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arXiv 2103.05104cs.CVstat.COstat.ML
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高精度同心圆目标检测新方法

New Methods for Detecting Concentric Objects With High Accuracy

California State University–Northridge(加州州立大学北岭分校)

Ali A. Al-Sharadqah, Lorenzo Rull

摘要:

在虹膜检测、自主导航和工业机器人操作等许多领域,将同心几何对象拟合到数字化数据是一个重要问题。有两种常见的方法来拟合几何形状的数据:几何(迭代)方法和代数(非迭代)方法。几何方法是一种非线性的迭代法,它使观测点到椭圆的欧氏距离的平方和最小,被认为是最精确的方法,但它需要一个好的初始猜测来提高收敛速度。代数方法是基于最小化的代数距离与参数空间上施加的一些约束。每一种代数方法都依赖于所施加的约束,并且可以借助于广义特征值问题来求解。文献中只有少数几种方法被用来解决同心椭圆问题。在这里,我们研究现有的方法的统计特性,首先建立一个通用的数学和统计框架,这个问题。使用严格的扰动分析,我们推导出每种方法的方差和偏差下的小西格玛模型。我们还开发了新的估计,这可以用来作为可靠的初始猜测其他迭代法。然后,我们比较了每种方法的性能,根据其理论精度。这里描述的方法不仅优于其他现有的非迭代法,它们对大噪声也相当鲁棒。这些方法和它们的实际性能进行了评估,通过一系列的数值实验合成和真实的数据。

英文摘要:

Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to data: the geometric (iterative) approach and algebraic (non-iterative) approach. The geometric approach is a nonlinear iterative method that minimizes the sum of the squares of Euclidean distances of the observed points to the ellipses and regarded as the most accurate method, but it needs a good initial guess to improve the convergence rate. The algebraic approach is based on minimizing the algebraic distances with some constraints imposed on parametric space. Each algebraic method depends on the imposed constraint, and it can be solved with the aid of the generalized eigenvalue problem. Only a few methods in literature were developed to solve the problem of concentric ellipses. Here we study the statistical properties of existing methods by firstly establishing a general mathematical and statistical framework for this problem. Using rigorous perturbation analysis, we derive the variances and biasedness of each method under the small-sigma model. We also develop new estimators, which can be used as reliable initial guesses for other iterative methods. Then we compare the performance of each method according to their theoretical accuracy. Not only do our methods described here outperform other existing non-iterative methods, they are also quite robust against large noise. These methods and their practical performances are assessed by a series of numerical experiments on both synthetic and real data.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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