Research On Plane Symmetry Groups Recognition Based On Fourier Transform

Plane symmetry groups are discontinuous subgroups of the isometries in the Euclidean plane.They are invariance under two linearly independent isometric translations in the plane.Plane symmetry groups have received great attention for their applications in crystallography,chemistry,physics,and pattern design.With the innate ability to perceive symmetry,one can classify the 17 plane symmetry group pattern.However,in the past decades,automatic classification of plane symmetry group patterns has remained a formidable challenge.The purpose of this paper is to find an automatic and effective method to identify these 17 plane symmetry groups from images.(1)In this paper,a novel symmetric pattern recognition approach combining discrete Fourier transform with convolutional neural networks is proposed to overcome the challenge posed to neural networks by patternspecific repetitive structures.The research in this paper focuses on two aspects.First of all,the coefficient relations of plane symmetry group patterns in the Fourier domain are derived mathematically,which lays foundation for classifying plane symmetry group patterns through two-dimensional spectrum images instead of raw images.Second,images are trained by neural network in frequency domain.(2)Plane symmetry group generators are designed in order to obtain a large number of datasets suitable for classification training.Using images from three sources(PASCAL-VOC2012 dataset,homemade art pictures,and computer simulation data)as the raw material for generating the basic units of the symmetry groups.Then the training-test data required for the experiment is obtained by the combined operation of four symmetry transformations.(3)By analyzing the features of plane symmetry groups,the highdimensional classification problem is decomposed,and a set of multi-class classification and multi-label classification strategies are designed.A neural network framework is built based on this.The results show that the neural network model obtained in this paper is able to perform basic classification of plane symmetry group patterns with an overall accuracy of 81.2%,which provides a feasible idea for the future problem of repeated symmetric image recognition.The study can be broadly applied to symmetry recognition and crystal structure analysis.