Image registration error analysis with applications in single molecule microscopy

This paper is concerned with assessing localization errors emanating from the image registration of two monochromatic fluorescence microscopy images. Assuming an affine transform exists between images, registration in this setting typically involves using control points to solve a multivariate linear regression problem; however with measurement errors existing in both sets of variables the use of linear least squares is inappropriate. It is shown that image registration is an errors-in-variable problem and as such the correct method is to use generalized least squares. Traditionally this requires the measurement errors to be independent and identically distributed (iid); an assumption that is rarely satisfied in practical situations. An extension of the multivariate generalized least squares estimator that allows non-iid noise is applied. The distributional properties of the estimators are used to derive localization errors emanating from the image registration process in terms of photon counts and experimental parameters.