Efficient Data Optimisation for Harmonic Inpainting with Finite Elements

TL;DR

This paper introduces a finite element-based approach for harmonic inpainting that enhances speed and quality, along with highly efficient algorithms enabling large-scale image processing for improved image compression.

Contribution

It replaces finite differences with finite elements, develops faster data optimisation algorithms, and enables handling of very large images efficiently.

Findings

Finite element discretisation improves inpainting quality.

Optimised algorithms are several orders faster than existing methods.

Method scales to very large images efficiently.

Abstract

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.