Silhouette Vectorization by Affine Scale-space

TL;DR

This paper introduces a mathematically grounded silhouette vectorization method that extracts shape outlines from raster images, representing them with minimal control points as cubic Bezier polygons and circles, invariant under affine transformations.

Contribution

The proposed method uniquely combines affine scale-space analysis with curvature extrema detection to produce stable, minimal, and geometrically meaningful vector representations of silhouettes.

Findings

Outperforms existing software in reducing control points while maintaining accuracy.

Control points are stable under affine transformations.

Effective in detecting and representing shape features with minimal data.

Abstract

Silhouettes or 2D planar shapes are extremely important in human communication, which involves many logos, graphics symbols and fonts in vector form. Many more shapes can be extracted from image by binarization or segmentation, thus in raster form that requires a vectorization. There is a need for disposing of a mathematically well defined and justified shape vectorization process, which in addition provides a minimal set of control points with geometric meaning. In this paper we propose a silhouette vectorization method which extracts the outline of a 2D shape from a raster binary image, and converts it to a combination of cubic B\'{e}zier polygons and perfect circles. Starting from the boundary curvature extrema computed at sub-pixel level, we identify a set of control points based on the affine scale-space induced by the outline. These control points capture similarity invariant geometric features of the given silhouette and give precise locations of the shape's corners.of the given silhouette. Then, piecewise B\'{e}zier cubics are computed by least-square fitting combined with an adaptive splitting to guarantee a predefined accuracy. When there are no curvature extrema identified, either the outline is recognized as a circle using the isoperimetric inequality, or a pair of the most distant outline points are chosen to initiate the fitting. Given their construction, most of our control points are geometrically stable under affine transformations. By comparing with other feature detectors, we show that our method can be used as a reliable feature point detector for silhouettes. Compared to state-of-the-art image vectorization software, our algorithm demonstrates superior reduction on the number of control points, while maintaining high accuracy.