Robust Cuboid Modeling from Noisy and Incomplete 3D Point Clouds Using Gaussian Mixture Model

A cuboid is a geometric primitive characterized by six planes with spatial constraints, such as orthogonality and parallelism. These characteristics uniquely define a cuboid. Therefore, previous modeling schemes have used these characteristics as hard constraints, which narrowed the solution space for estimating the parameters of a cuboid. However, under high noise and occlusion conditions, a narrowed solution space may contain only false or no solutions, which is called an over-constraint. In this paper, we propose a robust cuboid modeling method for point clouds under high noise and occlusion conditions. The proposed method estimates the parameters of a cuboid using soft constraints, which, unlike hard constraints, do not limit the solution space. For this purpose, a cuboid is represented as a Gaussian mixture model (GMM). The point distribution of each cuboid surface owing to noise is assumed to be a Gaussian model. Because each Gaussian model is a face of a cuboid, the GMM shares the cuboid parameters and satisfies the spatial constraints, regardless of the occlusion. To avoid an over-constraint in the optimization, only soft constraints are employed, which is the expectation of the GMM. Subsequently, the soft constraints are maximized using analytic partial derivatives. The proposed method was evaluated using both synthetic and real data. The synthetic data were hierarchically designed to test the performance under various noise and occlusion conditions. Subsequently, we used real data, which are more dynamic than synthetic data and may not follow the Gaussian assumption. The real data are acquired by light detection and ranging-based simultaneous localization and mapping with actual boxes arbitrarily located in an indoor space. The experimental results indicated that the proposed method outperforms a previous cuboid modeling method in terms of robustness.