new design can support full LOS and LOC testing, achieving an average TDF coverage of 92.67% in this combined mode for the ISCAS89 benchmarks. Adding a second slow global scan enable signal also allows mixed LOC/LOS tests, which can further increase coverage up to 94.86% on average for ISCAS89 benchmarks

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.