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Symmetry is an abstract concept that is easily noticed by humans that designers make new creations based on its use. Images of these designs belong to a general group called wallpaper images that exhibit a repetitive pattern. We present a novel computational framework for automatic classification method by symmetries, based on Symmetry Group theory features for wallpaper images. The existing methods have several drawbacks because of the use of heuristics. These methods have shown low classification values when images exhibit imperfections due to the fabrication or the hand made process. Also, there is no way to give some computation of the classification goodness-of-fit. We propose to obtain an automatic parameter estimation for symmetry analysis. Thus, the image classification is redefined as distances computation to the prototypes of a set of defined classes. Our experimental results improves the state of the art in wallpaper classification methods.

Symmetry is an abstract concept that is easily noticed by humans and as a result designers make new creations based on its use, e.g. textile and tiles. Images of these designs belong to a more general group called wallpaper images, and these images exhibit a repetitive pattern on a 2D space. In this paper, we present a novel computational framework for the automatic classification into symmetry groups of images with repetitive patterns. The existing methods in the literature, based on rules and trees, have several drawbacks because of the use of thresholds and heuristics. Also, there is no way to give some measurement of the classification goodness-of-fit. As a consequence, these methods have shown low classification values when images exhibit imperfections due to the manufacturing process or hand made process. To deal with these problems, we propose a classification method that can obtain an automatic parameter estimation for symmetry analysis. Using this approach, the image classification is redefined as distance computation to the binary prototypes of a set of defined classes. Our experimental results improve the state of the art in symmetry group classification methods.

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In many computer tasks it is necessary to structurally describe the contents of images for further processing, for example, in regular images produced in industrial processes such as textiles or ceramics. After reviewing the different approaches found in the literature, this work redefines the problem of periodicity in terms of the existence of local symmetries. Phase symmetry analysis is chosen to obtain these symmetries because of its robustness when dealing with image contrast and noise. Also, the multiresolution nature of the technique offers independence from using fixed thresholds to segment the image. Our adaptation of the original technique, based on lattice constraints, has result in a parameter free algorithm for determining the lattice. It offers a significant increase in computational speed with respect to the original proposal. Given that there is no set of images for assessing this type of techniques, various sets of images have been used, and the results are apresented. A measure to enable the evaluation of results is also introduced, so that each calculated lattice can be tagged with an index regarding its correctness. The experiments show that using this statistic, good results are reported from image collections. Possible applications of the lattice extraction are suggested.