ABSTRACT
The Fourier transform and the efficient algorithm for computing it, the fast Fourier transform, extend in a straightforward manner to two (or more) dimensions. The 2-D version of the Fourier transform can be applied to images providing a spectral analysis of the image content. Both the Fourier transform and the inverse Fourier transform are supported in two dimensions by MATLAB functions. The techniques of linear filtering described in the chapter can be directly extended to two dimensions and applied to images. In image processing, FIR filters are usually used because of their linear phase characteristics. The MATLAB Image Processing Toolbox provides considerable support for generating the filter coefficients. Several useful transformations take place entirely in the spatial domain. Spatial transformations perform a remapping of pixels and often require some form of interpolation in addition to possible antialiasing. In projective transformations, straight lines remain straight but parallel lines may converge. Unaided image registration usually involves the application of an optimization algorithm.
