A structured regularization framework for spatially smoothing semantic labelings of 3D point clouds

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.