Mapping to compensate radial geometrical distortion in pin-hole cameras

Moon images can be used to estimate spacecraft position using a visible camera. However, even though Moon is spherical, its contour on pin-hole camera imager is, in general, slightly elliptical. This is because pin-hole cameras perform gnomonic projections, projections affected by geometrical radial distortion. This geometrical radial distortion is usually corrected by Brown's distortion model. This model corrects the radial distortion by a truncated polynomial in terms of radius. In this paper, a new global mapping approach is provided to minimize geometrical radial distortion. Motivations come from the fact that many features extracting algorithms mistakenly use direct image coordinates and do not take into account the radial distortion. The f-radius sphere is introduced and two mathematical approaches to remove the radial distortion are presented, for continuous ideal imager and for a real imager with finite pixel dimensions. The presented techniques are devised to better perform star centroid using von Mises-Fisher distribution and to better estimate Moon center and radius using conical sigmoid functions.

Mapping to compensate radial geometrical distortion in pin-hole cameras Conference Paper