6255110
Computing real inflection points of cubic algebraic curves
Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inflection points of a planar cubic algebraic curve f = 0 by directly intersecting f = 0 and its Hessian curve H(f) = 0 requires solving a degree nine univariate polynomial equation, and thus is relatively inefficient. In this paper we present an algorithm for computing the real inflection points of a real planar cubic algebraic curve. The algorithm follows Hilbert's solution for computing the inflection points of a cubic algebraic curve in the complex projective plane. Hilbert's solution is based on invariant theory and requires solving only a quartic polynomial equation and several cubic polynomial equations. Through a detailed study with emphasis on the distinction between real and imaginary inflection points, we adapt Hilbert's solution to efficiently compute only the real inflection points of a cubic algebraic curve f = 0, without exhaustive but unnecessary search and root testing. To compute the real inflection points of f = 0, only two cubic polynomial equations need to be solved in our algorithm and it is unnecessary to solve numerically the quartic equation prescribed in Hilbert's solution. In addition, the invariants of f = 0 are used to analyze the singularity of a singular curve, since the number of the real inflection points of f = 0 depends on its singularity type.
16675497
Revisiting the [mu]-basis of a rational ruled surface
The µ-basis of a rational ruled surface P(s,t) = P0(s) + tP1(s) is defined in Chen et al. (Comput. Aided Geom. Design 18 (2001) 61) to consist of two polynomials p(x, y, z, s) and q(x, y, z, s) that are linear in x, y, z. It is shown there that the resultant of p and q with respect to s gives the implicit equation of the rational ruled surface; however, the parametric equation P(s, t) of the rational ruled surface cannot be recovered from p and q. Furthermore, the µ-basis thus defined for a rational ruled surface does not possess many nice properties that hold for the µ-basis of a rational planar curve (Comput. Aided Geom. Design 18 (1998) 803). In this paper, we introduce another polynomial r(x, y, z, s, t) that is linear in x, y, z and t such that p, q, r can be used to recover the parametric equation P(s, t) of the rational ruled surface; hence, we redefine the µ-basis to consist of the three polynomials p, q, r. We present an efficient algorithm for computing the newly-defined µ-basis, and derive some of its properties. In particular, we show that the new µ-basis serves as a basis for both the moving plane module and the moving plane ideal corresponding to the rational ruled surface.
2992545
Constrained 3D shape reconstruction using a combination of surface fitting and registration
We investigate 3D shape reconstruction from measurement data in the presence of constraints. The constraints may fix the surface type or set geometric relations between parts of an object's surface, such as orthogonality, parallelity and others. It is proposed to use a combination of surface fitting and registration within the geometric optimization framework of squared distance minimization (SDM). In this way, we obtain a quasi-Newton like optimization algorithm, which in each iteration simultaneously registers the data set with a rigid motion to the fitting surface and adapts the shape of the fitting surface. We present examples to show the applicability of our method to constrained 3D shape fitting for reverse engineering of CAD models and to high accuracy fitting with kinematic surfaces, which include surfaces of revolution (reconstructed from fragments of archeological pottery) and spiral surfaces, which are fitted to 3D measurement data of shells. Our optimization algorithm can combine registration of multiple scans of an object and model fitting into a single optimization process which is shown to be superior to the traditional procedure, which first registers the data and then fits a model to it.
45794206
Rational Quadratic Parameterizations of Quadrics
Every irreducible quadric in E3 has infinitely many different rational quadratic parameterizations. These parameterizations and the relationships between them are investigated. It is shown that every faithful rational quadratic parameterization of a quadric can be generated by a stereographic projection from a point on the quadric, called the center of projection (COP). Two such parameterizations for the same quadric are related by a rational linear reparameterization if they have the same COP; otherwise they are related by a rational quadratic reparameterization. We also consider unfaithful parameterizations for which, in general, a one-to-one correspondence between points on the surface and parameters in the plane does not exist. It is shown that all unfaithful rational quadratic parameterizations of a properly degenerate quadric can be characterized by a simple canonical form, and there exist no unfaithful rational quadratic parameterizations for a nondegenerate quadric. In addition, given a faithful rational quadratic parameterization of a quadric, a new technique is presented to compute its base points and inversion formula. These results are applied to solve the problems of parameterizing the intersection of two quadrics and reparameterizing a given quadric parameterization with respect to a different COP without implicitization.
