Survey of Techniques for Data-dependent Triangulations Approximating Color Images

We present a survey of different techniques to approximate a color image using a piecewise linear interpolation induced by a triangulation of the image domain. We also include a detailed description of a method called guided simulated annealing (GSA) we designed that reduces computation time significantly. Finally, we give a short overview of possible extensions.

[1]  W D Wright,et al.  Color Science, Concepts and Methods. Quantitative Data and Formulas , 1967 .

[2]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[3]  S. Rippa,et al.  Data Dependent Triangulations for Piecewise Linear Interpolation , 1990 .

[4]  S. Rippa.  Long and thin triangles can be good for linear interpolation , 1992 .

[5]  Larry L. Schumaker,et al.  Computing optimal triangulations using simulated annealing , 1993, Comput. Aided Geom. Des..

[6]  Hugues Hoppe,et al.  Progressive meshes , 1996, SIGGRAPH.

[7]  M. Garland,et al.  Fast Polygonal Approximation of Terrains and Height Fields , 1998 .

[8]  Hans Hagen,et al.  Data-Dependent Triangulation in the Plane with Adaptive Knot Placement , 1999, Geometric Modelling.

[9]  Bernd Hamann,et al.  On Simulated Annealing and the Construction of Linear Spline Approximations for Scattered Data , 1999, VisSym.

[10]  Hélio Pedrini.  An Improved Refinement and Decimation Method for Adaptive Terrain Surface Approximation , 2001, WSCG.

[11]  Vid Petrovic,et al.  Optimized construction of linear approximations to image data , 2003, 11th Pacific Conference onComputer Graphics and Applications, 2003. Proceedings..

[12]  Nira Dyn,et al.  Adaptive Thinning for Terrain Modelling and Image Compression , 2005, Advances in Multiresolution for Geometric Modelling.

[13]  Nira Dyn,et al.  Image compression by linear splines over adaptive triangulations , 2006, Signal Process..

[14]  Armin Iske,et al.  Adaptive image approximation by linear splines over locally optimal delaunay triangulations , 2006, IEEE Signal Processing Letters.

[15]  Bernd Hamann,et al.  Image Compression Using Data-Dependent Triangulations , 2007, ISVC.