Position Estimation and Tracking in Colloidal Particle Microscopy
Doktorsavhandling, 2005

This thesis presents methods for estimating the locations (including depth) of spherical colloidal particles in images recorded in video microscopy. Understanding the behavior of colloidal interactions and diffusion is of crucial importance in a vast number of areas. However, since the theory fails to predict the behavior of several important colloidal suspensions, observations and measurements on the microscopic level are needed. Examples of common, everyday colloids are milk, paint and pharmaceuticals. The positioning methods developed here can be used for tracking of particles in three dimensions observed in video microscopy. We make several suggestions on how the positioning method should be modified and implemented to be used for this purpose. Paper I introduces a method based on rotational symmetry to estimate the center of circular objects in images. Standard errors are also estimated. The accuracy of the estimates goes well beyond sub-pixel accuracy, which is validated in a simulation study. A modification of the local polynomial kernel estimator for censored data is also suggested. In Paper II we estimate the intensity profiles of particles at different known depths. These intensity profiles are then used for depth estimation in a template matching approach. The matching criterion takes into account both different background levels and censoring of pixel values. Paper III deals with the estimation of the diffusion coefficient from particle trajectories observed with measurement noise. The model includes two types of particles, fixed and diffusing. This is appropriate since this is the typical situation for particles in the images considered.

rotational symmetry

censored regression

diffusion coefficient

template matching

nonparametric function estimation

colloidal chemistry


video microscopy

depth estimation

position estimation


Mats Kvarnström

Chalmers, Matematiska vetenskaper, matematisk statistik

Göteborgs universitet





Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 2256