# Efficient Data Optimisation for Harmonic Inpainting with Finite Elements

arXiv: https://arxiv.org/abs/2105.01586 · HTML: https://mlsanity.com/paper/2105.01586/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2021.

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

- [Learning Sparse Masks for Diffusion-based Image Inpainting](https://mlsanity.com/paper/2110.02636/) (2021)
- [Efficient Neural Generation of 4K Masks for Homogeneous Diffusion Inpainting](https://mlsanity.com/paper/2303.10096/) (2023)
- [A Wasserstein GAN for Joint Learning of Inpainting and Spatial Optimisation](https://mlsanity.com/paper/2202.05623/) (2022)
- [Skeleton Sparsification and Densification Scale-Spaces](https://mlsanity.com/paper/2509.21398/) (2025)

## Abstract (arXiv)

Harmonic inpainting with optimised data is very popular for inpainting-based image compression. We improve this approach in three important aspects. Firstly, we replace the standard finite differences discretisation by a finite element method with triangle elements. This does not only speed up inpainting and data selection, but even improves the reconstruction quality. Secondly, we propose highly efficient algorithms for spatial and tonal data optimisation that are several orders of magnitude faster than state-of-the-art methods. Last but not least, we show that our algorithms also allow working with very large images. This has previously been impractical due to the memory and runtime requirements of prior algorithms.