We introduce the term skewed symmetry groups and provide a complete theoretical treatment for 2D wallpaper groups under affine transformations. For the first time, a given periodic pattern can be classified not simply by its Euclidean symmetry group but,by its highest "potential" symmetry group under affine deformation. A concise wallpaper group migration map is constructed that separates the 17 affinely deformed wallpaper groups into small, distinct orbits. The practical value of this result includes a novel indexing and retrieval scheme for regular patterns, and a maximal-symmetry-based method for estimating shape and orientation from texture under unknown views.


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    Title :

    Skewed symmetry groups


    Contributors:
    Yanxi Liu, (author) / Collins, R.T. (author)


    Publication date :

    2001-01-01


    Size :

    967419 byte





    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



    Skewed Symmetry Groups

    Liu, Y. / Collins, R. T. / IEEE | British Library Conference Proceedings | 2001


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    The Characterization and Detection of Skewed Symmetry

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    Bjoeheden, O. | Tema Archive | 1981


    Deceptively skewed underpass

    Barker, R.S. | Engineering Index Backfile | 1949