Image Vectorization with Depth: Convexified Shape Layers with Depth Ordering
Ho Law, Sung Ha Kang · SIAM Journal on Imaging Sciences · 2025
Abstract. Image vectorization is a process to convert a raster image into a scalable vector graphic format. The objective is to effectively remove pixelization effects while representing image boundaries by scalable parameterized curves. We propose a new image vectorization method which considers depth ordering among shapes and use curvature-based inpainting for convexifying shapes in the vectorization process. From a given color-quantized raster image, we first define each connected component of the same color as a shape layer and construct depth ordering among them using a newly proposed depth ordering energy. Global depth ordering among all shapes is described by a directed graph, and we propose an energy to remove cycles within the graph. After constructing a depth ordering of shapes, we convexify occluded regions by Euler’s elastica curvature-based variational inpainting and leverage the stability of Modica–Mortola double-well potential energy to inpaint large regions. This is following human vision perception, where boundaries of shapes extend smoothly, and we assume that shapes are likely to be convex. Finally, we fit Bézier curves to the boundaries and store vectorization results as a scalable vector graphics file, allowing superposition of curvature-based inpainted shapes following the depth ordering. This is a new way to vectorize images by decomposing an image into scalable shape layers with computed depth ordering. This approach makes editing shapes and images more natural and intuitive. We also consider grouping shape layers for semantic vectorization. We present various numerical results and comparisons against recent layer-based vectorization methods to validate the proposed model.