Fast calculation of best focus position

New computational technique based on linear-scale differential analysis (LSDA) of digital image is proposed to find the best focus position in digital microscopy by means of defocus estimation in two near-focal positions only. The method is based on the calculation of local gradients of the image on different scales using its convolution with a number of differential filters of linearly varying sizes, consequent removal of noisy pixels out of consideration, and selection of pixels at the edges of objects. It is shown that the mean values of the selected gradients decrease while the scale increases thus the rate of change of these mean values of gradients unambiguously determines the magnitude of digital image defocus as a function of scale. Using this method the value and sign of defocus can be found if the result of LSDA of captured images is compared with pre-defined look-up table. The robustness of the proposed method to spatial noise is achieved by ignoring pixels that are corrupted by spatial noise within the areas of the image outside the edges of objects. Most computational operations of the method are based on integer arithmetic that simplifies its practical implementation and significantly improves the performance. The latter aspect is particularly important for practical use in real-time imaging systems.