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#### Boolean Combinations

Combining binary images using Boolean logic makes it possible to select structures or objects based on multiple criteria. For example, the thresholded binary images from the red, green and blue channels in the example do not by themselves select balloons of a single color. The Boolean Combinations interactive tutorial shows how combinations of binary images can accomplish this.

Interactive Tutorial
 Boolean Combinations Discover how to combine binary images using Boolean logic to select structures.

The basic set of Boolean operators are AND (pixels that are on in both images), OR (pixels that are on in either image), and Exclusive-OR (pixels that are on in one or the other image but not both). Combined with NOT (the logical inverse) this allows selecting various sets of pixels as shown in the Boolean Operations interactive tutorial.

Interactive Tutorial
 Boolean Operations Explore combining binary images using Boolean logic.

By using Boolean combinations of images thresholded with different criteria, skeletons and skeleton components such as nodes and ends, outlines, and the results from various morphological erosions and dilations, it is often possible to isolate specific structures of interest for measurement, and to simplify those measurements. Boolean combinations are also used to superimpose grids of lines and points onto images as the basis for the stereological measurements shown below.

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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