An Active Contour Model for Silhouette Vectorization using Bézier Curves

TL;DR

The paper tackles silhouette vectorization by introducing an active contour model that represents the boundary with a collection of cubic Bézier curves. It casts the problem as a geodesic-active-contour energy minimization where end-points, tangent directions at regular points, and Bézier parameters are jointly optimized, starting from any initial vectorization. Key contributions include an explicit Bézier-based parameterization with tangent constraints, a tractable optimization scheme, and demonstrated improvements in boundary fidelity over Inkscape, Illustrator, and a curvature-based baseline, along with optional regularization to shorten curve lengths. This approach enhances accuracy and smoothness of vector silhouettes, with practical implications for graphic design and downstream vector-based rendering.

Abstract

In this paper, we propose an active contour model for silhouette vectorization using cubic Bézier curves. Among the end points of the Bézier curves, we distinguish between corner and regular points where the orientation of the tangent vector is prescribed. By minimizing the distance of the Bézier curves to the silhouette boundary, the active contour model optimizes the location of the Bézier curves end points, the orientation of the tangent vectors in the regular points, and the estimation of the Bézier 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 Bézier curves by reducing their lengths.

Figures (5)

• Figure 1: Horse silhouette and the asymptotic state of the active contour models using as initial guess the vectorization provided by different methods. Blue circles represent regular points and red circles corners.
• Figure 2: Cat silhouette and the asymptotic state of the active contour models using as initial guess the vectorization provided by different methods. Blue circles represent regular points and red circles corners.
• Figure 3: Camel silhouette and the asymptotic state of the active contour models using the vectorization provided by different methods as initial guess. Blue circles represent regular points and red circles corners.
• Figure 4: We present a zoom of different parts of the silhouettes. The asymptotic state of the active contour model is represented by blue circles (regular points) or red circles (corners) with the drawing of the Bézier curves in black. The original silhouette vectorization is represented in green.
• Figure 5: On the left, we present a zoom of the vectorization of the camel silhouette using the basic curvature method with the regularization default value $w_n \equiv 0$. On the right, we present the result obtained using $w_n=30$ as regularization parameter for the marked Bézier curve section.