Detecting if two images are visually identical

Question

Sometimes two image files may be different on a file level, but a human would consider them perceptively identical. Given that, now suppose you have a huge database of image

Answer 1

Cross-correlation or phase correlation will tell you if the images are the same, even with noise, degradation, and horizontal or vertical offsets. Using the FFT-based methods will make it much faster than the algorithm described in the question.

The usual algorithm doesn't work for images that are not the same scale or rotation, though. You could pre-rotate or pre-scale them, but that's really processor intensive. Apparently you can also do the correlation in a log-polar space and it will be invariant to rotation, translation, and scale, but I don't know the details well enough to explain that.

MATLAB example: Registering an Image Using Normalized Cross-Correlation

Wikipedia calls this "phase correlation" and also describes making it scale- and rotation-invariant:

The method can be extended to determine rotation and scaling differences between two images by first converting the images to log-polar coordinates. Due to properties of the Fourier transform, the rotation and scaling parameters can be determined in a manner invariant to translation.