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.
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.
3170428
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
Computing a curve to approximate data points is a problem encountered frequently in many applications in computer graphics, computer vision, CAD/CAM, and image processing. We present a novel and efficient method, called squared distance minimization (SDM), for computing a planar B-spline curve, closed or open, to approximate a target shape defined by a point cloud, that is, a set of unorganized, possibly noisy data points. We show that SDM significantly outperforms other optimization methods used currently in common practice of curve fitting. In SDM, a B-spline curve starts from some properly specified initial shape and converges towards the target shape through iterative quadratic minimization of the fitting error. Our contribution is the introduction of a new fitting error term, called the squared distance (SD) error term, defined by a curvature-based quadratic approximant of squared distances from data points to a fitting curve. The SD error term faithfully measures the geometric distance between a fitting curve and a target shape, thus leading to faster and more stable convergence than the point distance (PD) error term, which is commonly used in computer graphics and CAGD, and the tangent distance (TD) error term, which is often adopted in the computer vision community. To provide a theoretical explanation of the superior performance of SDM, we formulate the B-spline curve fitting problem as a nonlinear least squares problem and conclude that SDM is a quasi-Newton method which employs a curvature-based positive definite approximant to the true Hessian of the objective function. Furthermore, we show that the method based on the TD error term is a Gauss-Newton iteration, which is unstable for target shapes with high curvature variations, whereas optimization based on the PD error term is the alternating method that is known to have linear convergence.
15982467
On intrinsic representations of 3D polygons for shape blending
Abstract An intrinsic representation of a geometric object comprises a set of parameters that are invariant under Euclidean transformations and determine the shape and size of the object uniquely. Unlike the case of a two-dimensional polygon which has essentially only one intrinsic representation, a three-dimensional (3D) polygon allows several variations. We study three different intrinsic representations of a 3D polygon, focusing on properties regarding their applications in shape blending. We show that only one of these representations, which is a natural extension to the intrinsic functions of a 3D differentiable curve, is suitable for shape blending, while the others lead to discontinuous shape transformation. Detailed discussions about the evaluation criteria, numerical sensitivity, and an inherent difficulty in shape blending of 3D polygons are also presented.
14919460
Interpolation on quadric surfaces with rational quadratic spline curves
Abstract Given a sequence of points { X i } i =1 n on a regular quadric S : X T AX = 0 ⊂ E d , d ⩾ 3, we study the problem of constructing a G 1 rational quadratic spline curve lying on S that interpolates { X i } i =1 n . It is shown that a necessary condition for the existence of a nontrivial interpolant is ( X 1 T AX 2 )( X i T AX i +1 ) > 0, i = 1,2…, n − 1. Also considered is a Hermite interpolation problem on the quadric S : a biarc consisting of two conic arcs on S joined with G 1 continuity is used to interpolate two points on S and two associated tangent directions, a method similar to the biarc scheme in the plane (Bolton, 1975) or space (Sharrock, 1987). A necessary and sufficient condition is obtained on the existence of a biarc whose two arcs are not major elliptic arcs. In addition, it is shown that this condition is always fulfilled on a sphere for generic interpolation data.
11609470
Interpolating Polyhedral Models Using Intrinsic Shape Parameters
Metamorphosis, or morphing, is the gradual transformation of one shape into another. It generally consists of two subproblems: the correspondence problem and the interpolation problem. This paper presents a solution to the interpolation problem of transforming one polyhedral model into another. It is an extension of the intrinsic shape interpolation scheme (T. W. Sederberg, P. Gao, G. Wang and H. Mu, ‘2-D shape blending: an intrinsic solution to the vertex path problem, SIGGRAPH ’93, pp. 15–18.) for 2D polygons. Rather than considering a polyhedron as a set of independent points or faces, our solution treats a polyhedron as a graph representing the interrelations between faces. Intrinsic shape parameters, such as dihedral angles and edge lengths that interrelate the vertices and faces in the two graphs, are used for interpolation. This approach produces more satisfactory results than the linear or cubic curve paths would, and is translation and rotation invariant.  1997 by John Wiley & Sons, Ltd.
