Level-Set Parameters: Novel Representation for 3D Shape Analysis
This addresses the issue of discrete data limitations in 3D shape analysis for computer vision and graphics applications, though it appears incremental as it builds on neural fields.
The paper tackles the problem of 3D shape analysis being sensitive to input resolution variations by introducing level-set parameters from signed distance functions as a continuous representation, and demonstrates applications in shape classification, retrieval, and 6D object pose estimation.
3D shape analysis has been largely focused on traditional 3D representations of point clouds and meshes, but the discrete nature of these data makes the analysis susceptible to variations in input resolutions. Recent development of neural fields brings in level-set parameters from signed distance functions as a novel, continuous, and numerical representation of 3D shapes, where the shape surfaces are defined as zero-level-sets of those functions. This motivates us to extend shape analysis from the traditional 3D data to these novel parameter data. Since the level-set parameters are not Euclidean like point clouds, we establish correlations across different shapes by formulating them as a pseudo-normal distribution, and learn the distribution prior from the respective dataset. To further explore the level-set parameters with shape transformations, we propose to condition a subset of these parameters on rotations and translations, and generate them with a hypernetwork. This simplifies the pose-related shape analysis compared to using traditional data. We demonstrate the promise of the novel representations through applications in shape classification (arbitrary poses), retrieval, and 6D object pose estimation.