The new techniques of amplitude compensated matched filtering using circular harmonic expansion and a Mellin transform are presented. These techniques yield much better discrimination and sharper autocorrelation peaks compared with the classical matched spatial filtering. Aside from these advantages, the amplitude compensated circular harmonic expansion matched filtering can also yield rotation invariance, and the amplitude compensated Mellin transform matched filtering can yield scale invariance. By computer simulation, we have verified the unique advantages of the new methods. We also provide 3-D graphs of autocorrelation and cross correlation.