A Genetic Based Algorithm for Automatic Motif Detection of Periodic Patterns

In this paper, we introduce a new method to extract the basic unit cell of a periodic Islamic Geometrical Pattern (IGP). This method is based on the autocorrelation function (ACF), a function known to be appropriate to analyze and draw out a repetitive motif from a regular texture. The motif can be successfully extracted when the detected peaks in the autocorrelation function of an image are pertinent. In this paper, the pertinent peaks detection is considered as an optimization problem. For this purpose, we propose a criterion function that we optimize by using genetic algorithm. The proposed method is tolerant to geometric distortion, and photometric quality of the input image compared to classical ones. Tests on 166 images with different visual quality demonstrate the capability of the proposed method to extract the periodic motif automatically.