Spatial filtering is commonly used for the following purposes.
Filtering in the domain of image space
Generally local convolution with a window operator of n ´ n matrix is used. Table 5.2 shows several typical 3 x 3 window operators and their effects.
Sobel, Laplacian and Highpass filters are useful to detect or extract linear features and edges. Mean and Median filters are required to avoid high frequency noises, for example in the images of water surface with subtle tone change.
Filtering in the domain of spatial frequency
The Fourier transformation is conventionally used to convert from image space domain to spatial domain of which frequency is controlled by low pass, high pass and band pass filters. After such frequency domain filtering, image will reconstructed by using an inverse Fourier transformation.
Low pass filters will cut off high frequency to allow the output of only low frequency image, while high pass filters will cut off low frequency noises such as stripe noise or shading.
As the Fourier transformation will not be able to localize the frequency domain filtering, the Wavelet function has become more useful to detect particularly edges, because it enables to select an optimum window size locally.
Examples of images applied by various filters are shown in the front pages of this book.