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

TL;DR

It is shown that a deep neural network with an U-Net architecture can provide precise particle positions with a high detection rate and 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.

Abstract

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 the network correctly identifies 97.7\% of the particles while only creating 2.7 \% of 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 3.7\% of the particle diameter.

Figures (14)

• Figure 1: The U-Net architecture adopted in our study. The arrows show the flow of information. The contraction path (red arrows) and the expansion path (green arrows) form an U-shaped information bottleneck that forces the neural network to learn semantic content. Additionally, there are the copy and concatenation paths (gray arrows) which preserve the spatial resolution of the original image. The numbers on top of the blocks (and their width) indicate how many feature maps of that size are implemented.
• Figure 2: Deep learning identifies the particle positions significantly better than classical image processing methods: (a) Raw image from the drop tower experiment. (b) Synthetic background image illustrating inhomogeneous illumination and container reflections. (c) Semantic segmentation (white pixels indicate particles) via classical image processing. (d) Instance segmentation produced by a trained U-Net.
• Figure 3: Training of the network requires for each tile a mask image (the target) where the particle positions are indicated with white circular masks: (a) Original image tile. (b) Manually drawn circles in imageJ used to determine particle coordinates. (c) Corresponding mask image with mask radius equal to the particle radius. (d)-(f) Mask image with smaller mask radii $R$ = 10, 5, and 1 respectively. Smaller masks help to resolve overlapping particles, as discussed in Section \ref{['sec:mask_size']}.
• Figure 4: During training, the validation loss typically saturates after 30-60 epochs. Data is averaged over 10 different random initializations of the same model.
• Figure 5: Vectors $\vec{s}$ illustrating the discrepancy between manually identified particle positions (green rings) and the positions determined from the U-Net prediction (red dots). The length $s$ of each vector is magnified 10 times for visibility.