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.
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.
205873026
Control point adjustment for B-spline curve approximation
Pottmann et al. propose an iterative optimization scheme for approximating a target curve with a B-spline curve based on square distance minimization, or SDM. The main advantage of SDM is that it does not need a parameterization of data points on the target curve. Starting with an initial B-spline curve, this scheme makes an active B-spline curve converge faster towards the target curve and produces a better approximating B-spline curve than existing methods relying on data point parameterization. However, SDM is sensitive to the initial B-spline curve due to its local nature of optimization. To address this, we integrate SDM with procedures for automatically adjusting both the number and locations of the control points of the active spline curve. This leads to a method that is more robust and applicable than SDM used alone. Furthermore, it is observed that the most time consuming part of SDM is the repeated computation of the foot-point on the target curve of a sample point on the active B-spline curve. In our implementation, we speed up the foot-point computation by pre-computing the distance field of the target curve using the Fast Marching Method. Experimental examples are presented to demonstrate the effectiveness of our method. Problems for further research are discussed. q 2003 Elsevier Ltd. All rights reserved.
28890
Extension of Lower Probabilities and Coherence of Belief Measures
Coherence is an important concept which is introduced and discussed in a new mathematics branch, Imprecise Probability Theory. By using the Choquet integral, belief measures can be extended to be coherent lower previsions on the linear space consisting of all bounded functions. As a special case, we establish that all belief measures are coherent imprecise probabilities.
9409183
A Novel Hybrid Approach to the Permutation Problem of Frequency Domain Blind Source Separation
We explore the permutation problem of frequency domain blind source separation (BSS). Based on performance analysis of three approaches: exploiting spectral continuity, exploiting time envelope structure and beamforming alignment; we present a new hybrid method which incorporates a psychoacoustic filtering process for the misaligned permutations unable to be delt with by these approaches. We use a sub- space based method (MUSIC) rather than conventional beamforming for the accurate estimation of the direction of arrivals (DOAs) of the source components, and a frequency dependent distance for the correla- tion of time envelopes. The proposed methods are compared with other approaches by signal to interference ratio (SIR) evaluation, and the new hybrid approach is shown to have the best performance.
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.
9952702
Equitable Total Coloring of Graphs with Maximum Degree 3
Abstract. The equitable total chromatic number χrdquo;e(G) of a graph G is the smallest integer k for which G has a total k-coloring such that the number of vertices and edges in any two color classes differ by at most one. We prove in this paper that χrdquo;e(G)≤5 if G is a multigraph with maximum degree at most 3.
9332288
Choosability, Edge Choosability, and Total Choosability of Outerplane Graphs
Let ?l(G),?l? (G),?l?? (G), and ?(G) denote, respectively, the list chromatic number, the list chromatic index, the list total chromatic number, and the maximum degree of a non-trivial connected outerplane graph G. We prove the following results. (1) 2 ??l(G) ? 3 and?l (G) = 2 if and only if G is bipartite with at most one cycle. (2)?(G) ??l?(G) ??(G) + 1 and?l? (G) =?(G) + 1 if and only if G is an odd cycle. This proves the well-known list edge coloring conjecture for outerplane graphs. (3)?l??(G) =?(G) + 1 if ?(G) ? 4 and ?l??(G) ? 5 if ?(G) ? 3. This proves a conjecture of O. V. Borodin, A. V. Kostochka and D. R. Woodall, List edge and list total coloring of multigraphs, J. Comb. Theory B, 71 (1997), 184?204 for outerplane graphs.