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 colors, linear gradients, tonal art maps and textures. Lastly, we demonstrate temporal coherence for animations and compare our method with existing image triangulation tools.
