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Silhouette Vectorization by Affine Scale-Space

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Abstract

Silhouettes are building elements of logos, graphic symbols and fonts. These shapes can be designed and exchanged in vector form, but more often they are drawn, printed, scanned, or directly found in digital images. Such raster forms require vectorization to get scale-invariant exchangeable formats. There is a need for a mathematically well-defined and justified shape vectorization process, which also provides a minimal set of control points with geometric meaning. In this paper, we propose a new silhouette vectorization paradigm. It extracts the outline of a 2D shape from a raster binary image and converts it to a combination of cubic Bézier polygons and perfect circles. The proposed method uses the sub-pixel curvature extrema and affine scale-space for silhouette vectorization. By construction, our control points are geometrically stable under affine transformations. The proposed method can also be used as a reliable feature point detector for silhouettes. Compared to state-of-the-art image vectorization software, our algorithm demonstrates a superior reduction in the number of control points while maintaining high accuracy.

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Notes

  1. See (e.g.) https://en.wikipedia.org/wiki/Adobe_Illustrator or Vector Magic.

  2. https://fr.wikipedia.org/wiki/Scalable_Vector_Graphics.

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Authors and Affiliations

  1. Georgia Institute of Technology, Atlanta, Georgia

    Yuchen He & Sung Ha Kang

  2. École Normale Supérieure Paris-Saclay, Paris, France

    Jean-Michel Morel

Authors
  1. Yuchen He
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  2. Sung Ha Kang
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  3. Jean-Michel Morel
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Correspondence to Yuchen He.

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Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Yuchen He is supported in part by Chateaubriand Fellowship, Embassy of France in United States. Sung Ha Kang is supported in part by Simons Foundation Grant 584960. Jean-Michel Morel is supported by Fondation Mathématique Jacques Hadamard.

The algorithm introduced in this paper can be tested online on any image at https://ipolcore.ipol.im/demo/clientApp/demo.html?id=5555531082020.

Appendices

Silhouette Data Set

In Table 3, we collectively display the 20 silhouettes used in this paper. They are all downloadable from https://svgsilh.com, which are released under Creative Commons CC0.

Pseudocode for the Proposed Method

Here we present the pseudocode for our proposed method. In the description, we assume that the specified bilinear level set consists of only one Jordan curve for simplicity. In practice, the level set may contain multiple Jordan curves or self-crossing curves. If self-crossing occurs, we trace along the direction given by the level line at \(\lambda ^*+l\) for \(l>0\) sufficiently small [21]. Hence, it suffices to process each Jordan curve of the level set independently via the described algorithm.

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He, Y., Kang, S.H. & Morel, JM. Silhouette Vectorization by Affine Scale-Space. J Math Imaging Vis 64, 41–56 (2022). https://doi.org/10.1007/s10851-021-01053-z

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