Abstract
In computational geometry, the elastic geometric shape matching (EGSM) problem class is a generalisation of the well-known geometric shape matching problem class: Given two geometric shapes, the ‘pattern’ and the ‘model’, find a single transformation from a given transformation class that, if applied to the pattern, minimizes the distance between the transformed pattern and the model with respect to a suitable distance measure.
In EGSM, the pattern is divided into subshapes that are transformed by a ‘transformation ensemble’, i.e., a set of transformations. The goal is to minimize the distance between the union of the transformed subpatterns and the model in object space as well as the distance between specific transformations of the ensemble. The ‘neighborhood graph’ encodes which translations should be similar.
We present a fully polynomial time approximation scheme (FPTAS) for EGSM instances for point sequences under translations with fixed correspondence where the neighborhood graph is a simple cycle.
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Knauer, C., Sommer, L., Stehn, F. (2018). An FPTAS for an Elastic Shape Matching Problem with Cyclic Neighborhoods. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2018. ICCSA 2018. Lecture Notes in Computer Science(), vol 10961. Springer, Cham. https://doi.org/10.1007/978-3-319-95165-2_30
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DOI: https://doi.org/10.1007/978-3-319-95165-2_30
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