Fast axis estimation from a segment of rotationally symmetric object

This paper proposes a new method for estimating the symmetric axis of a pottery from its small fragment using surface geometry. For the automatic assembly of broken sherds, the axis estimation is an important measure [2]. When a fragment is small, it is difficult to estimate axis orientation since it looks like a patch of a sphere and conventional methods mostly fail, but the proposed method provides reliable axis estimation by using multiple constraints. The computational cost is also much lowered. To estimate the symmetric axis, the proposed algorithm uses three constraints: (1) the curvature is constant on a circumference C_H. (2) the curvature is invariant in any scale. (3) also the principal curvatures does not vary on C_H. C_H is a planar circle which is one of all the possible circumferences of a pottery or sherd. A hypothesis test for axis is performed using maximum likelihood. The variance of curvature, multi-scale curvature and principal curvatures are computed in the likelihood function. We also show that the principal curvatures can be used for grouping of sherds. The grouping of sherds will reduce the computation significantly by omitting impossible configurations in pottery assembly.