Sampling for Shape from Focus in Optical Microscopy

Shape from focus (SFF), which relies on image focus as a cue within sequenced images, represents a passive technique in recovering object shapes in scenes. Although numerous methods have been recently proposed, less attention has been paid to particular factors affecting them. In regard to SFF, one such critical factor impacting system application is the total number of images. A large data set requires a huge amount of computation power, whereas decreasing the number of images causes shape reconstruction to be crude and erroneous. The total number of images is inversely proportional to interframe distance or sampling step size. In this paper, interframe distance (or sampling step size) criteria for SFF systems have been formulated. In particular, light ray focusing is approximated by the use of a Gaussian beam followed by the formulation of a sampling expression using Nyquist sampling. Consequently, a fitting function for focus curves is also obtained. Experiments are performed on simulated and real objects to validate the proposed schemes.