Chojnacki Wojciech, Szpak Zygmunt L
J Opt Soc Am A Opt Image Sci Vis. 2019 Feb 1;36(2):212-233. doi: 10.1364/JOSAA.36.000212.
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.
在基于单个低分辨率图像确定参数化平面形状的参数时，常见的估计范式会导致参数估计不准确。估计结果不佳的背后原因是标准估计框架未能在足够详细的分析层面上对图像形成过程进行建模。我们提出了一种基于单个光子受限的低分辨率图像来估计平面椭圆形状参数的新方法。我们的技术将几个元素的影响——点扩散函数、离散化步长、量化步长和光子噪声——纳入一个统一且易于管理的统计模型中。虽然我们专注于估计椭圆形状参数这一特定任务，但我们的想法和方法具有更广泛的适用范围，可用于解决估计任意参数可表示的平面形状参数的问题。在模拟图像和真实图像上的综合实验结果表明，我们的方法能以前所未有的精度得出参数估计值。此外，我们的方法还提供了一个参数协方差矩阵作为估计参数不确定性的度量，以及一个平面置信区域作为可视化参数不确定性的手段。本文所开发的数学模型可能在各种处理分辨率极限图像的学科中有用。
