Topology- and Perception-Aware Image Vectorization

• Published in: Journal of mathematical imaging and vision 2023-12, Vol.65 (6), p.874-893
• Main Authors: He, Yuchen, Kang, Sung Ha, Morel, Jean-Michel
• Format: Article
• Language: English
• Subjects: Algorithms; Applications of Mathematics; Color imagery; Computer Science; Discontinuity; Image filters; Image Processing and Computer Vision; Mathematical Methods in Physics; Mathematics; Raster; Semigroups; Signal,Image and Speech Processing; Topology
• ISSN: 0924-9907; 1573-7683
• DOI: 10.1007/s10851-023-01149-8

We propose a new color image vectorization method converting raster images to resolution-independent scalable vector graphics. Starting from a quantized raster image, the method builds a hierarchical structure to represent its discontinuity set. The lowest level elements, called curve-elements, separate exactly two colors and end at T-junctions or X-junctions. The middle-level objects, called curvebases, are concatenations of curve-elements following perceptual rules and representing the apparent contours of objects. On the highest level, the jump set coincides with the discontinuity set of the quantized image input. A geometric filtering method removes pixelization effects by affine shortening of the curvebases while resolving the induced topological changes. All junctions are preserved, thus maintaining the highest level of perceptual fidelity even on tiny pixel art images. A single parameter controls the simplification of curves between two junctions. Theoretical bounds are given to guarantee the method’s topological consistency. This allows the method to be iterated such that it yields a smoothing semigroup. In both qualitative and quantitative experiments, our method compares favorably to multiple state-of-the-art algorithms and software.