Method
Given two input images and :
Apply a window function (e.g., a Hamming window) on both images to reduce edge effects. Then, calculate the discrete 2D Fourier transform of both images.
Calculate the cross-power spectrum by taking the complex conjugate of the second result, multiplying the Fourier transforms together elementwise, and normalizing this product elementwise.
Obtain the normalized cross-correlation by applying the inverse Fourier transform.
Determine the location of the peak in .
Commonly, interpolation methods are used to estimate the peak location to non-integer values, despite the fact that the data are discrete. Because the Fourier representation of the data has already been computed, it is especially convenient to use the Fourier shift theorem with real-valued shifts for this purpose. It is also possible to infer the peak location from phase characteristics in Fourier space without the inverse transformation, as noted by Stone
Read more about this topic: Phase Correlation
Famous quotes containing the word method:
“The method of authority will always govern the mass of mankind; and those who wield the various forms of organized force in the state will never be convinced that dangerous reasoning ought not to be suppressed in some way.”
—Charles Sanders Peirce (1839–1914)
“The method of painting is the natural growth out of a need. I want to express my feelings rather than illustrate them. Technique is just a means of arriving at a statement.... I can control the flow of paint: there is no accident, just as there is no beginning and no end.”
—Jackson Pollock (1912–1956)
““English! they are barbarians; they don’t believe in the great God.” I told him, “Excuse me, Sir. We do believe in God, and in Jesus Christ too.” “Um,” says he, “and in the Pope?” “No.” “And why?” This was a puzzling question in these circumstances.... I thought I would try a method of my own, and very gravely replied, “Because we are too far off.” A very new argument against the universal infallibility of the Pope.”
—James Boswell (1740–1795)