Machine learning techniques for the detection and 3D localization of tracer particles in astigmatic images
Creators: name: Franchini, Simon
Publisher: name: Imperial College London
Year: 2019

description: Flow and transport in porous media are driven by pore scale processes. Particle tracking in transparent porous media allows for the observation of these processes at the time scale of ms. We demonstrate an application of astigmatic particle tracking using brightfield illumination and a CMOS camera sensor. The resulting images have relatively high noise levels. For detailed observations of e.g. flow in porous media it is highly beneficial to maximise the number of tracked particles and to maximize the depth range of the method. The higher the particle density, the larger the number of overlapping particles. Previous astig- matic particle tracking techniques were not able to extract depth information from such overlap- ping particle images, limiting the methods to low seeding densities. To address this challenge, we developed a technique for locating particles in the out-of-plane direction. The methodology relies on extracting features of particle images by fitting generalized Gaussian distributions to particle images. A cascade fitting scheme is able to extract image features from partially over- lapping particle images. The resulting fitting parameters are then linked to the out-of-plane coordinates of particles using flexible machine learning tools. A workflow is presented which shows how to generate a training dataset of fitting parameters paired to known out-of-plane locations. Several regression models are tested on the resulting training dataset, of which a boosted regression tree ensemble produced the lowest cross-validation error. A second technique was developed which focused on improving particle detection rates. Particle detection poses the main bottleneck in maximising the depth range and the particle density of a particle tracking scheme. We show how a modern algorithm from the computer vision domain can be adapted to conduct both the particle detection and the 3D particle localization in one step. This allows for the combined detection and localization of highly defocused and highly overlapping particle images in one pass through a neural network. The computational cost is low in comparison to previous techniques, independent of the number of particle overlaps and almost independent of the number of particles. The efficiacy of both techniques is then examined in a laminar channel flow in a large measure- ment volume of 2048, 1152 and 3000 μm in length, width and depth respectively. The size of the test domain reflects the representative elementary volume of many fluid flow phenomena in porous media. Such large measurement depths require the collection of images at different focal levels. We acquired images at 21 focal levels 150 μm apart from each other. With the Generalized Gaussian localization method, the error in predicting the out-of-plane location in a single slice of 240 μm thickness was found to be 7 μm, while in-plane locations were determined with sub-pixel resolution (below 0.8 μm). The mean relative error in the velocity measurement was obtained by comparing the experimental results to an analytic model of the flow. The estimated displacement errors in the axial direction of the flow were 0.21 pixel and 0.22 pixel at flows rates of 1.0 mL/h and 2.5 mL/h, respectively. The deep learning model pushes the depth range of the method from 240 to 400 μm, increasing the depth range of the measurement volume by 67 % over previous detection methods. We achieve a similar error in the depth predictions to previous algorithms for non-overlapping objects. For overlapping objects, the location error increases with increasing degree of overlap. In experimental images the error peaks at twice it’s value when objects have the same center point location. We hope that this work opens up new applications of defocal particle tracking where large depth ranges or high object densities are required.