14471402
Computing quadric surface intersections based on an analysis of plane cubic curves
Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve is computed first and the intersection curve of the two quadrics is then found by transforming the cubic curve by a rational quadratic mapping. Topological classification and parameterization of the intersection curve are achieved by invoking results from algebraic geometry on plane cubic curves. 2003 Elsevier Science (USA). All rights reserved.
7101460
On the Difference Method for Drawing Conic Arcs
Abstract The difference method is an efficient way to generate an inscribed polygon of a conic section. We address the implementation issues of the difference method, that is, how to choose the difference parameter and initial points so that the inscribed polygon has a minimal number of line segments and is within a given tolerance of the conic arc. We also discuss how the difference method can be used to draw conic arcs represented by rational quadratic Bezier curves.
33629250
Robust Visual Tracking Via Incremental Maximum Margin Criterion
Robust visual object tracking is one of the key problems in computer vision. Subspace based tracking method is a promising approach in handling appearance variability. Linear Discriminant Analysis(LDA) has been applied to this problem, but LDA is not a stable algorithm especially for visual tracking. Maximum Margin Criterion(MMC) is a recently proposed discriminant criterion. Its promising specialities make it a better choice for the tracking problem. In this paper, we present a novel subspace tracking algorithm based on MMC. We also proposed an incremental version of the corresponding algorithm so that the tracker can update in realtime. Experiments show our tracking algorithm is able to track objects well under large lighting, pose and expression variation.
8024755
On Demand Phenotype Ranking through Subspace Clustering
High throughput biotechnologies have enabled scientists to collect a large number of genetic and phenotypic attributes for a large collection of samples. Computational methods are in need to analyze these data for discovering genotype-phenotype associations and inferring possible phenotypes from genotypic attributes. In this paper, we study the problem of on demand phenotype ranking. Given a query sample, for which only its genetic information is available, we want to predict the possible phenotypes it may have, ranked in descending order of their likelihood. This problem is challenging since genotype-phenotype databases are updated often and explicitly mine and maintain all patterns is impractical. We propose an on-demand ranking algorithm that uses a modified pattern-based subspace clustering algorithm to effectively identify the subspaces where these relevant clusters may reside. Using this algorithm, we can compute the clusters and their prediction significance for any phenotypes on the fly. Our experiments demonstrate the efficiency and effectiveness of our algorithm.
3416923
Efficient Computation of the Skyline Cube
Skyline has been proposed as an important operator for multi-criteria decision making, data mining and visualization, and user-preference queries. In this paper. we consider the problem of efficiently computing a SKYCUBE, which consists of skylines of all possible non-empty subsets of a given set of dimensions. While existing skyline computation algorithms can be immediately extended to computing each skyline query independently, such "shared-nothing" algorithms are inefficient. We develop several computation sharing strategies based on effectively identifying the computation dependencies among multiple related skyline queries. Based on these sharing strategies, two novel algorithms, Bottom-Up and Top-Down algorithms, are proposed to compute SKYCUBE efficiently. Finally, our extensive performance evaluations confirm the effectiveness of the sharing strategies. It is shown that new algorithms significantly outperform the naive ones.
68223
Off-line Chinese signature verification based on support vector machines
This paper proposes a novel off-line Chinese signature verification method based on support vector machines. The method uses both static features and dynamic features. The static features include moment features and 16-direction distribution (an improvement on 4-direction distribution). The dynamic features include gray distribution and stroke width distribution. At last, support vector machine is used to classify the signatures. The main steps of constructing a signature verification system are discussed and experiments on real data sets show that the average error rate can reach 5%, which is obviously satisfactory. w that the average error rate can reach 5%, which is obviously satisfactory.
19971560
Successfully Adopting IT for Social Welfare Program Management
In DGO 2003, we first introduced the long-standing Work First project that is inter-disciplinary between social work and computer science at the University of North Carolina at Chapel Hill (UNC-CH) with the collaboration of the North Carolina Department of Health and Human Services (NC DHHS). Based on the success in our Work First project, the NC DHHS and UNC-CH have extended the collaboration to work on a similar project to assist in the evaluation of changes to the Food Stamp employment and training (E&T) program in North Carolina. In this paper, we reflect on our experience to discuss some important aspects of successfully adopting information technology in government agencies in order to replicate them in the new Food Stamp project.