ABSTRACT
After the image has been transformed into the frequency or sequency domain, we may want to modify the resulting spectrum. Filtering modifies the frequency or sequency spectrum by selectively retaining, removing or scaling the various components of the spectrum. High-frequency information can be removed with a lowpass filter, which will have the effect of blurring an image, or low-frequency information can be removed with a highpass filter, which will tend to sharpen the image by emphasizing rapid changes. We may want to extract the frequency information in specific parts of the spectrum by bandpass filtering. Alternately, bandreject filtering can be employed to eliminate specific parts of the spectrum, for example, to remove unwanted noise. Equations for ideal filters with an abrupt transition in the filter function and the non-ideal Butterworth filters with a gradual change in the filter function are included along with numeric and visual examples. Filters in both the frequency/sequency domain and the spatial domain are considered. The wavelet transform is included with an implementation via 1-D spatial domain convolution filters. Along with the text are 21 illustrative figures and 91 associated monochrome and color images. The end of chapter exercises include problems and programming exercises.
