769 research outputs found
Pattern Matching for sets of segments
In this paper we present algorithms for a number of problems in geometric
pattern matching where the input consist of a collections of segments in the
plane. Our work consists of two main parts. In the first, we address problems
and measures that relate to collections of orthogonal line segments in the
plane. Such collections arise naturally from problems in mapping buildings and
robot exploration.
We propose a new measure of segment similarity called a \emph{coverage
measure}, and present efficient algorithms for maximising this measure between
sets of axis-parallel segments under translations. Our algorithms run in time
O(n^3\polylog n) in the general case, and run in time O(n^2\polylog n) for
the case when all segments are horizontal. In addition, we show that when
restricted to translations that are only vertical, the Hausdorff distance
between two sets of horizontal segments can be computed in time roughly
O(n^{3/2}{\sl polylog}n). These algorithms form significant improvements over
the general algorithm of Chew et al. that takes time . In the
second part of this paper we address the problem of matching polygonal chains.
We study the well known \Frd, and present the first algorithm for computing the
\Frd under general translations. Our methods also yield algorithms for
computing a generalization of the \Fr distance, and we also present a simple
approximation algorithm for the \Frd that runs in time O(n^2\polylog n).Comment: To appear in the 12 ACM Symposium on Discrete Algorithms, Jan 200
A novel framework for making dominant point detection methods non-parametric
Most dominant point detection methods require heuristically chosen control parameters. One of the commonly used control parameter is maximum deviation. This paper uses a theoretical bound of the maximum deviation of pixels obtained by digitization of a line segment for constructing a general framework to make most dominant point detection methods non-parametric. The derived analytical bound of the maximum deviation can be used as a natural bench mark for the line fitting algorithms and thus dominant point detection methods can be made parameter-independent and non-heuristic. Most methods can easily incorporate the bound. This is demonstrated using three categorically different dominant point detection methods. Such non-parametric approach retains the characteristics of the digital curve while providing good fitting performance and compression ratio for all the three methods using a variety of digital, non-digital, and noisy curves
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New Applications of the Nearest-Neighbor Chain Algorithm
The nearest-neighbor chain algorithm was proposed in the eighties as a way to speed up certain hierarchical clustering algorithms. In the first part of the dissertation, we show that its application is not limited to clustering. We apply it to a variety of geometric and combinatorial problems. In each case, we show that the nearest-neighbor chain algorithm finds the same solution as a preexistent greedy algorithm, but often with an improved runtime. We obtain speedups over greedy algorithms for Euclidean TSP, Steiner TSP in planar graphs, straight skeletons, a geometric coverage problem, and three stable matching models. In the second part, we study the stable-matching Voronoi diagram, a type of plane partition which combines properties of stable matchings and Voronoi diagrams. We propose political redistricting as an application. We also show that it is impossible to compute this diagram in an algebraic model of computation, and give three algorithmic approaches to overcome this obstacle. One of them is based on the nearest-neighbor chain algorithm, linking the two parts together
A multiscale approach to decompose a digital curve into meaningful parts
International audienceA multi-scale approach is proposed for polygonal repre- sentation of a digital curve by using the notion of blurred seg- ment and a split-and-merge strategy. Its main idea is to de- compose the curve into meaningful parts that are represented by detected dominant points at the appropriate scale. The method uses no threshold and can automatically decompose the curve into meaningful parts
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
Quad Meshing
Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing
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