An Application of the Frame Theory for Signature Extraction in the Analysis of 3D Point Clouds

In this work a novel way for the recognition and classification of objects inside a scene, inspired by the well-known frame theory, is described. First of all, three-dimensional (3D) point clouds have been obtained using a laser triangulation system of high resolution, in order to achieve low noise datasets for the method validation. Once specific areas are extracted following a novel autonomous algorithm, a fit of the second order is defined on these acquired samples to find local curvatures. Such information is compared to the words of a precomputed dictionary made of curvatures, which constitutes the frame basis. The results of the comparison give evidence to the presence of particular objects in the scene under investigation. As a matter of fact, introducing a threshold value ?, similarities can be found and thus objects can be recognized. Specifically, the final results state the effectiveness of the method to distinguish objects having different surface properties. Moreover, the agreement of results is proven despite of the contribution of the measurement noise which produces outlier points.