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.
9604504
Bloom Histogram: Path Selectivity Estimation for XML Data with Updates
Cost-based XML query optimization calls for accurate estimation of the selectivity of path expressions. Some other interactive and internet applications can also benefit from such estimations. While there are a number of estimation techniques proposed in the literature, almost none of them has any guarantee on the estimation accuracy within a given space limit. In addition, most of them assume that the XML data are more or less static, i.e., with few updates. In this paper, we present a framework for XML path selectivity estimation in a dynamic context. Specifically, we propose a novel data structure, bloom histogram, to approximate XML path frequency distribution within a small space budget and to estimate the path selectivity accurately with the bloom histogram. We obtain the upper bound of its estimation error and discuss the trade-offs between the accuracy and the space limit. To support updates of bloom histograms efficiently when underlying XML data change, a dynamic summary layer is used to keep exact or more detailed XML path information. We demonstrate through our extensive experiments that the new solution can achieve significantly higher accuracy with an even smaller space than the previous methods in both static and dynamic environments.
6853966
Total chromatic number of planar graphs with maximum degree ten
14611333
TAR: temporal association rules on evolving numerical attributes
Data mining has been an area of increasing interest. The association rule discovery problem in particular has been widely studied. However, there are still some unresolved problems. For example, research on mining patterns in the evolution of numerical attributes is still lacking. This is both a challenging problem and one with significant practical applications in business, science, and medicine. In this paper we present a temporal association rule model for evolving numerical attributes. Metrics for qualifying a temporal association rule include the familiar measures of support and strength used in traditional association rule mining and a new metric called density. The density metric not only gives us a way to extract the rules that best represent the data, but also provides an effective mechanism to prune the search space. An efficient algorithm is devised for mining temporal association rules, which utilizes all three thresholds (especially the strength) to prune the search space drastically. Moreover, the resulting rules are represented in a concise manner via rule sets to reduce the output size. Experimental results on real and synthetic data sets demonstrate the efficiency of our algorithm.
1498767
Clustering by pattern similarity in large data sets
Clustering is the process of grouping a set of objects into classes of similar objects. Although definitions of similarity vary from one clustering model to another, in most of these models the concept of similarity is based on distances, e.g., Euclidean distance or cosine distance. In other words, similar objects are required to have close values on at least a set of dimensions. In this paper, we explore a more general type of similarity. Under the pCluster model we proposed, two objects are similar if they exhibit a coherent pattern on a subset of dimensions. For instance, in DNA microarray analysis, the expression levels of two genes may rise and fall synchronously in response to a set of environmental stimuli. Although the magnitude of their expression levels may not be close, the patterns they exhibit can be very much alike. Discovery of such clusters of genes is essential in revealing significant connections in gene regulatory networks. E-commerce applications, such as collaborative filtering, can also benefit from the new model, which captures not only the closeness of values of certain leading indicators but also the closeness of (purchasing, browsing, etc.) patterns exhibited by the customers. Our paper introduces an effective algorithm to detect such clusters, and we perform tests on several real and synthetic data sets to show its effectiveness.
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.