Abstract

Much attention on edge detection has centered around the development of algorithms which process the sampled image data obtained by an image acquisition system [1]. While considerable work on designing (general-purpose) image gathering optics also exists the interrelationships between the two design processes has received little attention. This paper formulates a combined stochastic optimization problem where the optical transfer function (OTF) of the image gathering optics, the sampling lattice, the noise level and the image processing algorithm are all design parameters to be selected according to the optimization criterion. The optimization criterion used is the minimization of the spatially averaged mean-squared error in estimating a characteristic or a spatial feature related the object scene. Edge detection is treated as a special case of the general problem where the related characteristic contains edge information. This formulation recognizes that the objective is to determine the edges in the object scene rather than the edges of an already blurred and noisy image. As both image acquisition parameters and image processing algorithms can have significant effects on the mean-squared error, the optimization formulated provides an approach to obtain the most compatible acquisition and processing systems.

© 1985 Optical Society of America