An Active Contour Model for Silhouette Vectorization using B\'ezier Curves

In this paper, we propose an active contour model for silhouette vectorization using cubic B\'ezier curves. Among the end points of the B\'ezier curves, we distinguish between corner and regular points where the orientation of the tangent vector is prescribed. By minimizing the distance of the B\'ezier curves to the silhouette boundary, the active contour model optimizes the location of the B\'ezier curves end points, the orientation of the tangent vectors in the regular points, and the estimation of the B\'ezier curve parameters. This active contour model can use the silhouette vectorization obtained by any method as an initial guess. The proposed method significantly reduces the average distance between the silhouette boundary and its vectorization obtained by the world-class graphic software Inkscape, Adobe Illustrator, and a curvature-based vectorization method, which we introduce for comparison. Our method also allows us to impose additional regularity on the B\'ezier curves by reducing their lengths.