A computational model for periodic pattern perception based on frieze and wallpaper groups

摘要: We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each N-dimensional Euclidean space, finite number symmetry groups can characterize structures an infinite variety patterns. 2D there are seven frieze describing monochrome patterns that repeat along one direction and 17 wallpaper two linearly independent directions to tile plane. develop set computer algorithms "understand" given by automatically finding its underlying lattice, identifying group, extracting representative motifs. also extend this near-periodic using geometric AIC. Applications such include indexing, texture synthesis, image compression, gait analysis.