Graph Spectral Image Processing over Adaptive Triangulations

Abstract

With the rapidly advancing developement of smartphones with integrated cameras, digital image compression is still a relevant and ongoing research topic. Conventional schemes, such as JPEG or JPEG 2000, rely on fixed transforms over regular grids. Opposed to this, adaptive thinning is an image compression scheme that reconstructs an image with linear splines over the anisotropic Delaunay triangulation of a set of adaptively chosen significant pixels

The main objective of this thesis is to improve the performance of this scheme, especially on textured images. To this end, we propose a post-processing procedure that improves selected regions of the reconstruction by utilizing graph signal processing as a tool to define frequency spectra on irregular, triangular image domains.

Our approach designs adaptive graphs to exploit signal smoothness of graph signals. To this end, significant triangular image blocks are classified via the structure tensor based on their textural content. Graphs are constructed that promote sparseness of the graph Fourier spectrum. This is achieved either by graph learning methods or a discrete weight model, where the edge weight is chosen optimally.

Based on the constructed graphs, the signal is transformed via the graph Fourier transform to the graph spectral domain, where thresholding and quantization can be performed efficiently.

Finally, we show how to implement this scheme, focusing on the transformation and quantization. We compare it with the adaptive thinning scheme on geometric and natural images.