Several factors influence our computation of the correlation. First, we want to account for different translations, or shifts, of the fingerprint image. For example, if a print from one individual is in the upper left corner of the print area and a print from the same individual is located in the lower right corner, our system should identify the two prints as being highly correlated. Second, we need to consider computational complexity and the time it takes to perform this calculation. Because of these issues, we chose to implement a convolution based method of the convolution calculation.
Convolution is an inner product calculation with various shifts.
Thus, it works nicely to solve our issue of translation of a fingerprint in the print area. Now, because convolution computes the inner product of the two images for all possible shifts, we can simply extract the maximum value from the convolution result matrix and call this our correlation for the two images. In this manner, we implement a method for comparing the two grayscale images. The other issue we are faced with is computational expense. Performing multiplication in the Fourier domain is equivalent to a circular convolution in the sample domain.