Rotation invariant local geometric descriptor

(a) Bead a is described by the constellation of its three nearest neighbors b, c and d. (b) The local x-axis is defined by the vector pointing from a to d. Optionally scale invariance can be achieved by normalizing the length of the local x-axis, which is, however, for this particular registration case not necessary. (c) The first-nearest neighbor b and the third-nearest neighbor d define a plane. (d) The local y -axis lies perpendicular to the local x-axis in this plane pointing towards b. (e) The local z-axis lies perpendicular to the local x and y-axes pointing towards c. (f) Six rotation invariant values are extracted from the local geometric descriptor using the defined coordinate system; the length of d, xy - coordinates of b and xyz-coordinates of c. For scale invariant descriptors, only five values are extracted as the length of d on the x-axis is always one.