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, discretization step, quantization 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 visualizing parameter uncertainty. The mathematical model developed in this paper may prove useful in a variety of disciplines that operate with imagery at the limits of resolution.
@cite_15: This paper considers the problem of subpixel edge detection. In particular, a new reconstructive approach is introduced. The method determines subpixel edge position based on the properties of the Gaussian function used for modeling gradient profile at the edge. The results showing the robustness of the new method against averaging, Gaussian blur and Gaussian noise are presented. In all the experiments the introduced method is compared with other state-of-the-art methods of subpixel edge detection. The comparison clearly shows that the new method outperforms the existing ones.
It is possible to obtain data points with sub-pixel coordinates by using sub-pixel edge detection methods @cite_15 . However, sub-pixel techniques usually do not characterise the uncertainty or bias of their estimates, and so one cannot attribute meaningful covariance matrices to the sub-pixel data points. The inability to characterise the uncertainty and bias of the sub-pixel points is a severe limitation and, effectively, violates the modelling assumptions associated with point-based ellipse fitting methods. Moreover, the sub-pixel estimation methods are themselves sensitive to noise and do not take quantisation into account.