Regular algebraic curve segments (II) - Interpolation and approximation
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: Quality meshing of implicit solvation models of biomolecular structures
abstract: This paper describes a comprehensive approach to construct quality meshes for implicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, a smooth volumetric electron density map is constructed from atomic data using weighted Gaussian isotropic kernel functions and a two-level clustering technique. This enables the selection of a smooth implicit solvation surface approximation to the Lee-Richards molecular surface. Next, a modified dual contouring method is used to extract triangular meshes for the surface, and tetrahedral meshes for the volume inside or outside the molecule within a bounding sphere/box of influence. Finally, geometric flow techniques are used to improve the surface and volume mesh quality. Several examples are presented, including generated meshes for biomolecules that have been successfully used in finite element simulations involving solvation energetics and binding rate constants.

title: Convergence Analysis of Discrete Differential Geometry Operators over Surfaces
abstract: 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: A subdivision scheme for hexahedral meshes
abstract: In a landmark paper, Catmull and Clark described a simple generalization of the subdivision rules for bi-cubic B-splines to arbitrary quadrilateral surface meshes. This subdivision scheme has become a mainstay of surface modeling systems. Joy and MacCracken described a generalization of this surface scheme to volume meshes. Unfortunately, little is known about the smoothness and regularity of this scheme due to the complexity of the subdivision rules. This paper presents an alternative subdivision scheme for hexahedral volume meshes that consist of a simple split and average algorithm. Along extraordinary edges of the volume mesh, the scheme provably converges to a smooth limit volume. At extraordinary vertices, the authors supply strong experimental evidence that the scheme also converges to a smooth limit volume. The scheme automatically produces reasonable rules for non-manifold topology and can easily be extended to incorporate boundaries and embedded creases expressed as Catmull–Clark surfaces and B-spline curves.

title: Hierarchical multiresolution reconstruction of shell surfaces
abstract: We present an adaptive, hierarchical Hh-multiresolution reconstruction algorithm to model shell surface objects from a matched pair of triangulated surfaces. Shell surfaces are an interval of contours of trivariate functions with prismatic support. In the H-direction, a hierarchical representation of the scaffold is constructed. For any adaptively extracted scaffold from the hierarchy, a sequence of functions in the h-direction (regularly subdivided mesh) is constructed so that their contours approximate the input shell to within a given error e. The shell surfaces can be made to capture sharp curve creases on the shell while being C1 smooth everywhere else. Using an interval of iso-contours of smooth trivariate spline functions, rather than a pair of inner and outer surface splines, one avoids the need for interference checks between the inner and outer surface boundaries.

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: Efficient Fourier-Based Approach for Detecting Orientations and Occlusions in Epipolar Plane Images for 3D Scene Modeling
abstract: This paper presents a Fourier-based approach for automatically constructing a 3D panoramic model of a natural scene from a video sequence. The video sequences could be captured by an unstabilized camera mounted on a moving platform on a common road surface. As the input of the algorithms, “seamles” panoramic view images (PVIs) and epipolar plane images (EPIs) are generated after image stabilization if the camera is unstabilized. A novel panoramic EPI analysis method is proposed that combines the advantages of both PVIs and EPIs efficiently in three important steps: locus orientation detection in the Fourier frequency domain, motion boundary localization in the spatio-temporal domain, and occlusion/resolution recovery only at motion boundaries. The Fourier energy-based approaches in literature were usually for low-level local motion analysis and are therefore not accurate for 3D reconstruction and are also computationally expensive. Our panoramic EPI analysis approach is both accurate and efficient for 3D reconstruction. Examples of layered panoramic representations for large-scale 3D scenes from real world video sequences are given.

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.

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.