Optical multiscale morphological processor using a complex-valued kernel

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Abstract
Morphological transformations are typically performed on binary images by convolution with a binary kernel, which is followed by a threshold. We present an alternate approach that uses a complex-valued kernel with odd symmetry to perform these morphological operations. The complex-valued kernel increases the information-processing ability of the processor with no increase in system complexity. One advantage is that the processor operates on all constant regions of a gray-level image in parallel. A scale–space representation of this processor is obtained by varying the size of the kernel continuously through a range of scales. By using redundant information in the scale representation, this system is found to be robust in the presence of noise and spatial nonuniformities in the image. An optical system to perform morphological filtering based on this system is presented.