Interpolation

The Abstract Interpolation Problem

We present the abstract interpolation problem and show how it is related to common interpolation and approximation tasks.

Matlab Code (image processing and numerical optimization)

Over the years I have written quite a lot of Matlab code. The code is available here, here, here, and here and covers mostly image processing and interpolation/approximation topics. All the code is released under a GPL v3 licence (unless specified differently).

Optimising Data for PDE-Based Inpainting and Compression

Oral presentation

Evaluating the True Potential of Diffusion Based Inpainting in a Compression Context

Partial differential equations (PDEs) are able to reconstruct images accurately from a small fraction of their image points. The inpainting capabilities of sophisticated anisotropic PDEs allow compression codecs with suboptimal data selection …

High Quality Image Compression

Oral presentation

From Optimised Inpainting with Linear PDEs Towards Competitive Image Compression Codecs

For inpainting with linear partial differential equations (PDEs) such as homogeneous or biharmonic diffusion, sophisticated data optimisation strategies have been found recently. These allow high-quality reconstructions from sparse known data. While …

Why does non-binary mask optimisation work for diffusion-based image compression?

Finding optimal data for inpainting is a key problem for image-compression with partial differential equations. Not only the location of important pixels but also their values should be optimal to maximise the quality gain. The position of important …

Why does non-binary mask optimisation work for diffusion-based image compression?

Oral presentation

An Optimal Control Approach to Find Sparse Data for Laplace Interpolation

Finding optimal data for inpainting is a key problem in the context of partial differential equation-based image compression. We present a new model for optimising the data used for the reconstruction by the underlying homogeneous diffusion process. …

Continuous Spatial and Tonal Point Optimisation for Interpolation and Approximation of Convex Signals with Homogeneous Diffusion

Oral presentation