Segmenting Periodic Reliefs on Triangle Meshes

Decorative reliefs are widely used for e.g. packaging and porcelain design. In periodic reliefs, the relief repeats a pattern, for example all the way around an underlying surface of revolution. Reverseengineering of existing reliefs allows them to be re-applied to different base surfaces; we show here how to segment a single repeat unit of a periodic relief starting from a scanned triangle mesh. We first briefly review how we segment the relief from the background surface using our previous work. The rest of the paper then concentrates on how we extract a single repeat unit from the relief. To do so, the user provides two points on one relief boundary which are in approximate correspondence on consecutive repeats of the relief. We first refine the relative locations of these points, and then determine a third corresponding point using relief boundary information. These are used to determine three initial cutting planes across the relief. Then surface registration strategies are utilised to refine the correspondence between adjacent repeat units. Finally, we refine the exact locations of the cutting planes by considering only surface information close to the cutting planes. This allows a repeat unit of the periodic relief to be extracted. We demonstrate that our algorithm is successful and practical, using various real scanned models: user input can be quite imprecise, and we can cope with hand-made reliefs in which the pattern units are only approximately copies of each other.

[1]  Johannes Wallner,et al.  Integral invariants for robust geometry processing , 2009, Comput. Aided Geom. Des..

[2]  Least squares estimation of curvature and torsion , 2008 .

[3]  H. Ney,et al.  Local Features for Image Classification , .

[4]  S. Zucker,et al.  Finding structure in Co-occurrence matrices for texture analysis , 1980 .

[5]  Michal Strzelecki,et al.  Texture Analysis Methods - A Review , 1998 .

[6]  Chris C. Handley The analysis and reconstruction of repetitive textures , 1998, Proceedings. Computer Graphics International (Cat. No.98EX149).

[7]  Luc Van Gool,et al.  Matching of 3-D curves using semi-differential invariants , 1995, Proceedings of IEEE International Conference on Computer Vision.

[8]  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.

[9]  François X. Sillion,et al.  Accurately Detecting Symmetries of 3D Shapes , 2005 .

[10]  Robert M. Haralick,et al.  Textural Features for Image Classification , 1973, IEEE Trans. Syst. Man Cybern..

[11]  Changming Sun,et al.  3D Symmetry Detection Using The Extended Gaussian Image , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Luc Van Gool,et al.  Efficient matching of space curves , 1995, CAIP.

[13]  Leonidas J. Guibas,et al.  Partial and approximate symmetry detection for 3D geometry , 2006, ACM Trans. Graph..

[14]  Ching-Chung Li,et al.  Determination of structure component in image texture using wavelet analysis , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[15]  Shenglan Liu,et al.  Segmenting Geometric Reliefs from Textured Background Surfaces , 2007 .

[16]  François X. Sillion,et al.  Accurate detection of symmetries in 3D shapes , 2006, TOGS.

[17]  Dana H. Ballard,et al.  Computer Vision , 1982 .

[18]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Ralph R. Martin,et al.  Segmenting reliefs on triangle meshes , 2006, SPM '06.

[20]  Andrew W. Fitzgibbon,et al.  Simultaneous registration of multiple range views for use in reverse engineering , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[21]  Andrew W. Fitzgibbon,et al.  Simultaneous Registration of Multiple Range Views for Use in Reverse Engineering of CAD Models , 1998, Comput. Vis. Image Underst..