Silhouette Vectorization by Affine Scale-Space

Silhouettes are building elements of logos, graphic symbols and fonts. These shapes can be designed and exchanged in vector form, but more often they are drawn, printed, scanned, or directly found in digital images. Such raster forms require vectorization to get scale-invariant exchangeable formats. There is a need for a mathematically well-defined and justified shape vectorization process, which also provides a minimal set of control points with geometric meaning. In this paper, we propose a new silhouette vectorization paradigm. It extracts the outline of a 2D shape from a raster binary image and converts it to a combination of cubic Bézier polygons and perfect circles. The proposed method uses the sub-pixel curvature extrema and affine scale-space for silhouette vectorization. By construction, our control points are geometrically stable under affine transformations. The proposed method can also be used as a reliable feature point detector for silhouettes. Compared to state-of-the-art image vectorization software, our algorithm demonstrates a superior reduction in the number of control points while maintaining high accuracy.