Error bounded regular algebraic spline curves
i=0 Pn n=0 bijB m i (u)B n j (v) of bi-degree (m;n) has total degree m + n, however, the class of Gmn(u; v) is a subset of polynomials of total degree m + n. G (resp G) continuity implies curve segments share the same tangent(curvature) at join points(knots). In each of the G and G constructions, we develop a spline curve family whose member satis es given interpolation conditions. Each family depends on one free parameter that is related linearly to coe cients of Gmn(u; v). Compared with A-spline segments de ned in triangular (barycentric) BB-form , these algebraic curve segments in tensor product form have the following distinct features: (a) They are easy to construct. The coe cients of the bivariate polynomial that de ne the curve are explicitly given. (b) There exist convenient geometric control handles to locally modify the shape of the curve, essential for interactive curve design.  Each curve segment of the spline curve has either no in ection points if the corresponding edge is convex, or one in ection point otherwise, and the join points of the curve segments are not in ection points.  Since the required bi-degree (m;n) for G and G is low(in this paper, minfm;ng 2), the curve can be evaluated and displayed extremely fast. We explore both display via parameterization as well as recursive subdivision techniques(see [11]). (f) In the six spline families we discuss in sections 2 and 3, there are four cases with minfm;ng = 1. In these cases, rational parametric expressions are easily derived. Hence, for

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: 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: 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: 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: 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: Multi-cue-based face and facial feature detection on video segments
abstract: An approach is presented to detect faces and facial features on a video segment based on multi-cues, including gray-level distribution, color, motion, templates, algebraic features and so on. Faces are first detected across the frames by using color segmentation, template matching and artificial neural network. A PCA-based (Principal Component Analysis) feature detector for still images is then used to detect facial features on each single frame until the resulting features of three adjacent frames, named as base frames, are consistent with each other. The features of frames neighboring the base frames are first detected by the still-image feature detector, then verified and corrected according to the smoothness constraint and the planar surface motion constraint. Experiments have been performed on video segments captured under different environments, and the presented method is proved to be robust and accurate over variable poses, ages and illumination conditions.

title: Low voltage test in place of fast clock in DDSI delay test
abstract: By testing the CUT at lower supply voltages, the CUT slows down and thus slow, low-cost testers can be used to perform DDSI (defect detection within slack intervals) tests. Apart from this, because the delay fault size is known in a DDSI test, this information can be further used to diagnose the causing mechanism behind the delay faults. Experimental results are presented to investigate the potential of the method.

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: 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.