Nonnegative mixed-norm preconditioning for microscopy image segmentation.

Image segmentation in microscopy, especially in interference-based optical microscopy modalities, is notoriously challenging due to inherent optical artifacts. We propose a general algebraic framework for preconditioning microscopy images. It transforms an image that is unsuitable for direct analysis into an image that can be effortlessly segmented using global thresholding. We formulate preconditioning as the minimization of nonnegative-constrained convex objective functions with smoothness and sparseness-promoting regularization. We propose efficient numerical algorithms for optimizing the objective functions. The algorithms were extensively validated on simulated differential interference (DIC) microscopy images and challenging real DIC images of cell populations. With preconditioning, we achieved unprecedented segmentation accuracy of 97.9% for CNS stem cells, and 93.4% for human red blood cells in challenging images.