Monte Carlo evaluations of ten focus measures

A high-performance focus measure is one of the key components in any autofocus system based on digital image processing. More than a dozen of focus measures have been proposed and evaluated in the literature, yet there have be no comprehensive evaluations that include most of them. The purpose of the current study is to evaluate and compare the performance of ten focus measures using Monte Carlo simulations, run on a self-built scalable inhomogeneous computer cluster with distributed computing capacity. From the perspective of a general framework for focus measure evaluations, we calculate the true point spread functions (PSFs) from aberrations represented by OSA standard Zernike polynomials using fast Fourier transform. For each run, a range of defocus levels are generated, the PSF for each defocus level is convoluted with an original image, and a certain amount of noise is added to the resulting defocused image. Each focus measure is applied to all the blurred images to obtain a focus measure curve. The procedure is repeated on a few representative images for different types and levels of noise (Gaussian, salt & pepper, and speckle). The performance of the ten focus measures is compared in terms of monotonicity, unimodality, defocus sensitivity, noise sensitivity, effective range, computational efficiency and variability.