Invariant grey-scale features for 3D sensor-data

A technique for the construction of invariant features of 3D sensor-data is proposed. Invariant grey-scale features are characteristics of grey-scale sensor-data which remain constant if the sensor-data is transformed according to the action of a transformation group. The proposed features are capable of recognizing 3D objects independent of their orientation and position, which can be used e.g. in medical image analysis. The computation of the proposed invariants needs no preprocessing like filtering, segmentation, or registration. After the introduction of the general theory for the construction of invariant features for 3D sensor-data, the paper focuses on the special case of 3D Euclidean motion which is typical for rigid 3D objects. Due to the fact that we use the function of local support the calculated invariants are also robust with respect to independent Euclidean motion, articulated objects, and even topological deformations. The complexity of the method is linear in the data-set size which may be too high for large 3D objects. Therefore approaches for the acceleration of the computation are given. First experimental results for artificial 3D objects are presented in the paper to demonstrate the invariant properties of the proposed features