General Defocusing Particle Tracking: fundamentals and uncertainty assessment

General Defocusing Particle Tracking (GDPT) is a single-camera, three-dimensional particle tracking method that determines the particle depth positions from the defocusing patterns of the corresponding particle images. GDPT relies on a reference set of experimental particle images which is used to predict the depth position of measured particle images of similar shape. While several implementations of the method are possible, its accuracy is ultimately limited by some intrinsic properties of the acquired data, such as the signal-to-noise ratio, the particle concentration, as well as the characteristics of the defocusing patterns. GDPT has been applied in different fields by different research groups, however, a deeper description and analysis of the method fundamentals has hitherto not been available. In this work, we first identity the fundamental elements that characterize a GDPT measurement. Afterwards, we present a standardized framework based on synthetic images to assess the performance of GDPT implementations in terms of measurement uncertainty and relative number of measured particles. Finally, we provide guidelines to assess the uncertainty of experimental GDPT measurements, where true values are not accessible and additional image aberrations can lead to bias errors. The data were processed using DefocusTracker, an open-source GDPT software. The datasets were created using the synthetic image generator MicroSIG and have been shared in a freely-accessible repository

Particle detection and tracking in fluorescence time-lapse imaging: a contrario approach

This paper proposes a probabilistic approach for the detection and the tracking of particles in fluorescent time-lapse imaging. In the presence of a very noised and poor-quality data, particles and trajectories can be characterized by an a contrario model, that estimates the probability of observing the structures of interest in random data. This approach, first introduced in the modeling of human visual perception and then successfully applied in many image processing tasks, leads to algorithms that neither require a previous learning stage, nor a tedious parameter tuning and are very robust to noise. Comparative evaluations against a well-established baseline show that the proposed approach outperforms the state of the art.Comment: Published in Journal of Machine Vision and Application

A New Robust Regression Method Based on Minimization of Geodesic Distances on a Probabilistic Manifold: Application to Power Laws

In regression analysis for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. In many situations, the assumptions underlying OLS are not fulfilled, and several other approaches have been proposed. However, most techniques address only part of the shortcomings of OLS. We here discuss a new and more general regression method, which we call geodesic least squares regression (GLS). The method is based on minimization of the Rao geodesic distance on a probabilistic manifold. For the case of a power law, we demonstrate the robustness of the method on synthetic data in the presence of significant uncertainty on both the data and the regression model. We then show good performance of the method in an application to a scaling law in magnetic confinement fusion.Comment: Published in Entropy. This is an extended version of our paper at the 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), 21-26 September 2014, Amboise, Franc