7789266
LMT-skeleton heuristics for several new classes of optimal triangulations
Abstract Given a planar point set, we consider three classes of optimal triangulations: (1) the minimum weight triangulation with angular constraints (constraints on the minimum angle and the maximum angle in a triangulation), (2) the angular balanced triangulation which minimizes the sum of the ratios of the maximum angle to the minimum angle for each triangle, and (3) the area balanced triangulation which minimizes the variance of the areas of triangles in the triangulation. With appropriate definition of local optimality for each class, a simple unified method is established for the computation of the subgraphs of optimal triangulations. Computational experiments demonstrate that the method successfully identifies large portion of edges of the optimal triangulations of each class for all problem instances tested, and hence optimal triangulations for each class can be obtained from them by applying dynamic programming.
29567956
Curve reconstruction from noisy samples
359856
Curve reconstruction from noisy samples
We present an algorithm to reconstruct a collection of disjoint smooth closed curves from n noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation of each point in the normal direction with a magnitude smaller than the minimum local feature size. The reconstruction is faithful with a probability that approaches 1 as n increases.We expect that our approach can lead to provable algorithms under less restrictive noise models and for handling non-smooth features.
16505104
Approximate minimum weight Steiner triangulation in three dimensions
ApproximateMinimumWeightSteinerTriangulationinThreeDimensionsSiu-WingChengyTamal K. DeyAbstractDicultyofminimumweighttriangulationap oinsetinR2is well known.In this pap er we study the minimumweight triangulation problem for p olyhedra and general ob-stacle set in three dimensions.The weight of a triangulationin three dimensionsis assumed to b e the total surface areaof alltrianglesinvolved.It isshownthat ap olyhedronPof sizencan b e triangulated withO(2log) tetrahedra intimeO(n2log3) approximating the minimum weight trian-gulation ofPwithin a constant factor. No such prior resultisknown.Thesameb oundsalsoholdfor a3Dp ointsettriangulationallowingSteiner p oints.We consider anothersetting called general obstacle set, where the convex hull ofa set ofntrianglesis triangulatedconforming to the inputtriangles.In thiscase we show thatour metho dpro ducesa triangulati onof sizeO(n3log) in time) ap-proximating the weight of the minimum wt triangulationwithin a constant factor. This is a considerable improvementover theO(n6) b ound known for this case [3]. It is shown in[3] that minimumweighttriangulationisgo o dfor averagecase ray sho oting in three dimensions.This further substan-tiates the signi cance of our result.1Intro ductionThe minimum weight triangulation (MWT) problem ismostwell-knownintheplane,whereatriangulationwiththeminimumtotaledgelengthissoughtfora2Dp ointset.Theproblemisnotknowntob eNP-hard but no p olynomial-time algorithm is known.Re-centlyanapproximation algorithm withconstantfac-tor p erformance guarantee has b een designed for MWTby Levcop oulos and Krznaric[10].In another versionof theproblem Steinerp ointsareallowed andamini-mum weight Steinertriangulation (MWST)among allp ossibleSteinertriangulationsisdesired.Inparticu-lar, MWT is also a Steiner triangulation but with zeroSteiner p oints.Eppstein [8] showed how to approximatethe MWST of a 2Dp oint set within a constant factor.Instead of a 2Dp oint set, general inputs such as planarstraight line graphs (PSLG) have also b eenconsideredDepartment of Computer Science, HKUST, Hong Kong.e-mail: scheng@cs.ust.hkyDepartmentofCSE,I ITKharagpur,Kharagpur721302,India. e-mail: dey@cse.iitkgp.ernet.infor their applications in ray sho oting [3, 7]. A triangula-tion of a PSLG is the decomp osition of the convex hullof its verticeswhere the input line segments app ear asedges.When Steiner p oints are allowed these segmentsmay app ear as union of edges.Aronov and Fortune [3]observe that the technique of [8] applies to this case topro duce a p olynomial size triangulation approximatingMWSTwithinaconstantfactor.Inthesp ecialcasewhen the input PSLG is a p olygon p ossibly with holes,Cheng and Lee [7] presented an algorithm with b oth sizeand running timeO(nlog), whereis the numb er ofedges.Thetriangulationofap