Abstract : In this paper, we introduce a mathematical framework for obtaining spatially smooth semantic labelings of 3D point clouds from a pointwise classification.
We argue that structured regularization offers a more versatile alternative to the standard graphical model approach. Indeed, our framework allows us to choose between a wide range of fidelity functions and regularizers, influencing the properties of the solution. In particular, we investigate the conditions under which the smoothed labeling remains probabilistic in nature, allowing us to measure the uncertainty associated with each label. Finally, we present efficient algorithms to solve the corresponding optimization problems. To demonstrate the performance of our approach, we present classification results derived for standard benchmark datasets. We demonstrate that the structured regularization framework offers higher accuracy at a lighter computational cost in comparison to the classic graphical model approach.