Fractional derivatives of two-dimensional images have been discussed theoretically in terms of Fourier optics and computer simulated. Filters that realize the half-order differentiation can be either complex or real. We prove, in terms of fractional calculus, that the semiderivative filter is useful for the visualization of phase changes in a phase object in such a way that the output-image intensity is directly proportional to the first derivative of the input object. We give computer-simulated results of one-dimensional semidifferentiating.
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