Efficient conic fitting with an analytical Polar-N-Direction geometric distance
作者：
Highlights：
• Sampson distance is revisited and its geometric meaning is exhibited.
• A new geometric distance between a point and a conic, called Polar-N-Direction distance, is given. It 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 and accurate.
• Polar-N-Direction distance is represented explicitly and analytically. This geometric distance based fitting is greatly easy to be implemented.
• A new cost function based on Polar-N-Direction distance is constructed. The conic fitting optimization by minimizing this cost function is very efficient.
摘要
•Sampson distance is revisited and its geometric meaning is exhibited.•A new geometric distance between a point and a conic, called Polar-N-Direction distance, is given. It 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 and accurate.•Polar-N-Direction distance is represented explicitly and analytically. This geometric distance based fitting is greatly easy to be implemented.•A new cost function based on Polar-N-Direction distance is constructed. The conic fitting optimization by minimizing this cost function is very efficient.
论文关键词：Conic fitting,Geometric distance,Sampson distance
论文评审过程：Received 18 December 2018, Accepted 13 January 2019, Available online 5 February 2019, Version of Record 14 February 2019.
论文官网地址：https://doi.org/10.1016/j.patcog.2019.01.023
