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.