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    • 31-Issue 5
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    Microtiles: Extracting Building Blocks from Correspondences

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    Date
    2012
    Author
    Kalojanov, Javor
    Bokeloh, Martin
    Wand, Michael
    Guibas, Leonidas
    Seidel, Hans-Peter ORCID
    Slusallek, Philipp ORCID
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    Abstract
    In this paper, we develop a theoretical framework for characterizing shapes by building blocks. We address two questions: First, how do shape correspondences induce building blocks? For this, we introduce a new representation for structuring partial symmetries (partial self-correspondences), which we call "microtiles". Starting from input correspondences that form point-wise equivalence relations, microtiles are obtained by grouping connected components of points that share the same set of symmetry transformations. The decomposition is unique, requires no parameters beyond the input correspondences, and encodes the partial symmetries of all subsets of the input. The second question is: What is the class of shapes that can be assembled from these building blocks? Here, we specifically consider r-similarity as correspondence model, i.e., matching of local r-neighborhoods. Our main result is that the microtiles of the partial r-symmetries of an object S can build all objects that are (r+e)-similar to S for any e>0. Again, the construction is unique. Furthermore, we give necessary conditions for a set of assembly rules for the pairwise connection of tiles. We describe a practical algorithm for computing microtile decompositions under rigid motions, a corresponding prototype implementation, and conduct a number of experiments to visualize the structural properties in practice.
    BibTeX
    @article {10.1111:j.1467-8659.2012.03165.x,
    journal = {Computer Graphics Forum},
    title = {{Microtiles: Extracting Building Blocks from Correspondences}},
    author = {Kalojanov, Javor and Bokeloh, Martin and Wand, Michael and Guibas, Leonidas and Seidel, Hans-Peter and Slusallek, Philipp},
    year = {2012},
    publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
    ISSN = {1467-8659},
    DOI = {10.1111/j.1467-8659.2012.03165.x}
    }
    URI
    http://dx.doi.org/10.1111/j.1467-8659.2012.03165.x
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    • 31-Issue 5
    • SGP12: Eurographics Symposium on Geometry Processing

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