Time Warp Edit Distance with Stiffness Adjustment for Time Series Matching

In a way similar to the string-to-string correction problem we address time series similarity in the light of a time-series-to-time-series-correction problem for which the similarity between two time series is measured as the minimum cost sequence of "edit operations" needed to transform one time series into another. To define the "edit operations" we use the paradigm of a graphical editing process and end up with a dynamic programming algorithm that we call Time Warp Edit Distance (TWED). TWED is slightly different in form from Dynamic Time Warping, Longest Common Subsequence or Edit Distance with Real Penalty algorithms. In particular, it highlights a parameter which drives a kind of stiffness of the elastic measure along the time axis. We show that the similarity provided by TWED is a metric potentially useful in time series retrieval applications since it could benefit from the triangular inequality property to speed up the retrieval process while tuning the parameters of the elastic measure. In that context, a lower bound is derived to relate the matching of time series into down sampled representation spaces to the matching into the original space. Empiric quality of the TWED distance is evaluated on a simple classification task. Compared to Edit Distance, Dynamic Time Warping, Longest Common Subsequnce and Edit Distance with Real Penalty, TWED has proven to be quite effective on the considered experimental task

A multi-objective approach for the segmentation issue

Special Issue: Multi-objective metaheuristics for multi-disciplinary engineering applicationsThis work presents and formalizes an explicit multi-objective evolutionary approach for the segmentation issue according to Piecewise Linear Representation, which consists in the approximation of a given digital curve by a set of linear models minimizing the representation error and the number of such models required. Available techniques are focused on the minimization of the quality of the obtained approximation, being the cost of that approximation considered, in general, only for certain comparison purposes. The multi-objective nature of the problem is analysed and its treatment in available works reviewed, presenting an a posteriori approach based on an evolutionary algorithm. Three representative curves are included in the data set, comparing the proposed technique to nine different techniques. The performance of the presented approach is tested according to single and multiobjective perspectives. The statistical tests carried out show that the experimental results are, in general, significantly better than available approaches from both perspectives.This work was supported in part by Projects CICYT TIN2008-06742-C02-02/TSI, CICYT TEC2008-06732-C02-02/TEC, CAM CONTEXTS (S2009/TIC-1485) and DPS2008-07029-C02-02.Publicad

Topologically reliable approximation of curves and surfaces

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1997.Includes bibliographical references (p. [213]-222).by Wonjoon Cho.Ph.D

Automatic constraint-based synthesis of non-uniform rational B-spline surfaces

In this dissertation a technique for the synthesis of sculptured surface models subject to several constraints based on design and manufacturability requirements is presented. A design environment is specified as a collection of polyhedral models which represent components in the vicinity of the surface to be designed, or regions which the surface should avoid. Non-uniform rational B-splines (NURBS) are used for surface representation, and the control point locations are the design variables. For some problems the NURBS surface knots and/or weights are included as additional design variables. The primary functional constraint is a proximity metric which induces the surface to avoid a tolerance envelope around each component. Other functional constraints include: an area/arc-length constraint to counteract the expansion effect of the proximity constraint, orthogonality and parametric flow constraints (to maintain consistent surface topology and improve machinability of the surface), and local constraints on surface derivatives to exploit part symmetry. In addition, constraints based on surface curvatures may be incorporated to enhance machinability and induce the synthesis of developable surfaces;The surface synthesis problem is formulated as an optimization problem. Traditional optimization techniques such as quasi-Newton, Nelder-Mead simplex and conjugate gradient, yield only locally good surface models. Consequently, simulated annealing (SA), a global optimization technique is implemented. SA successfully synthesizes several highly multimodal surface models where the traditional optimization methods failed. Results indicate that this technique has potential applications as a conceptual design tool supporting concurrent product and process development methods

Digital Image Processing

This book presents several recent advances that are related or fall under the umbrella of 'digital image processing', with the purpose of providing an insight into the possibilities offered by digital image processing algorithms in various fields. The presented mathematical algorithms are accompanied by graphical representations and illustrative examples for an enhanced readability. The chapters are written in a manner that allows even a reader with basic experience and knowledge in the digital image processing field to properly understand the presented algorithms. Concurrently, the structure of the information in this book is such that fellow scientists will be able to use it to push the development of the presented subjects even further