Detection of objects in quantum-noise-limited images

Abstract

A method is presented that allows the automatic detection of single particles against an extremely noisy background, e.g., biological macromolecules in a low dose electron micrograph. In this method each image element is replaced by the image variance in its environment. This convolution-like operation leads to the “variance image” which is an efficient detector of objects with the same average density as the background (such as phase objects). The variance image is essentially a simple measure of texture. The human visual system appears to be equipped with an equally powerful detector. A separate class of objects is comprised of objects that have an average density different from that of the background. These objects are often best detected by a low-pass filtering operation. The quantum-noise limits of both methods of detection are calculated and compared to the noise limits of “matched filtering” methods. Fast algorithms are provided to calculate the variance image. Model calculations confirm the theoretical noise limits. The Rose equation is discussed in the context of the two operators treated in this paper.