Automatic location of microscopic focal planes for computerized stereology

When applying design-based stereology to biological tissue, there are two primary applications for an auto-focusing function in the software of computerized stereology system. The system must first locate the in-focus optical planes at the upper and lower surfaces of stained tissue sections, thus identifying the top and bottom as well as the thickness of the tissue. Second, the system must find the start and end along the Z-axis of stained objects within a Z-stack of images through tissue sections. In contrast to traditional autofocus algorithms that seek a global maximum or peak on the focus curve, the goal of this study was to find the two "knees" of the focus curve that represent the "just out-of-focus" focal planes. The upper surface of the tissue section is defined as the image just before focus is detected moving down the Z-stack. Continuing down, the lower surface is defined as the first image of the last set of adjacent images where focus is no longer detected. The performance of seven focus algorithms in locating the top and bottom focal planes of tissue sections was analyzed by comparing each algorithm on 34 Z-stacks including a total of 828 images. The Thresholded Absolute Gradient algorithm outperformed all others, correctly identifying the top or bottom focal plane within an average of 1 mu m on the training data as well as the test data.