Curvelet transforms - Advanced methods for data representation
PR, BA, DA
Description
The efficient representation of data is a core concern throughout computer science. In computer graphics, spatial data is of special importance in the form of images. These represent the spatial distribution not only of colors but also of various radiometric quantities (radiance, irradiance, photon density) or surface detail in the form of height maps. In this project, we will deal with spatial data that encodes the light distribution in 3D scenes and we will have global illumination algorithms as our main use case.
A common way to efficiently represent image data is to convert it into a different base, i.e. describing the data as the sum of (a hopefully low number) of well known basis functions. The standard raster image is a representation of the data as a sum of block functions that are 1 on a gives pixel and 0 on all others. This is an efficient way to encode white noise but the regularity of normal images can be exploited for more suited formats. Using the Discrete Cosine Transform, as it is done in the JPEG image compression standard, allows the efficient encoding of image region that have largely the same color. In the JPEG2000 standard, an advanced set of basis functions, namely wavelets, are used to achieve significantly better compression ratios with the same reconstruction quality. Special purpose basis functions are for example Spherical Harmonics, which are well suited to compress slowly varying data that is present in indirect illumination. A recent and largely unexplored set of basis functions are curvelets, which allow the highly efficient representation of data with line discontinuities, i.e. data where the regions of different values are separated by boundary curves. Visibility data is a prime example of such images, as the visibility changes abruptly across the silhouettes of objects.
The goal of this project would be to develop efficient implementation of various image transform on both the CPU and GPU.
Tasks
- Familiarize yourself with the literature on various advanced image transforms (wavelets, curvelets, contourlets).
- Study their reference implementations (if available).
- Develop efficient implementations on both the CPU and the GPU (using OpenCL or CUDA).
- Evaluate their suitability for usage in global illumination settings.
Requirements
- Motivation to explore a topic that contains a fair share of mathematics.
- Knowledgeable in C++.
- Knowledge of the GPU computing model (OpenCL, CUDA) beneficial.
- Knowledge of Matlab is beneficial.
Literature
General information on curvelets: curvelet.org
Introduction to wavelets in the JPEG2000 standard: IEEE Signal Processing Magazine
Contact
Email: thomas.auzinger@cg.tuwien.ac.at
Homepage: Thomas Auzinger
Phone: +43 1 58801-18683
