Direct type-specific conic fitting and eigenvalue bias correction
Direct type-specific conic fitting and eigenvalue bias correction
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DOI：
10.1016/j.imavis.2006.12.006
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发表时间：
2008-03
期刊：
影响因子：
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通讯作者：
M. Harker;P. O’Leary;P. Zsombor-Murray
中科院分区：
文献类型：
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作者：
M. Harker;P. O’Leary;P. Zsombor-Murray
介绍了一种将特定类型的圆锥曲线拟合到分散数据点上的新方法。通过对二次系数施加二次约束来实现椭圆和双曲线的直接、具体拟合，从而设计了一种改进的设计矩阵划分，从而通过消除拟合过程中的冗余方面来提高计算效率和数值稳定性。抛物线的拟合是通过确定二次项系数在格拉斯曼空间中的正交基向量集来实现的。利用拉格朗日乘子确定了满足抛物条件且残差范数最小的基向量的线性组合。这是已知的第一个抛物线特定拟合的直接解。此外，解决了线性二次拟合的固有偏差。我们提出了一种线性方法来纠正这种偏差，产生更好的几何拟合，但仍然局限于特定的圆锥型。
A new method to fit specific types of conics to scattered data points is introduced. Direct, specific fitting of ellipses and hyperbolae is achieved by imposing a quadratic constraint on the conic coefficients, whereby an improved partitioning of the design matrix is devised so as to improve computational efficiency and numerical stability by eliminating redundant aspects of the fitting procedure. Fitting of parabolas is achieved by determining an orthogonal basis vector set in the Grassmannian space of the quadratic terms’ coefficients. The linear combination of the basis vectors that fulfills the parabolic condition and has a minimum residual norm is determined using Lagrange multipliers. This is the first known direct solution for parabola specific fitting. Furthermore, the inherent bias of a linear conic fit is addressed. We propose a linear method of correcting this bias, producing better geometric fits which are still constrained to specific conic type.