# Inverse Diffusion Curves using Shape Optimization

arXiv: https://arxiv.org/abs/1610.02769 · HTML: https://mlsanity.com/paper/1610.02769/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2016.

## Built on by (most cited first, 12 of 12)

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- [LayerPeeler: Autoregressive Peeling for Layer-wise Image Vectorization](https://mlsanity.com/paper/2505.23740/) (2025)
- [Image Vectorization: a Review](https://mlsanity.com/paper/2306.06441/) (2023)
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- [Hierarchical Vectorization for Portrait Images](https://mlsanity.com/paper/2205.11880/) (2022)
- [Optimize and Reduce: A Top-Down Approach for Image Vectorization](https://mlsanity.com/paper/2312.11334/) (2023)
- [Clair Obscur: an Illumination-Aware Method for Real-World Image Vectorization](https://mlsanity.com/paper/2511.20034/) (2025)
- [ProxyImg: Towards Highly-Controllable Image Representation via Hierarchical Disentangled Proxy Embedding](https://mlsanity.com/paper/2602.01881/) (2026)
- [SemLayer: Semantic-aware Generative Segmentation and Layer Construction for Abstract Icons](https://mlsanity.com/paper/2603.24039/) (2026)

## Abstract (arXiv)

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.