Monte Carlo optimization for gradient meshes

Vector graphics provide continuous and often even smooth geometric representations of images. While recent approaches to automatically vectorize images lead to relatively good results, they typically leave ample room for improvement: the geometry and color of the vector graphics primitives can be further (automatically) optimized. We propose a novel method that generates high-quality vectorizations based on optimizing input curved triangle meshes (optionally with mesh colors). To overcome the key challenge of establishing a differentiable mapping between the input parameters, i.e., geometry and (mesh) colors of the gradient mesh, and the difference between the vectorized and input image, we treat the input image as a continuous bilinear interpolatory spline and employ Monte Carlo integration. We test our algorithm on various images and show that it can effectively and efficiently improve the quality of an initial vectorization. • We introduce a differentiable error function to drive optimization. • We derive an explicit gradient from the error function using the Monte Carlo method. • We illustrate the effectiveness of the method on various examples.