用贝塞尔曲线优化轮廓矢量化，提升精度并控制曲线简洁性。
An Active Contour Model for Silhouette Vectorization using Bézier Curves
- 基于贝塞尔曲线构建主动轮廓模型，区分角点与普通点。
- 显著降低矢量化结果与原始轮廓的平均距离，优于Inkscape等工具。
- 可控制曲线长度，增强矢量图的规则性，适合图形设计应用。
本文提出一种基于三次贝塞尔曲线的主动轮廓模型，用于轮廓矢量化。模型中，贝塞尔曲线的端点分为角点与普通点，角点处切线方向固定，普通点处则优化其切线方向。通过最小化贝塞尔曲线与轮廓边界的距离，模型同时优化端点位置、普通点切线方向及曲线参数。该方法可接受任意矢量化结果作为初始猜测。实验表明，本方法显著降低与世界顶级图形软件Inkscape、Adobe Illustrator以及所提曲率基矢量化方法之间的平均距离。此外，可通过缩短曲线长度进一步增强贝塞尔曲线的规则性。
原文摘要 · Abstract (English)
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.
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