Investigation into Building an Invariant Surface Model from Sparse Data

This paper addresses the problem of forming surface depth estimates from sparse information, which are invariant to three-dimensional rotations and translations of the surface in the chosen coordinate system. We begin this investigation by examining a simplified version of this problem, that of forming invariant curve estimates from sparse data, to help gain insight into the more complex problem in higher dimensions. Two new algorithms are proposed and studied in detail, and several examples are presented to demonstrate their effectiveness. The extension of these algorithms to surfaces in threedimensional space is also briefly discussed.