Project B16 (finished)

Project B16 - Combining Adaptive Thinning with Graph Signal Processing

Principal Investigator: Armin Iske

Background and Motivation

Adaptive Thinning (AT) is a recent method for image and video compression. The algorithm AT utilizes linear splines over anisotropic Delaunay triangulations (tetrahedralizations), where the vertices of the triangulations are chosen to locally adapt the regularity of the image (video). Thereby, AT yields a sparse approximation of the input image (video). Since AT works with piecewise linear functions, high frequency components of the image (video), i.e., textures and noise, are removed. This, however, may lead to a mismatch concerning the human viewer’s visual perception.

Aims and Objectives

The aim of this project is to further develop the concept of image compression by AT. We focus on texture encoding to improve the image quality on specifically chosen triangles of the triangulation. To this end, we apply signal processing methods on graphs, which merges algebraic and spectral graph theoretic concepts with computational harmonic analysis. In this procedure, we interpret the given data as a graph signal over each triangle, on which we apply the graph Fourier transform. In the graph spectral domain we are then able to apply filtering methods on the data. Our research focuses on the construction of suitable graph Fourier transforms, where we also employ suitable filtering methods to ensure optimal encoding.

Publications

Armin Iske and Niklas Wagner: From image to video approximation by adaptive splines over tetrahedralizations. Sampling Theory in Signal and Image Processing 17, 2018, 43-55.

Armin Iske and Niklas Wagner: Sparse approximation of videos by adaptive linear splines over anisotropic tetrahedralizations. IEEE International Conference Sampling Theory and Applications (SampTA2017), 2017, 514-517. DOI: 10.1109/SAMPTA.2017.8024442.

PhD Student: Niklas Wagner succesfully defended his PhD thesis on September 4, 2021.