Segmentation, Inference and Classification of Partially Overlapping Nanoparticles

This paper presents a method that enables automated morphology analysis of partially overlapping nanoparticles in electron micrographs. In the undertaking of morphology analysis, three tasks appear necessary: separate individual particles from an agglomerate of overlapping nano-objects; infer the particle´s missing contours; and ultimately, classify the particles by shape based on their complete contours. Our specific method adopts a two-stage approach: the first stage executes the task of particle separation, and the second stage conducts simultaneously the tasks of contour inference and shape classification. For the first stage, a modified ultimate erosion process is developed for decomposing a mixture of particles into markers, and then, an edge-to-marker association method is proposed to identify the set of evidences that eventually delineate individual objects. We also provided theoretical justification regarding the separation capability of the first stage. In the second stage, the set of evidences become inputs to a Gaussian mixture model on B-splines, the solution of which leads to the joint learning of the missing contour and the particle shape. Using twelve real electron micrographs of overlapping nanoparticles, we compare the proposed method with seven state-of-the-art methods. The results show the superiority of the proposed method in terms of particle recognition rate.