Inferring and representing three-dimensional shapes is an important part of robotic perception. However, it is challenging to build accurate models of novel objects based on real sensory data, because observed data is typically incomplete and noisy. Furthermore, imperfect sensory data suggests that uncertainty about shapes should be explicitly modeled during shape estimation. Such uncertainty models can usefully enable exploratory action planning for maximum information gain and efficient use of data. This paper presents a probabilistic approach for acquiring object models, based on visual and tactile data. We study Gaussian Process Implicit Surface (GPIS) representation. GPIS enables a non-parametric probabilistic reconstruction of object surfaces from 3D data points, while also providing a principled approach to encode the uncertainty associated with each region of the reconstruction. We investigate different configurations for GPIS, and interpret an object surface as the level-set of an underlying sparse GP. Experiments are performed on both synthetic data, and also real data sets obtained from two different robots physically interacting with objects. We evaluate performance by assessing how close the reconstructed surfaces are to ground-truth object models. We also evaluate how well objects from different categories are clustered, based on the reconstructed surface shapes. Results show that sparse GPs enable a reliable approximation to the full GP solution, and the proposed method yields adequate surface representations to distinguish objects. Additionally the presented approach is shown to provide computational efficiency, and also efficient use of the robot’s exploratory actions.
