基于切线的椭球体
Ellipsoids from Tangents
AI总结：
本文提出一种基于切线的多椭球体检测拟合算法，利用切线提供更多方程减少样本需求，通过参数空间聚类鲁棒求解，在二维性能优于现有技术，还可用于线性方程组鲁棒求解。
摘要：
本文提出一种在二维、三维及更高维数据中检测和拟合多个椭球体的算法。该表示基于椭球体的切线及其接触点，而非仅基于点。一条切线贡献d个独立方程，而一个点仅贡献1个，因此每个假设所需的样本更少，进而减少了恢复每个椭球体所需的迭代次数。该问题被表述为线性方程组，其解（即椭球体参数）通过参数空间中的聚类进行鲁棒恢复。该算法适用于所有维度，且在二维场景中优于现有技术。该方法一般适用于线性方程组的鲁棒求解，因此除椭球体拟合外还有其他应用价值。
英文摘要：
This paper presents an algorithm for detecting and fitting multiple ellipsoids in 2D, 3D and higher-dimensional data. The representation is based on tangents to the ellipsoid together with their contact points, rather than on points alone. A tangent contributes d independent equations where a point contributes one, so each hypothesis needs fewer samples, which in turn reduces the number of iterations required to recover every ellipsoid. The problem is posed as sets of linear equations whose solutions -- the ellipsoid parameters -- are recovered robustly by clustering in parameter space. The algorithm works in all dimensions and outperforms the state of the art in 2D. The approach applies in general to the robust solution of linear equations, and so has utility beyond ellipsoid fitting.
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。
