# Finding Correlation response in fourier domain

Lets say I have a system that is trying to find a small image (assume all images are grayscale) within in an image by using correlation. So this system has the baseline image, and I input 5 different images (the five input images are bigger or have more data points than the baseline image) and do correlation of my baseline images against the five input images. From this I would get 5 "tables" of correlation values, and from each tables I select the highest value as the metric to how similar the input image is to the baseline image.

Now lets say I want to upgrade my system to do the correlation in the fourier domain. I pad the smaller image with zeros, do the fft, multiply the data by the conjugate of the baseline to do correlation, and I get the power spectral density at each point through some PSD estimator method, like Bartlett, welch, blackman-tukey, etc.

From my understanding, the more spread out, or the less dense the power spectrum is over a set number of frequency bins, the less correlated the two signals are, and vice versa.

But my question is, in the frequency domain, particularly for a two-dimensional signal, would the metric for measuring how spread the power is simply be the maximum value within the table I would attain after the correlation and PSD estimate, as in the spatial domain case?

Also if you could cite your answers whether it be a book or article, that would be much appreciated

• i ain't an image-processing person, but my understanding of correlating one piece of data to another piece of data (of the same size) is that the result is number, not a table of numbers. if you have a reference image (that's what i would call it) and 5 other images that you will correlate the reference to, the result is 5 (likely different) numbers. – robert bristow-johnson Sep 12 '15 at 22:07
• See my edit on what type of correlation I am speaking of – IkeJoka Sep 12 '15 at 23:20
• okay, so are the 5 test images scaled up from where you might expect to see the same image in the reference? is it like you have a good, high-resolution image of a gun (or a person's face) and you want to find that object, scaled arbitrarily, in some larger image with many other objects? then you will have a table indeed and it would have 3 dimensions: x position, y position, and scale factor. and you would want to pick the maximum correlation value out of that. – robert bristow-johnson Sep 12 '15 at 23:43
• Sorry I should have clarified that these are grayscale images – IkeJoka Sep 13 '15 at 0:10
• @robert bristow-johnson thanks for your answer – IkeJoka Sep 13 '15 at 23:43