This interactive tutorial explores the application of boolean operations to binary digital images. The tutorial initializes with one of a group of randomly selected specimen images appearing in the left-hand window entitled Specimen Images. The group of specimen images consists of an original color or grayscale image, along with two binary images that were obtained by digitally processing the original image. The Display Image radio button panel determines which of the three specimen images is displayed in the Specimen Images window. Adjacent to the Specimen Images window is the Boolean Image window that displays the image that results from applying a series of boolean operations to the two binary specimen images. To operate the tutorial, select a group of images from the Choose a Specimen pull-down menu, and select a binary operation to perform from the Choose an Operation pull-down menu. Visitors should examine the two binary images from each set of specimen images, and visitors should explore the results of applying the various boolean operations to the binary image pair.

Binary images have only two possible intensity values, on or off. In the tutorial, on pixels are represented by white, and off pixels are represented by black. Binary (Boolean) logic operations can be applied to binary images. In the tutorial, the four available binary logic operations are AND, OR, XOR, and NOT. AND, OR, and XOR operate on two input binary images, and NOT operates on a single binary image. Each operation produces a single binary image as a result. AND requires that pixels in both input binary images be on in order to be on in the result. OR sets the resulting pixel on if it is on in either of the two input binary images. XOR turns a pixel on in the result if it is on in either of the input binary images, but not if it is on in both. NOT turns an on pixel off, and turns an off pixel on. There are a total of 16 possible binary images that can be produced by applying a series of Boolean operations to two fixed input binary images. In actuality, as few as two Boolean operations (NOT and OR or NOT and AND) are sufficient for generating any of the 16 possible binary images. Because of this inherent redundancy of binary operators, the XOR operation is sometimes excluded from image processing software that includes binary logic operations.

Boolean operations are useful for isolating features of interest in a digital image. Often, two copies of a specimen image are processed separately to accentuate the details of interest. Then, the processed images are thresholded at variable threshold levels to produce binary images. The binary images can then be processed with Boolean operations. One approach that is often used is to threshold an input digital image on multiple color planes and then to apply a series of Boolean operations to the resulting images. For example, the outline of an object can be obtained by performing a dilation operation on a binary image and then XORing the result with the same binary image. Also, multiple binary images can be easily combined by ORing them together.

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