Directional decomposition of an image consists of separating it into several components, each containing directional information in some specific directions. It has many applications in digital image processing, such as image improvement or linear feature detection, and could be used on seismic data to help geophysicists finding faults. In this thesis, we look at a directional filter bank (DFB) introduced by Bamberger and Smith and how to implement it efficiently on CPU and GPU. Graphics Processing Units (GPUs) are becoming increasingly more suitable for general scientific computing, and applications with suitable properties run much quicker on a GPU than a CPU. For instance, NVIDIA CUDA (Compute Unified Device Architecture) is a new progra...