Precise particle tracking against a complicated background: polynomial fitting with Gaussian weight

We present a new particle tracking software algorithm designed to accurately track the motion of low-contrast particles against a background with large variations in light levels. The method is based on a polynomial fit of the intensity around each feature point, weighted by a Gaussian function of the distance from the centre, and is especially suitable for tracking endogeneous particles in the cell, imaged with bright field, phase contrast or fluorescence optical microscopy. Furthermore, the method can simultaneously track particles of all different sizes, and allows significant freedom in their shape. The algorithm is evaluated using the quantitative measures of accuracy and precision of previous authors, using simulated images at variable signal-to-noise ratios. To these we add new tests: the error due to a non-uniform background, and the error due to two particles approaching each other. Finally the tracking of particles in real cell images is demonstrated. The method is made freely available for non-commercial use as a software package with a graphical user-interface, which can be run within the Matlab programming environment.