ointsetin3Disthedecomp osition of its convex hull into disjoint tetrahedra.The weight of the triangulation is the sum of the area ofthe triangles in it.Instead of p oint sets, the input mayconsist of a set of triangles with disjoint relative interior,acounterpartofPSLGin3D.Inthissettingcalledgeneral obstacle set, a minimum weight triangulation ofthe convex hull is sought where the input triangles haeto b e conformed.A sp ecial case arises when the inputtrianglesformtheb oundaryofap olyhedronwhoseinterioristob etriangulatedwithminimumweight.Noticethattheformulationofminimumweighttriangulation problem in these cases must allow Steinerp oints since there are arrangements of triangles in threespace such as the b oundary of Schonardt p olyhedron forwhich no triangulation is p ossible without Steiner p oints[12].WeconsiderMWSTproblemforthreedi erentcategories of inputs:p olyhedra, p oint sets, and generalobstaclesets.Of course,thisleaves op entheproblemof MWT of a 3Dp oint set since a p oint set can alwaysb e triangulated without Steiner p oints.ResultonMWSTprobleminthreedimensionsisscarce.Eppstein, in his pap er [8], acknowledges the dif- culty of the problem and observes the obstacles in gen-eralizing a metho d working in two dimension. When thelengths of the edges are taken as weights, he shows thatthemetho dcanb emo di edtopro duceanO(logn)-factorapproximation toMWSTofap ointset.How-ever,withareasoftrianglestakenastheweights,metho d could not b e generalized.Aronov and Fortune[3], building up on the technique of Eppstein showed hotopro duceanO(n6)sizetriangulation approximatingthe MWST of a general obstacle set.They argued that1
2549315
Quality meshing with weighted Delaunay refinement
Delaunay meshes with bounded circumradius to shortest edge length ratio have been proposed in the past for quality meshing. The only poor quality tetrahedra called slivers that can occur in such a mesh can be eliminated by the sliver exudation method. This method has been shown to work for periodic point sets, but not with boundaries. Recently a randomized point-placement strategy has been proposed to remove silvers while conforming to a given boundary. In this paper we present a deterministic algorithm for generating a weighted Delaunay mesh which respects the input boundary and has no poor quality tetrahedron including silvers. This success is achieved by combining the weight pumping method for sliver exudation and the Delaunay refinement method for boundary conformation. We show that an incremental weight pumping can be mixed seamlessly with vertex insertions in our weighted Delaunay refinement paradigm.
5215240
Sliver exudation
A sliver is a tetrahedron whose four vertices lie close to a plane and whose projection to that plane is a convex quadrilateral with no short edge. Slivers are notoriously common in 3-dimensional Delaunay triangulations even for well-spaced point sets. We show that if the Delaunay triangulation has the ratio property introduced in [15] then there is an assignment of weights so the weighted Delaunay triangulation contains no slivers. We also give an algorithm to compute such a weight assignment.
2936245
On failure recoverability of client-server applications in mobile wireless environments
Analytical results for the Cdf of the failure recovery time for client-server applications in mobile wireless environments characterized by logging, and mobility handoff strategies for facilitating failure recovery are reported in the paper. The results can be applied to determine if a mobile application can satisfy its recoverability requirement upon a mobile host failure when operating under a set of parameter values characterizing the mobile application, the underlying client-server environment, and the logging & mobility handoff strategies adopted by the mobile application. Model parameters which affect the shape of the failure recovery time Cdf for two mobility handoff strategies, namely, Eager and Lazy, are identified, and their effects are analyzed, with numerical data and result interpretations given. A tradeoff analysis between the cost invested by these two mobility handoff strategies for maintaining the logging and checkpoint information before failure versus the return of investment in terms of improved failure recoverability is given, and the best checkpoint interval period that would yield the best return of investment for the eager mobility handoff strategy over the lazy strategy is identified.
