# Image Vectorization with Depth: convexified shape layers with depth ordering

arXiv: https://arxiv.org/abs/2409.06648 · HTML: https://mlsanity.com/paper/2409.06648/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 64 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 11 of 11)

- [Im2Vec: Synthesizing Vector Graphics without Vector Supervision](https://mlsanity.com/paper/2102.02798/) (2021)
- [A Learned Representation for Scalable Vector Graphics](https://mlsanity.com/paper/1904.02632/) (2019)
- [Towards Layer-wise Image Vectorization](https://mlsanity.com/paper/2206.04655/) (2022)
- [Geometry-Aware Symmetric Domain Adaptation for Monocular Depth Estimation](https://mlsanity.com/paper/1904.01870/) (2019)
- [Joint Semantic Segmentation and Depth Estimation with Deep Convolutional Networks](https://mlsanity.com/paper/1604.07480/) (2016)
- [P-Cloth: Interactive Complex Cloth Simulation on Multi-GPU Systems using Dynamic Matrix Assembly and Pipelined Implicit Integrators](https://mlsanity.com/paper/2008.00409/) (2020)
- [Deep Vectorization of Technical Drawings](https://mlsanity.com/paper/2003.05471/) (2020)
- [Layered Image Vectorization via Semantic Simplification](https://mlsanity.com/paper/2406.05404/) (2024)
- [Monocular Object Instance Segmentation and Depth Ordering with CNNs](https://mlsanity.com/paper/1505.03159/) (2015)
- [Silhouette Vectorization by Affine Scale-space](https://mlsanity.com/paper/2007.12117/) (2020)
- [A Binary Characterization Method for Shape Convexity and Applications](https://mlsanity.com/paper/2203.11395/) (2022)

## Built on by (most cited first, 4 of 4)

- [LayerPeeler: Autoregressive Peeling for Layer-wise Image Vectorization](https://mlsanity.com/paper/2505.23740/) (2025)
- [Illustrator's Depth: Monocular Layer Index Prediction for Image Decomposition](https://mlsanity.com/paper/2511.17454/) (2025)
- [SemLayer: Semantic-aware Generative Segmentation and Layer Construction for Abstract Icons](https://mlsanity.com/paper/2603.24039/) (2026)
- [CubicSplat: Differentiable Vector Graphics via Error-Bounded Forward Relaxation](https://mlsanity.com/paper/2608.20803/) (2026)

## Abstract (arXiv)

Image vectorization is a process to convert a raster image into a scalable vector graphic format. Objective is to effectively remove the pixelization effect while representing boundaries of image by scaleable parameterized curves. We propose new image vectorization with depth which considers depth ordering among shapes and use curvature-based inpainting for convexifying shapes in vectorization process.From a given color quantized raster image, we first define each connected component of the same color as a shape layer, and construct depth ordering among them using a newly proposed depth ordering energy. Global depth ordering among all shapes is described by a directed graph, and we propose an energy to remove cycle within the graph. After constructing depth ordering of shapes, we convexify occluded regions by Euler's elastica curvature-based variational inpainting, and leverage on the stability of Modica-Mortola double-well potential energy to inpaint large regions. This is following human vision perception that boundaries of shapes extend smoothly, and we assume shapes are likely to be convex. Finally, we fit B'ezier curves to the boundaries and save vectorization as a SVG file which allows superposition of curvature-based inpainted shapes following the depth ordering. This is a new way to vectorize images, by decomposing an image into scalable shape layers with computed depth ordering. This approach makes editing shapes and images more natural and intuitive. We also consider grouping shape layers for semantic vectorization. We present various numerical results and comparisons against recent layer-based vectorization methods to validate the proposed model.