Upright orientation of 3D shapes via tensor rank minimization

In general, the upright orientation of a model is beneficial for human to recognize this model and is widely used in geometry processing and computer graphics. However, the orientation of the model obtained by existing technologies, such as 3D scanning systems or modeling, may be far away from the right orientation. In order to solve this problem, a robust and efficient upright method is needed. We observe that when the model is aligned with the three axes, the rank of the three-order tensor constructed by this model is the lowest usually. Inspired by this observation, we formulate the alignment of the 3D model with axes as a low-rank tensor optimization problem which is a global and unsupervised method and the genetic algorithm (GA) is used to solve this optimization problem. After the 3D model has been aligned with the three axes, some geometric properties can be used to pick out the best upright orientation from the six candidate supporting bases easily. The three-order tensor is constructed by voxelizing the bounding box of the 3D model, and then filling the voxel element with zero or one based on whether it contains the points of the model or not. The experimental results demonstrate that our method is robust, efficient and effective for all kinds of the models (manifold or non-manifold, man-made or non-artificial, or point cloud).