| Fan filters with directional sensitivity are important in practice and have been used for processing in the areas of robotics and computer vision, seismology, image enhancement, and to some extent in image coding. Similarly, filters for subband analysis/synthesis which allow a two-dimensional input signal to be represented by a sum of maximally decimated subband images and then reconstructed from these decimated images are also of great importance for image processing, primarily in the area of image coding. In the past, much attention has been devoted to one-dimensional decimated filter banks and methods of reconstruction from the decimated channels. More recently, reconstruction methods for two-dimensional filter banks have received a great deal of attention. In these methods, the constituent filter banks are lowpass, bandpass, and highpass filters. Maximum decimation and directional sensitivity are clearly useful filter bank properties and to date have only been treated separately. This thesis presents a new two-dimensional filter bank which explicitly combines these two properties. The new filter bank decomposes images into directional components which can be maximally decimated while still allowing the original image to be exactly reconstructed from its decimated channels.;First, this thesis relates several concepts from the geometry of numbers to the theory of multidimensional signals and systems. These relationships allow for multidimensional upsampling and downsampling to be conveniently described. Based on this development of multidimensional multirate systems, the geometrical aspects of designing multidimensional filter banks are discussed in depth. The required analysis/synthesis filters for the directional filter bank are designed from one-dimensional prototypes. The main design methodology used in the thesis, design via change of variables, yields filters which can be implemented in a computationally efficient, rectangularly-separable polyphase form.;In addition to investigating the theory and design of the directional filter bank, applications of this new filter bank are also investigated. In particular, the directional filter bank is used as a part of an orientation analysis tool. The orientation analysis then governs feature detection and enhancement algorithms for applications such as the automated detection of cell boundaries in biomedical images and the automated enhancement of fingerprints. The use of the directional filter bank in building subband image coding systems which attempt to exploit the directional sensitivity of the human visual system are also investigated. |
