Partial Differential Equation

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 …

Shape Matching

The main task in three-dimensional non-rigid shape correspondence is to retrieve similarities between two or more similar three-dimensional objects. We analysed how well partial differential equations may be used to solve this problem.

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.

Towards PDE-Based Video Compression with Optimal Masks and 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 optimal data. For the possible …

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 …

A Study of Spectral Expansion for Shape Correspondence

The main task in three dimensional non-rigid shape correspondence is to retrieve similarities between two or more similar three dimensional objects. A useful way to tackle this problem is to construct a simplified shape representation, called …

Classic Wave Equation Can Do Shape Correspondence

A major task in non-rigid shape analysis is to retrieve correspondences between two almost isometric 3D objects. An important tool for this task are geometric feature descriptors. Ideally, a feature descriptor should be invariant under isometric …

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 …

Shape Matching by Time Integration of Partial Differential Equations

The main task in three dimensional shape matching is to retrieve correspondences between two similar three dimensional objects. To this end, a suitable point descriptor which is invariant under isometric transformations is required. A commonly used …