ABSTRACT
The objectives and mathematical principles of morphological analysis are presented leading to the development of invariant Fourier descriptors via (R,?) the method. There are two stages in the historical development of morphological analysis. In the first stage, advantage was taken of the incredible human ability to observe, recognize, and codify particles of differing shapes. The second stage began with the developments of J. K. Beddow and G. C. Philip, R. Ehrlich and B. J. Weinberg, and T. P. Meloy. When an image is either magnified or reduced in size during the morphological analysis process it is especially important that the morphic descriptors remain invariant. Chemical properties include gross as well as point-to-point chemical analysis. Chemical kinetics may also be included. The properties of size and shape may be collected together as particle geometry. In order to measure the shape of a particle profile, the sample set of coordinate points satisfying the definition must be obtained.
