U-Net based particle localization in granular experiments: accuracy limits and optimization

Identifying the positions of granular particles from experimental images is often complicated by their partial overlap in two dimensional projections. Uneven backgrounds and inhomogeneous illuminations can add to the challenge. Conventional image-processing methods are often unable to analyze such images. We show that a deep neural network with an U-Net architecture can provide precise particle positions with a high detection rate. For our challenging test image set, the network correctly identifies 97.5% of the particles while producing only 3.5% false positives. The training of the U-Net requires a number of target images where the position of all particles have been identified by humans. Those positions are then indicated in the target images by setting a small number of mask pixels to white in an otherwise black image. We demonstrate that the design of these masks critically determines performance: mask size controls the resolution of overlapping particles, anti-aliased masks enable subpixel accuracy, and systematic human labeling biases set a measurable lower bound on achievable precision. Our final network achieves an accuracy of the particle coordinate of 3.6% of the particle diameter. Trained by raw images containing overlapping particles under uneven illumination conditions (left), our neural network of U-Net architecture (middle) is able to predict masks (right) that can be used to locate the particle centers despite all the complications in the raw images.