The parameters of an elliptic contour given by a set of sampling points {xi} i=1,...,N shall be identified. The data points representing the ellipse are distorted on one hand due to image guided sampling of the points that is considered to be Gaussian. On the other hand the data contains even more severe errors due to outward inflations on certain ellipse segments. In general these faulty segments are not known and induce heavy outliers in the data. Hence the least squares solution is useless. Under the assumption that there are still enough error-free contour segments that enclose the ellipse area, it is still possible to get good approximation results by inscribing an ellipse with maximum surface area.
Hoffmann, R, Truyen, B & Cornelis, J 2009, Technical Note: Maximizing ellipses within contours: Part 5 - Final report project "Tools, Technology, Research for implant placement with guided system". ETRO-IRIS Research Group, Faculty of Engineering, Vrije Universiteit Brussel, Belgium, Brussels, Belgium.
Hoffmann, R., Truyen, B., & Cornelis, J. (2009). Technical Note: Maximizing ellipses within contours: Part 5 - Final report project "Tools, Technology, Research for implant placement with guided system". ETRO-IRIS Research Group, Faculty of Engineering, Vrije Universiteit Brussel, Belgium.
@book{c3d09e3a3df648e696b3142376eee34c,
title = "Technical Note: Maximizing ellipses within contours: Part 5 - Final report project {"}Tools, Technology, Research for implant placement with guided system{"}",
abstract = "The parameters of an elliptic contour given by a set of sampling points {xi} i=1,...,N shall be identified. The data points representing the ellipse are distorted on one hand due to image guided sampling of the points that is considered to be Gaussian. On the other hand the data contains even more severe errors due to outward inflations on certain ellipse segments. In general these faulty segments are not known and induce heavy outliers in the data. Hence the least squares solution is useless. Under the assumption that there are still enough error-free contour segments that enclose the ellipse area, it is still possible to get good approximation results by inscribing an ellipse with maximum surface area.",
keywords = "ellipse, parameter fitting, contour, least squares",
author = "Ronny Hoffmann and Bart Truyen and Jan Cornelis",
year = "2009",
month = dec,
day = "3",
language = "English",
publisher = "ETRO-IRIS Research Group, Faculty of Engineering, Vrije Universiteit Brussel, Belgium",
}