Inpainting

Towards PDE-Based Video Compression with Optimal Masks Prolongated by Optic Flow

Lossy image compression methods based on partial differential equations have received much attention in recent years. They may yield high-quality results but rely on the computationally expensive task of finding an optimal selection of data. For the …

PDE-based image reconstruction and compression

It is possible to compress/inpaint images from very little data. In order to obtain reconstructions that are comparable to the original image it is necessary to optimize the underlying interpolation data.

Theoretical Foundation of the Weighted Laplace Inpainting Problem

Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed, where …

Clustering-Based Quantisation for PDE-Based Image Compression

Optimal known pixel data for inpainting in compression codecs based on partial differential equations is real-valued and thereby expensive to store. Thus, quantisation is required for efficient encoding. In this paper, we interpret the quantisation …

Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian

Oral presentation

Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian

Partial differential equations are well suited for dealing with image reconstruction tasks such as inpainting. One of the most successful mathematical frameworks for image reconstruction relies on variations of the Laplace equation with different …

Understanding Image Inpainting with the Help of the Helmholtz Equation

Partial differential equations have recently been used for image compression purposes. One of the most successful frameworks solves the Laplace equation using a weighting scheme to determine the importance of individual pixels. We provide a physical …

Optimising Data for PDE-Based Inpainting and Compression

Oral presentation

Optimizing Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic …

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 …