Abstract

Mathematical morphology is a branch of mathematics that has proven its usefulness in many image-processing and computer-vision problems.¹ We present the application of an optical-centroid scale-space processor for the computation of basic morphological operations. The centroid scale-space map² extracts centroids of the image that are defined within a local neighborhood whose size is specified by the kernel (x + iy) limited by a circular window. Properties of these centroids, as they are tracked through scale, permit one to obtain a great deal of information from the image in a simple and straightforward manner. One property of these maps is that solid regions of centroids are produced when the kernel is completely enclosed within a constant region of the input. One may use this information to compute various morphological transformations, such as erosions, dilations, and medial-axis transformations (MAT). Redundancies in the representation result in a method for the MAT that is robust in the presence of noise. In addition, the map works simultaneously on all constant regions of a gray-level image. The optical system is based on a joint-transform correlator that uses an optically addressed ferroelectric liquid-crystal spatial light modulator. A complete range of scales is scanned by winking an iris between open and closed. Results from this optical system will be presented.

© 1990 Optical Society of America