7654975
Using low-discrepancy sequences and the Crofton formula to compute surface areas of geometric models
The surface area of a geometric model, like its volume, is an important integral property that needs to be evaluated frequently and accurately in practice. In this paper, we present a new quasi-Monte Carlo method using low-discrepancy sequences for computing the surface area of a 3D object. We show that the new method is more efficient than a Monte Carlo method using pseudo-random numbers. This method is based on the Cauchy ‐ Crofton formula from integral geometry, and it computes the surface area of a 3D body B by counting the number of intersection points between the boundary surface of B and a set of straight lines in E 3 . Low discrepancy sequences are used to generate the set of lines in E 3 to reduce the estimation errors that would be caused by using statistically uniformly distributed lines. We study and compare two different methods for generating 3D random lines, and demonstrate their validity theoretically and experimentally. Experiments suggest that the new quasi-Monte Carlo method is also more efficient than the conventional approach based on surface tessellation. q 2002 Elsevier Science Ltd. All rights reserved.
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.
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.
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.
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.
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.
33099797
Compression of cDNA and inkjet microarray images
Microarray image technology is a powerful tool for monitoring the expression of thousands of genes simultaneously. Each microarray experiment produces immense amounts of image data, and efficient storage and transmission requires compression that utilizes the microarray image's structure and unique analysis goals. We have developed a progressive compression scheme for microarray images which can be either lossy or lossless. Our scheme has a coded data structure that allows fast decoding and reprocessing of image subsets, and includes summary statistics and image segmentation information. Since visual fidelity is not the end goal for microarray images, we introduce a new measure of distortion for lossy compression: the sensitivity of microarray information extraction to compression loss. We find that a lossy compression ratio of 8:1 for cDNA microarrays minimally affects downstream processing. The average lossless compression ratio is 1.83:1 for cDNA images and 2.43:1 for inkjet images, comparable to state-of-the-art lossless schemas, yet with added flexibility and information.
3251955
Containment join size estimation: models and methods
Recent years witnessed an increasing interest in researches in XML, partly due to the fact that XML has now become the de facto standard for data interchange over the internet. A large amount of work has been reported on XML storage models and query processing techniques. However, few works have addressed issues of XML query optimization. In this paper, we report our study on one of the challenges in XML query optimization: containment join size estimation. Containment join is well accepted as an important operation in XML query processing. Estimating the size of its results is no doubt essential to generate efficient XML query processing plans. We propose two models, the interval model and the position model, and a set of estimation methods based on these two models. Comprehensive performance studies were conducted. The results not only demonstrate the advantages of our new algorithms over existing algorithms, but also provide valuable insights into the tradeoff among various parameters.
884789
A Fast Algorithm for Approximate Quantiles in High Speed Data Streams
We present a fast algorithm for computing approximate quantiles in high speed data streams with deterministic error bounds. For data streams of size N where N is unknown in advance, our algorithm partitions the stream into sub-streams of exponentially increasing size as they arrive. For each sub-stream which has a fixed size, we compute and maintain a multi-level summary structure using a novel algorithm. In order to achieve high speed performance, the algorithm uses simple block-wise merge and sample operations. Overall, our algorithms for fixed-size streams and arbitrary-size streams have a computational cost of O(N log(1/epsivlogepsivN)) and an average per-element update cost of O(log logN) if epsiv is fixed.
12276338
User-oriented reliability modeling for a Web system
We develop a user-oriented reliability model, a simple yet effective approach, to address huge amounts of Web contents, and more importantly tackle users' dynamic navigation behaviors for a Web system. The users' intrinsic capabilities and behaviors, unlike programs' common recurring behaviors, call for a new approach for modeling the reliability of an organization's Web system. Our approach differs in the modeling scope of the Web system and the means of modeling user behaviors. We exploit the idea of cyclomatic complexity to cover the maximum number of independent paths, which overcome the less likely repetitive user navigations, and still maintain the dynamic nature of Web surfing. The modeling process takes Web senders' access, error, and referrer information as inputs, and translates them into a flow graph. A transition tree is then derived from the flow graph, based on depth-first traversal and dynamic programming. Accordingly, the reliability of the Web system can be computed by excluding those unreliable paths. This model is further applied to prioritize the error removal sequence to assist in allocating resources and effort.
17218997
Profiling program behavior for anomaly intrusion detection based on the transition and frequency property of computer audit data
Intrusion detection is an important technique in the defense-in-depth network security framework. In recent years, it has been a widely studied topic in computer network security. In this paper, we present two methods, namely, the Hidden Markov Models (HMM) method and the Self Organizing Maps (SOM) method, to profile normal program behavior for anomaly intrusion detection based on computer audit data. The HMM method utilizes the transition property of events while SOM method relies on the frequency property of events. Two data sets, CERT synthetic Sendmail system call data collected in the University of New Mexico (UNM) and Live FTP system call data collected in the CNSIS lab of Xi'an Jiaotong University, were used to assess the two methods. Testing results show that the HMM method using the transition property of events produces good detection performance while high computational expense is required both for training and detection. The HMM method is better than other two methods reported previously in terms of detection accuracy for the same data set. The SOM method considering the frequency property of events, on the other hand, is suitable for real-time intrusion detection because of its capability of processing a large amount of data with low computational overhead.