Abstract

Finding meaningful, structured representations of 3Dpoint cloud data (PCD) has become a core task for spa-tial perception applications. In this paper we introducea method for constructing compact generative representations of PCD at multiple levels of detail. As opposed todeterministic structures such as voxel grids or octrees, wepropose probabilistic subdivisions of the data through lo-cal mixture modeling, and show how these subdivisions canprovide a maximum likelihood segmentation of the data.The final representation is hierarchical, compact, para-metric, and statistically derived, facilitating run-time occupancy calculations through stochastic sampling. Unlike traditional deterministic spatial subdivision methods, our technique enables dynamic creation of voxel grids according the application’s best needs. In contrast to other generative models for PCD, we explicitly enforce sparsity among points and mixtures, a technique which we call expectation sparsification. This leads to a highly parallel hierarchical Expectation Maximization (EM) algorithm well-suited for the GPU and real-time execution. We explore the trade-offsbetween model fidelity and model size at various levels of detail, our tests showing favorable performance when compared to octree and NDT-based methods.