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.
Abstract (translated)
在这篇论文中，我们提出了一种使用三次Bézier曲线进行轮廓向矢量图转化的主动轮廓模型。在Bézier曲线的端点之间，我们将它们区分为角点和普通点，在这些普通点上切线向量的方向被规定。通过最小化Bézier曲线与轮廓边界之间的距离，该主动轮廓模型优化了Bézier曲线端点的位置、普通点处切线向量的方向以及对Bézier曲线参数的估计。这种主动轮廓模型可以使用任何方法获得的初始轮廓矢量化结果作为起始猜测。 我们提出的方法显著减少了轮廓边界与其通过世界一流的图形软件（如Inkscape和Adobe Illustrator）以及基于曲率的矢量化方法得到的矢量图之间的平均距离，后者用于比较参考。我们的方法还允许通过对缩短Bézier曲线长度来施加额外的规则性。
URL
https://arxiv.org/abs/2505.05132
