A simple polar parameterisation method to show quantitative spatial variation between delineations on medical image datasets

Any single valued function over a sphere or cylinder can be parameterised in terms of the spherical or cylindrical coordinate systems respectively. An organ structure created during medical image segmentation can be written as such a function if the shape is polar (i.e. star shaped), the polar radial distance from a reference point inside the structure to its surface becoming a function of the polar parameters. The parameterisation allows shape variation (as a function of the polar parameters) between multiple structures to be analysed quantitatively, improving on the traditional measure of radiotherapy delineation variability, the delineated structures' volume statistics. We include an example inter-observer delineation variability case study. The parameterised variability maps were found to match well with measurements taken from superimposed contour outlines.