Stylized Image Triangulation

The art of representing images with triangles is known as image triangulation, which purposefully uses abstraction and simplification to guide the viewer's attention. The manual creation of image triangulations is tedious and thus several tools have been developed in the past that assist in the placement of vertices by means of image feature detection and subsequent Delaunay triangulation. In this paper, we formulate the image triangulation process as an optimization problem. We provide an interactive system that optimizes the vertex locations of an image triangulation to reduce the root mean squared approximation error. Along the way, the triangulation is incrementally refined by splitting triangles until certain refinement criteria are met. Thereby, the calculation of the energy gradients is expensive and thus we propose an efficient rasterization‐based GPU implementation. To ensure that artists have control over details, the system offers a number of direct and indirect editing tools that split, collapse and re‐triangulate selected parts of the image. For final display, we provide a set of rendering styles, including constant colours, linear gradients, tonal art maps and textures. Finally, we demonstrate temporal coherence for animations and compare our method with existing image triangulation tools.

[1]  Michael D. Adams,et al.  An optimization-based mesh-generation method for image representation , 2015, 2015 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM).

[2]  Michael S. Brown,et al.  Fast and Effective L0 Gradient Minimization by Region Fusion , 2015, 2015 IEEE International Conference on Computer Vision (ICCV).

[3]  Frank Nielsen,et al.  Statistical region merging , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  T. W. Ridler,et al.  Picture thresholding using an iterative selection method. , 1978 .

[5]  Qi Zhang,et al.  100+ Times Faster Weighted Median Filter (WMF) , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[6]  A. Iske,et al.  Advances in Digital Image Compression by Adaptive Thinning , 2003 .

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

[8]  Musbah J. Aqel,et al.  Survey on Image Segmentation Techniques , 2015 .

[9]  Michael D. Adams.  A highly-effective incremental/decremental Delaunay mesh-generation strategy for image representation , 2013, Signal Process..

[10]  Marc Alexa,et al.  Laplacian mesh optimization , 2006, GRAPHITE '06.

[11]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[12]  A. Sekar,et al.  A Survey on Image Segmentation Techniques , 2015 .

[13]  Cewu Lu,et al.  Image smoothing via L0 gradient minimization , 2011, ACM Trans. Graph..

[14]  Neil A. Dodgson,et al.  Stylized multiresolution image representation , 2008, J. Electronic Imaging.

[15]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.

[16]  Agus Zainal Arifin,et al.  Image segmentation by histogram thresholding using hierarchical cluster analysis , 2006, Pattern Recognit. Lett..

[17]  Nira Dyn,et al.  Adaptive multiresolution analysis based on anisotropic triangulations , 2012, Math. Comput..

[18]  Keith Price,et al.  Picture Segmentation Using a Recursive Region Splitting Method , 1998 .

[19]  M. Adams,et al.  Improved mesh models of images through the explicit representation of discontinuities , 2013, Canadian Journal of Electrical and Computer Engineering.

[20]  Greg Humphreys,et al.  Physically Based Rendering: From Theory to Implementation , 2004 .

[21]  D. Greig,et al.  Exact Maximum A Posteriori Estimation for Binary Images , 1989 .

[22]  Minh N. Do,et al.  Fast Global Image Smoothing Based on Weighted Least Squares , 2014, IEEE Transactions on Image Processing.

[23]  Adam Finkelstein,et al.  Real-time hatching , 2001, SIGGRAPH.

[24]  Bo Liu,et al.  Survey on clustering-based image segmentation techniques , 2016, 2016 IEEE 20th International Conference on Computer Supported Cooperative Work in Design (CSCWD).

[25]  Michael D. Adams.  A Flexible Content-Adaptive Mesh-Generation Strategy for Image Representation , 2011, IEEE Transactions on Image Processing.

[26]  Christof Koch,et al.  Image Signature: Highlighting Sparse Salient Regions , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  Yongyi Yang,et al.  A fast approach for accurate content-adaptive mesh generation , 2003, IEEE Trans. Image Process..

[28]  S. Mitra,et al.  Unsupervised segmentation of color images based on k-means clustering in the chromaticity plane , 1999, Proceedings IEEE Workshop on Content-Based Access of Image and Video Libraries (CBAIVL'99).

[29]  Pascal Barla,et al.  Diffusion curves: a vector representation for smooth-shaded images , 2008, ACM Trans. Graph..

[30]  Neil A. Dodgson,et al.  Voronoi video stylisation , 2009, CGI.

[31]  Adrian Secord,et al.  Weighted Voronoi stippling , 2002, NPAR '02.

[32]  Herbert Edelsbrunner,et al.  Incremental topological flipping works for regular triangulations , 1992, SCG '92.

[33]  Douglas DeCarlo,et al.  Stylization and abstraction of photographs , 2002, ACM Trans. Graph..

[34]  M. S. Sonawane,et al.  A Brief Survey on Image Segmentation Methods , 2015 .

[35]  Marc Alexa,et al.  Pixelated image abstraction , 2012, NPAR '12.

[36]  Andreas Weinmann,et al.  Jump-Sparse and Sparse Recovery Using Potts Functionals , 2013, IEEE Transactions on Signal Processing.

[37]  Fan Meng,et al.  Image Segmentation via Improving Clustering Algorithms with Density and Distance , 2015, ITQM.

[38]  N. Otsu.  A threshold selection method from gray level histograms , 1979 .

[39]  Ming Zeng,et al.  Feature-preserving filtering with L0 gradient minimization , 2014, Comput. Graph..

[40]  Tobias Isenberg,et al.  State of the "Art”: A Taxonomy of Artistic Stylization Techniques for Images and Video , 2013, IEEE Transactions on Visualization and Computer Graphics.

[41]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..