3126850
Recent innovations in speech-to-text transcription at SRI-ICSI-UW
We summarize recent progress in automatic speech-to-text transcription at SRI, ICSI, and the University of Washington. The work encompasses all components of speech modeling found in a state-of-the-art recognition system, from acoustic features, to acoustic modeling and adaptation, to language modeling. In the front end, we experimented with nonstandard features, including various measures of voicing, discriminative phone posterior features estimated by multilayer perceptrons, and a novel phone-level macro-averaging for cepstral normalization. Acoustic modeling was improved with combinations of front ends operating at multiple frame rates, as well as by modifications to the standard methods for discriminative Gaussian estimation. We show that acoustic adaptation can be improved by predicting the optimal regression class complexity for a given speaker. Language modeling innovations include the use of a syntax-motivated almost-parsing language model, as well as principled vocabulary-selection techniques. Finally, we address portability issues, such as the use of imperfect training transcripts, and language-specific adjustments required for recognition of Arabic and Mandarin
2372115
PoClustering: Lossless Clustering of Dissimilarity Data
Given a set of objects V with a dissimilarity measure between pairs of objects in V , a PoCluster is a collection of sets P ⊂ powerset(V ) partially ordered by the ⊂ relation such that S ⊂ T iff the maximal dissimilarity among objects in S is less than the maximal dissimilarity among objects in T . PoClusters capture categorizations of objects that are not strictly hierarchical, such as those found in ontologies. PoClusters can not, in general, be constructed using hierarchical clustering algorithms. In this paper, we examine the relationship between PoClusters and dissimilarity matrices and prove that PoClusters are in one-to-one correspondence with the set of dissimilarity matrices. The PoClustering problem is NP-Complete, and we present a heuristic algorithm for it in this paper. Experiments on both synthetic and real datasets demonstrate the quality and scalability of the algorithms.
6124530
Discovering High-Order Periodic Patterns
Abstract.Discovery of periodic patterns in time series data has become an active research area with many applications. These patterns can be hierarchical in nature, where a higher-level pattern may consist of repetitions of lower-level patterns. Unfortunately, the presence of noise may prevent these higher-level patterns from being recognized in the sense that two portions (of a data sequence) that support the same (high-level) pattern may have different layouts of occurrences of basic symbols. There may not exist any common representation in terms of raw symbol combinations; and hence such (high-level) pattern may not be expressed by any previous model (defined on raw symbols or symbol combinations) and would not be properly recognized by any existing method. In this paper, we propose a novel model, namely meta-pattern, to capture these high-level patterns. As a more flexible model, the number of potential meta-patterns could be very large. A substantial difficulty lies in how to identify the proper pattern candidates. However, the well-known Apriori property is not able to provide sufficient pruning power. A new property, namely component location property, is identified and used to conduct the candidate generation so that an efficient computation-based mining algorithm can be developed. Last, but not least, we apply our algorithm to some real and synthetic sequences and some interesting patterns are discovered.
14374205
Understanding Social Welfare Service Patterns Using Sequential Analysis
Classical exploratory data analysis methods in statistics and many of the earlier KDD methods tend to focus only on basic data types, (interval or categorical data) as the unit of analysis. However, some information cannot be interpreted unless the data is treated as a unit. For example, viewing the data as sequences of sets can reveal useful information that could not be extracted in any other way. Analyzing suitable databases from such a perspective can assist many social scientists in their work.
2396831
Mining coherent patterns from heterogeneous microarray data
Microarray technology is a powerful tool for geneticists to monitor interactions among tens of thousands of genes simultaneously. There has been extensive research on coherent subspace clustering of gene expressions measured under consistent experimental settings. However, these methods assume that all experiments are run using the same batch of microarray chips with similar characteristics of noise. Algorithms developed under this assumption may not be applicable for analyzing data collected from heterogeneous settings, where the set of genes being monitored may be different and expression levels may be not directly comparable even for the same gene. In this paper, we propose a model, F-cluster, for mining subspace coherent patterns from heterogeneous gene expression data. We compare our model with previously proposed models. We analyze the search space of the problem and give a naïve solution for it.