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EDM-Based Morphological Operations
The basic morphological functions are erosion, the removal of pixels from the periphery of a feature, or dilation, the adding of pixels to that periphery. Classical erosion removes any pixel that has a background neighbor (any of the eight neighbors that share an edge or corner). Conversely, classical dilation adds any pixel that touches a pixel in the feature. Of course, both of these operations change the size of features or structures and so they are most often used together. An opening is an erosion followed by a dilation, while a closing is a dilation followed by an erosion. These operations can smooth irregular borders, and fill in or remove isolated pixel noise and fine lines.
More isotropic and also faster application of erosion and dilation is possible using the Euclidean distance map (EDM). This function assigns gray values to each feature pixel in a binary image with a value that corresponds to the distance from that pixel to the nearest background pixel. Thresholding the EDM of the feature produces erosion, while thresholding the EDM of the background produces dilation. The distance can be adjusted accurately and the results retain feature shapes. However, the conditional iterative morphological tools are also useful because of their ability to select isolated points and lines. This interactive tutorial illustrates the use of morphological operations based on the Euclidean Distance Map.
The tutorial initializes with a randomly selected specimen appearing in the Specimen Image window. The Choose A Specimen pull-down menu provides a selection of thresholded binary images, in addition to the initial randomly chosen one. The Operation buttons select Erosion, Dilation, Opening or Closing. The Distance slider adjusts the threshold used on the EDM, which controls the distance in pixels used for the erosion and dilation. The result of the selected operation and setting is shown in the Processed Image at the right.
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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