Determining ellipses from low-resolution images with a comprehensive image formation model
This addresses the challenge of precise shape parameter estimation in low-resolution imaging for fields like microscopy or remote sensing, though it is incremental as it builds on existing estimation frameworks by adding detailed modeling.
The paper tackles the problem of accurately estimating parameters of planar elliptic shapes from single low-resolution, photon-limited images by proposing a method that models the image formation process, including point-spread function, discretisation, quantisation, and photon noise. The result is parameter estimates with unprecedented accuracy, as demonstrated in experiments on simulated and real imagery, along with uncertainty measures like a parameter covariance matrix and planar confidence region.
When determining the parameters of a parametric planar shape based on a single low-resolution image, common estimation paradigms lead to inaccurate parameter estimates. The reason behind poor estimation results is that standard estimation frameworks fail to model the image formation process at a sufficiently detailed level of analysis. We propose a new method for estimating the parameters of a planar elliptic shape based on a single photon-limited, low-resolution image. Our technique incorporates the effects of several elements - point-spread function, discretisation step, quantisation step, and photon noise - into a single cohesive and manageable statistical model. While we concentrate on the particular task of estimating the parameters of elliptic shapes, our ideas and methods have a much broader scope and can be used to address the problem of estimating the parameters of an arbitrary parametrically representable planar shape. Comprehensive experimental results on simulated and real imagery demonstrate that our approach yields parameter estimates with unprecedented accuracy. Furthermore, our method supplies a parameter covariance matrix as a measure of uncertainty for the estimated parameters, as well as a planar confidence region as a means for visualising the parameter uncertainty. The mathematical model developed in this paper may prove useful in a variety of disciplines which operate with imagery at the limits of resolution.