Abstract
The purpose of this research was to design a spatial domain convolution filter capable of directional edge detection which has a specific relationship to a pre-defined filter in the frequency domain. Nobody has designed a directional filter in the spatial domain that is the dual of a specific directional filter in the frequency domain. In other words, the weights of the spatial domain filter are derived from a distinct frequency domain filter. The importance of a spatial domain filter is manifested by two facts: (1) Filtering can be achieved exclusively in one domain, and (2) it can be efficiently implemented. Filtering in the frequency domain requires an image be transformed to the frequency domain, via the Fourier transform. Then the transformed image is filtered with a frequency domain filter; subsequently, this result is inverse-Fourier-transformed to realize a filtered image in the spatial domain. The filtering process of this research is briefly summarized by the following steps: ³A bandpass filter was defined in the frequency domain. Its defining parameters were assigned based on image data. Chapters 11 and IV discuss the theory and parameters associated with this filter. Directionality was incorporated into the frequency domain filter by creating a special two-dimensional window to truncate the bandpass filter's frequency response. This allowed edges in any arbitary direction to be detected. Chapters 11 and IV discuss the criteria and parameters associated with this window. Once the directional filter in the frequency domain was designed, its characteristics were transferred to the weights of the spatial domain filter. A detailed outline of this process is presented in Chapter 111. Finally, the image was convolved with the spatial domain filter, and after postprocessing, an edge map was produced. The most prominent result of this research is demonstrated by the fact that the directional edge detection process developed, defined, and discussed in this thesis was applied to a digital test image to produce an edge map with no gaps in its contiguous edge segments.
Yeary, Mark Bradley (1994). Design of a finite impulse response filter for the purpose of directional edge detection via spatial domain convolution. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -1994 -THESIS -Y39.