Dynamic Time Warping of Cyclic Strings for Shape Matching

Marzal, Andrés; Palazón, Vicente

doi:10.1007/11552499_71

Cited by 14 publications

(8 citation statements)

References 12 publications

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“…Many geometric measures (e.g. [2,3,22]) require a matching between geometric objects; though we have such implicitly, this defeats the purpose of quantifying a first impression through the overall composition. The popular Hausdorff distance [18] is a "bottleneck" measure, only quantifying similarity through a locally worst situation.…”

Section: Projection Characteristicsmentioning

confidence: 99%

Small Multiples with Gaps

Meulemans

Dykes

Slingsby

et al. 2017

IEEE Trans. Visual. Comput. Graphics

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Fig. 1: The effects of adding gaps (whitespace) to a small-multiples layout (blue squares) representing the 12 provinces of the Netherlands, measured via our suite of metrics. Each metric is represented by a colored line in the chart, indicating at each axis how well the layout below performs in the metric. The layout algorithm here optimizes for the displacement metric-which aims to preserve the spatial (geographic) distribution-as whitespace is increased from left to right. Although some metrics show improvement as gaps are added, others reflect the resulting smaller and more dispersed distribution, which may hinder comparison. Permanent repository linkAbstract-Small multiples enable comparison by providing different views of a single data set in a dense and aligned manner. A common frame defines each view, which varies based upon values of a conditioning variable. An increasingly popular use of this technique is to project two-dimensional locations into a gridded space (e.g. grid maps), using the underlying distribution both as the conditioning variable and to determine the grid layout. Using whitespace in this layout has the potential to carry information, especially in a geographic context. Yet, the effects of doing so on the spatial properties of the original units are not understood. We explore the design space offered by such small multiples with gaps. We do so by constructing a comprehensive suite of metrics that capture properties of the layout used to arrange the small multiples for comparison (e.g. compactness and alignment) and the preservation of the original data (e.g. distance, topology and shape). We study these metrics in geographic data sets with varying properties and numbers of gaps. We use simulated annealing to optimize for each metric and measure the effects on the others. To explore these effects systematically, we take a new approach, developing a system to visualize this design space using a set of interactive matrices. We find that adding small amounts of whitespace to small multiple arrays improves some of the characteristics of 2D layouts, such as shape, distance and direction. This comes at the cost of other metrics, such as the retention of topology. Effects vary according to the input maps, with degree of variation in size of input regions found to be a factor. Optima exist for particular metrics in many cases, but at different amounts of whitespace for different maps. We suggest multiple metrics be used in optimized layouts, finding topology to be a primary factor in existing manually-crafted solutions, followed by a trade-off between shape and displacement. But the rich range of possible optimized layouts leads us to challenge single-solution thinking; we suggest to consider alternative optimized layouts for small multiples with gaps. Key to our work is the systematic, quantified and visual approach to exploring design spaces when facing a trade-off between ma...

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Section: Projection Characteristicsmentioning

confidence: 99%

Small Multiples with Gaps

Meulemans

Dykes

Slingsby

et al. 2017

IEEE Trans. Visual. Comput. Graphics

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“…this is the discrete summed Fréchet distance, but instead of using the Euclidean distance between points, any function can be used to evaluate the distance. Marzal and Palazón [2005] suggest to use curvature. This causes the method to be invariant to rotation, scale and translation.…”

Section: A Optimizing Distance Measuresmentioning

confidence: 99%

Area-Preserving Simplification and Schematization of Polygonal Subdivisions

Buchin

Meulemans

Renssen

et al. 2016

ACM Trans. Spatial Algorithms Syst.

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In this paper, we study automated simplification and schematization of territorial outlines. We present a quadratic-time simplification algorithm based on an operation called an edge-move. We prove that the number of edges of any nonconvex simple polygon can be reduced with this operation. Moreover, edge-moves preserve area and topology and do not introduce new orientations. The latter property in particular makes the algorithm highly suitable for schematization in which all resulting lines are required to be parallel to one of a given set of lines (orientations). To obtain such a result, we need only to preprocess the input to use only lines that are parallel to one of the given set. We present an algorithm to enforce such orientation restrictions, again without changing area or topology. Experiments show that our algorithms obtain results of high visual quality.

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“…This approach is applied for every pair of symmetry axis curves extracted from both meshes, C 1 = {C It would be possible to improve the speed even further by a factor of O(N/ log N) using a method by [MP05], but we did not implement it since the speed of this step is fast already.…”

Section: Symmetry Axis Alignmentmentioning

confidence: 99%

Finding Surface Correspondences Using Symmetry Axis Curves

Liu

Kim

2012

Computer Graphics Forum

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In this paper, we propose an automatic algorithm for finding a correspondence map between two 3D surfaces. The key insight is that global reflective symmetry axes are stable, recognizable, semantic features of most real-world surfaces. Thus, it is possible to find a useful map between two surfaces by first extracting symmetry axis curves, aligning the extracted curves, and then extrapolating correspondences found on the curves to both surfaces. The main advantages of this approach are efficiency and robustness: the difficult problem of finding a surface map is reduced to three significantly easier problems: symmetry detection, curve alignment, and correspondence extrapolation, each of which has a robust, polynomial-time solution (e.g., optimal alignment of 1D curves is possible with dynamic programming). We investigate of this approach on a wide range of examples, including both intrinsically symmetric surfaces and polygon soups, and find that it is superior to previous methods in cases where two surfaces have different overall shapes but similar reflective symmetry axes, a common case in computer graphics.

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Dynamic Time Warping of Cyclic Strings for Shape Matching

Cited by 14 publications

References 12 publications

Small Multiples with Gaps

Small Multiples with Gaps

Area-Preserving Simplification and Schematization of Polygonal Subdivisions

Finding Surface Correspondences Using Symmetry Axis Curves

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