Image Vectorization Based On Gradient Meshes

Image vectorization is an important problem in digital image processing. It has lots of applications in the fields of CAD, GIS and so on. During the last few decades, various image vectorization algorithms have been proposed for the engineering drawings, cartoon drawings, and the other binary images. Recently, some algorithms were developed to vectorize the colorful photographic images. The optimized gradient meshes algorithm has become a popular approach for vectorizing the photographic images as it is simple, easy to edit, and of small data storage.Firstly, we improve the optimized gradient meshes algorithm in two aspects. By adaptively refining gradient meshes in a recursive manner, we can reduce the pixel approximation error until the vectorization result satisfies the given error tolerance. Furthermore, T knot is introduced to the mesh so that we can use T-mesh to vectorize the image locally. The adaptive refinement and T mesh algorithm can produce meshes with fewer vertices and patches within the same approximation error.Secondly, we propose the gradient triangular mesh and use it for image vectorization. The algorithm also benefits from the non-linear optimization framework with minor modification. The triangular mesh can be adaptively refined, simplified, and modified in some local ways. The new algorithm has some advantages: the number of vertices and patches in the results are significantly reduced; it can vectorize different images with complicated topology such as the image with interior holes; and the result can preserve the feature.Finally, these two algorithms are compared using various examples. Gradient triangular meshes can be applied to objects with holes or with complex boundaries using only one mesh while quadrilateral gradient meshes couldn't. Meanwhile, the number of vertices and patches that are produced by gradient triangular meshes are much less than those of quadrilateral gradient meshes. In conclusion, gradient triangular meshes algorithm can be applied to more images and works better.