9588683
Performance evaluation of an admission control algorithm: dynamic threshold with negotiation
An admission control algorithm for a multimedia server is responsible for determining if a new request can be accepted without violating the QoS requirements of the existing requests in the system. Most admission control algorithms treat every request uniformly and hence optimize the system performance by maximizing the number of admitted and served requests. In practice, requests might have different levels of importance to the system. Requests offering high contribution or reward to the system performance deserve priority treatment. Failure of accepting a high-priority request would incur high penalty to the system.A novel threshold-based admission control algorithm with negotiation for two priority classes of requests is proposed in our previous study. The server capacity is divided into three partitions based on the threshold values: one for each class of requests and one common pool shared by two classes of requests. Reward and penalty are adopted in the proposed system model. High-priority requests are associated with higher values of reward as well as penalty than low-priority ones. In this paper, given the characteristics of the system workload, the proposed analytical models aim to finds the best partitions, optimizing the system performance based on the objective function of the total reward minus the total penalty. The negotiation mechanism reduces the QoS requirements of several low-priority clients, by cutting out a small fraction of the assigned server capacity, to accept a new high-priority client and to achieve a higher net earning value. Stochastic Petri-Net model is used to find the optimal threshold values and two analytical methods are developed to find sub-optimal settings. The experiment results show that the sub-optimal solutions found by the proposed analytical methods are very close to optimal ones. The methods enable the algorithm to dynamically adjust the threshold values, based on the characteristics of the system workload, to achieve higher system performance.
15145046
A novel approach to diagnose diabetes based on the fractal characteristics of retinal images
A novel diagnostic scheme to develop quantitative indexes of diabetes is introduced in this paper. The fractal dimension of the vascular distribution is estimated because we discovered that the fractal dimension of a severe diabetic patient's retinal vascular distribution appears greater than that of a normal human's. The issue of how to yield an accurate fractal dimension is to use high-quality images. To achieve a better image-processing result, an appropriate image-processing algorithm is adopted in this paper. Another important fractal feature introduced in this paper is the measure of lacunarity, which describes the characteristics of fractals that have the same fractal dimension but different appearances. For those vascular distributions in the same fractal dimension, further classification can be made using the degree of lacunarity. In addition to the image-processing technique, the resolution of original image is also discussed here. In this paper, the influence of the image resolution upon the fractal dimension is explored. We found that a low-resolution image cannot yield an accurate fractal dimension. Therefore, an approach for examining the lower bound of image resolution is also proposed in this paper. As for the classification of diagnosis results, four different approaches are compared to achieve higher accuracy. In this study, the fractal dimension and the measure of lacunarity have shown their significance in the classification of diabetes and are adequate for use as quantitative indexes.
10474032
Dynamic quota-based admission control with sub-rating in multimedia servers
Abstract. An admission control algorithm for a multimedia server is responsible for determining if a new request can be accepted without violating the Quality of Service (QoS) requirements of the existing requests in the system. A novel quota-based admission control algorithm with sub-rating for two priority classes of requests is proposed in this study. The server capacity is divided into three partitions based on the quota values: one for each class of requests and one common pool shared by two classes of requests. Reward and penalty are adopted in the proposed system model. High-priority requests are associated with higher values of reward as well as penalty than low-priority ones. Given the characteristics of the system workload, the proposed algorithm finds the best partitions, optimizing the system performance based on the objective function of the total reward minus the total penalty. The sub-rating mechanism will reduce the QoS requirements of several low- priority clients, by cutting out a small fraction of the assigned server capacity, to accept a new high- priority client and to achieve a higher net earning value. A stochastic Petri-Net model is used to find the optimal quota values and two approximation approaches are developed to find sub-optimal settings. The experiment results show that the proposed algorithm performs better than one without sub-rating mechanism, and that the sub-optimal solutions found by the proposed approximation approaches are very close to optimal ones. The approximation approaches enable the algorithm to dynamically adjust the quota values, based on the characteristics of the system workload, to achieve higher system performance.
8002270
Audio coding and image denoising based on the nonuniform modulated complex lapped transform
Xiong and Malvar recently introduced a nonuniform modulated complex lapped transform (NMCLT) with good time-localization and controllable frequency resolution by using an oversampled nonuniform filter bank to generate its real and the imaginary components. In this paper, we first show that oversampling in the NMCLT is not necessary in theory but a by-product of fast implementation in practice. We also point out that the amount of oversampling, which can be flexibly controlled, depends on the application. We then describe in detail the implementation of the inverse transform, which was not addressed clearly by Xiong and Malvar. We present the first applications of the NMCLT to audio coding and image denoising. A scalable audio coder has been implemented by controlling the amount of oversampling and exploiting redundancy among the NMCLT coefficients via predictive coding. Experimental results show that the audio coder reduces pre-echoes and improves the sound quality of audio clips with transient sounds. A simple denoising algorithm based on the NMCLT has also been devised to provide images with better visual quality than those obtained with wavelet-based soft thresholding.