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Cross Correlation
Another very useful Fourier-space technique is cross-correlation. This requires two images, one of a scene containing objects of interest that may be difficult to locate or count because of their appearance or because of a complex surroundings, including camouflage. The second image contains just a single object of the type being sought. Fourier transforms of the two images are multiplied together with a phase shift and the result re-transformed to the pixel domain, to produce bright spots where the objects were located. The top hat filter, introduced above, may then be used to locate the spots.
This interactive tutorial illustrates the use of cross-correlation to locate simple targets in an image. In the tutorial, although it is easy to recognize the various letters visually, counting each one is difficult because of the irregular layout. Using each letter as a target, performing cross correlation, and applying a top hat filter produces a result that makes the counting process simple.
The tutorial initializes with a specimen image composed of black letters on a white background appearing in the Specimen Image window. The Choose A Target pull-down menu selects which of the various target images to use. The Display Image buttons display on the right either the selected Target image, or the result of Cross-Correlation (in which the brightness of the spots measures the goodness of the match with the target), or the result of applying a Top Hat filter to the cross-correlation result, which locates the brightest spots and thus marks the location of the original target letters.
Contributing Authors
John C. Russ - Materials Science and Engineering Dept., North Carolina State University, Raleigh, North Carolina, 27695.
Matthew Parry-Hill, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.
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