A Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data
A Bayesian Method for Fitting Parametric and Nonparametric Models to Noisy Data
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DOI：
10.1109/34.922710
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发表时间：
2001-05
期刊：
影响因子：
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通讯作者：
M. Werman;D. Keren
中科院分区：
文献类型：
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作者：
M. Werman;D. Keren
我们提出了一个简单的范例，用于将参数和非参数模型拟合到噪声数据，这解决了与经典 MSE 算法相关的一些问题。这是通过将模型上的每个点视为每个数据点的可能来源来完成的。该范式可用于解决经典 MSE 方法中不适定的问题，例如拟合线段（而不是直线）。它被证明是无偏的，并且即使存在强烈的不连续性，也能在一般曲线上取得优异的结果。显示了许多拟合问题的结果，包括直线、圆、椭圆弧、线段、矩形和一般曲线，受到高斯和均匀噪声的污染。
We present a simple paradigm for fitting models, parametric and nonparametric, to noisy data, which resolves some of the problems associated with classical MSE algorithms. This is done by considering each point on the model as a possible source for each data point. The paradigm can be used to solve problems which are ill-posed in the classical MSE approach, such as fitting a segment (as opposed to a line). It is shown to be nonbiased and to achieve excellent results for general curves, even in the presence of strong discontinuities. Results are shown for a number of fitting problems, including lines, circles, elliptic arcs, segments, rectangles, and general curves, contaminated by Gaussian and uniform noise.