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In this paper a method based on the well-known frame theory is presented for the identification and classification of objects inside a scene. Three-dimensional (3D) point clouds have been firstly acquired using a laser triangulation system exploiting a high resolution camera, in order to derive accurate datasets for the method validation. The method performs a quadratic fit on the acquired samples and then extracts local curvatures from the analytical reconstructed surfaces. Such information is referred to a vocabulary of curvatures, created making use of the frame basis. Meaningful signatures can be finally analyzed to derive the recurrences of objects in the investigated scene. Specifically, by fixing a threshold value ζ, similarities can be estimated and thus objects can be recognized. Results prove the capability of the method to distinguish surface properties among several objects, validating this algorithm against the contributions of the measurement noise. Keywords– Object Recognition; Mean and Gaussian Curvatures; Frame Theory; Robot Pose Estimation.

Signature Extraction from 3D Point Clouds using Frame Theory for Environmental Modeling