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.

[1]  T. Gangopadhyay,et al.  Further Tiling Patterns Involving Islamic Stars with an Odd Number of Vertices , 2013 .

[2]  Jitendra Malik,et al.  Detecting, localizing and grouping repeated scene elements from an image , 1996, ECCV.

[3]  Richard W. Conners,et al.  Toward a Structural Textural Analyzer Based on Statistical Methods , 1981 .

[4]  José María Gomis,et al.  A Computational Model for Pattern and Tile Designs Classification Using Plane Symmetry Groups , 2005, CIARP.

[5]  Makoto Nagao,et al.  Structural analysis of natural textures by Fourier transformation , 1983, Comput. Vis. Graph. Image Process..

[6]  Yanxi Liu,et al.  A Lattice-Based MRF Model for Dynamic Near-Regular Texture Tracking , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  David A. Forsyth.  Shape from Texture without Boundaries , 2002, ECCV.

[8]  David A. Forsyth,et al.  Recovering shape and irradiance maps from rich dense texton fields , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[9]  P. Nagabhushan,et al.  Automatic extraction of texture-periodicity using superposition of distance matching functions and their forward differences , 2012, Pattern Recognit. Lett..

[10]  D. Schattschneider.  The Plane Symmetry Groups: Their Recognition and Notation , 1978 .

[11]  Stephen J. McKenna,et al.  Classifying and Comparing Regular Textures for Retrieval using Texel Geometry , 2009, VISAPP.

[12]  Jitendra Malik,et al.  Recognizing surfaces using three-dimensional textons , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[13]  Richard W. Conners,et al.  Toward a Structural Textural Analyzer Based on Statistical Methods , 1980 .

[14]  Jitendra Malik,et al.  Textons, contours and regions: cue integration in image segmentation , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[15]  Andrew Zisserman,et al.  Geometric Grouping of Repeated Elements within Images , 1999, Shape, Contour and Grouping in Computer Vision.

[16]  Luc Van Gool,et al.  Noncombinatorial Detection of Regular Repetitions under Perspective Skew , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Manuel Agustí-Melchor,et al.  Lattice Extraction Based on Symmetry Analysis , 2008, VISAPP.

[18]  Shi-Nine Yang,et al.  Extracting periodicity of a regular texture based on autocorrelation functions , 1997, Pattern Recognit. Lett..

[19]  Yan Gui,et al.  Texel Based Regular and Near-Regular Texture Characterization , 2011, 2011 International Conference on Multimedia and Signal Processing.

[20]  Jan-Olof Eklundh,et al.  Detecting Symmetry and Symmetric Constellations of Features , 2006, ECCV.

[21]  Jia-Guu Leu,et al.  On indexing the periodicity of image textures , 2001, Image Vis. Comput..

[22]  Yanxi Liu,et al.  A computational model for periodic pattern perception based on frieze and wallpaper groups , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Stephen J. McKenna,et al.  Regular Texture Analysis as Statistical Model Selection , 2008, ECCV.

[24]  Jingrui He,et al.  Automatic Peak Number Detection in Image Symmetry Analysis , 2004, PCM.

[25]  Shi-Nine Yang,et al.  Automatic determination of the spread parameter in Gaussian smoothing , 1996, Pattern Recognit. Lett..

[26]  Yanxi Liu,et al.  The Promise and Perils of Near-Regular Texture , 2004, International Journal of Computer Vision.

[27]  Alexei A. Efros,et al.  Discovering Texture Regularity as a Higher-Order Correspondence Problem , 2006, ECCV.

[28]  G. C. Shephard,et al.  Tilings and Patterns , 1990 .

[29]  Dimitrios Charalampidis,et al.  Texture synthesis: textons revisited , 2006, IEEE Transactions on Image Processing.

[30]  Dmitry Chetverikov.  Pattern regularity as a visual key , 2000, Image Vis. Comput..