Automatic coarse registration by invariant features

The increasing availability of relatively low-cost range sensors such as scanner lasers and structured light systems in cultural heritage applications has dramatically changed the traditional approaches to the documentation, monitoring and fruition of cultural heritage findings. Three-dimensional shape modelling is often the final goal of the processing pipeline which starts from the acquisition of overlapping scans of the entire work of art. An important step of the processing pipeline is the optimal alignment of the scan set in a common coordinate system, the so called registration step. This paper presents a new feature-based approach to the coarse registration between partially overlapping range images. Our approach extracts from the range images "feature points" and then characterises them by invariants to Euclidean transformations. The novelty of the approach is that the choice and the design of the invariants is supported by the theory of moving frames recently developed by J.Olver. This provides us with an algorithm to find the fundamental sets of invariants necessary to parameterise a signature manifold that characterises the original manifold up to Euclidean transformations. To maximise performance against noise we can design invariants that depend on distances and 1st order derivatives only. To reduce the overall computational complexity the invariant are not estimated on all the points of the scans, but only on a reduced subset of them. This subset, the feature points, are determined by the Gaussian curvature maxima of the surface underlying the data. Preliminary results on standard 3D data sets from web repositories and on original scans of works of art show the effectiveness of the proposed registration algorithm.