Efficient conic fitting with an analytical Polar-N-Direction geometric distance
Efficient conic fitting with an analytical Polar-N-Direction geometric distance
复制标题
具有解析极北方向几何距离的高效圆锥拟合
DOI：
10.1016/j.patcog.2019.01.023
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发表时间：
2019-06
影响因子：
8
通讯作者：
Wang Zhiheng
中科院分区：
文献类型：
--
作者：
Wu Yihong;Wang Haoren;Tang Fulin;Wang Zhiheng
二次曲线的图像拟合是其广泛应用的基础。基于几何距离的拟合方法优于基于代数距离的拟合方法，这是一个常识。然而，很长一段时间以来，一直没有一个几何距离之间的一个点和一个一般的圆锥曲线，允许容易计算，并同时实现高精度。虽然桑普森距离被广泛接受，但它只是一阶近似。对于其他几何距离，计算过于复杂，在实践中不受欢迎。本文导出了点到一般二次曲线的一个新的几何距离，称为极N向距离。距离可以适应投影变换，因为它是沿着点的极线的法线方向沿着计算的，从而使二次曲线拟合更稳健。此外，极-N-方向距离是精确的，同时仍然是解析的显式表示，这是很容易实现的。然后，基于距离，构造了一个新的成本函数。通过最小化该代价函数的二次曲线拟合优化具有基于几何距离的方法的所有优点，同时避免了它们的局限性。实验结果表明，二次曲线拟合方法是非常有效的。
Fitting conics from images is a preliminary step for its plentiful applications. It is a common sense that geometric distance based fitting methods are better than algebraic distance based ones. However, for a long time, there has not been a geometric distance between a point and a general conic that allows easy computation and achieves high accuracy simultaneously. Though Sampson distance is widely accepted, it is only a first-order approximation. For other geometric distances, the computations are too complex to be popular in practice. In this paper, we derive a new geometric distance between a point and a general conic, called Polar-N-Direction distance. The distance can be adapted to a projective transformation because it is computed along the normal direction of the polar line of the point, making conic fitting more robust. Moreover, Polar-N-Direction distance is accurate and simultaneously still analytical in an explicit representation, which is quite easy to be implemented. Then, based on the distance, a new cost function is constructed. The conic fitting optimization by minimizing this cost function has all the merits of the geometric distance based methods and simultaneously avoids their limitations. Experiments show that the conic fitting method is greatly efficient.
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