Total Generalized Variation Regularized Piecewise Smooth Mumford-Shah Point Cloud Surface Segmentation

The Mumford-Shah (MS) model is an important tool for data segmentation. The previous research on piecewise constant MS segmentation model with total variation regularization pursued the shortest length of boundaries. By contrast, in this article, we propose a novel piecewise smooth Mumford-Shah segmentation model by utilizing the total generalized variation (TGV) regularization, which assumes that the feature function of a data can be approximated by the sum of a piecewise constant function and a smooth function. The newly introduced TGV regularized piecewise smooth model is effective in segmenting point cloud surfaces with irregular structures and getting the optimal boundaries rather than the shortest boundaries. We solve the piecewise smooth MS model by alternating minimization and alternating direction method of multipliers (ADMM), where the subproblems are solved by either the closed-form solution or numerical packages. Our algorithm is discussed from several aspects, and comparisons with the piecewise constant MS model. Experimental results show that our TGV regularized segmentation method can yield competitive results when compared to other approaches.