Lattice Extraction Based on Symmetry Analysis

Abstract

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.