Neural network speeds and improves 3D shape analysis and generation
NeuralSRNF: Neural Square Root Normal Fields for the Statistical Shape Analysis and Generation of Nonrigid 3D and 4D Objects
Computer Vision and Pattern Recognition
Summary
Analyzing and creating 3D and 4D shapes that bend and move is hard and slow with traditional methods. The authors developed NeuralSRNF, a neural network that makes these tasks faster and more accurate by improving the way shapes are mathematically represented and converted back. This new method works well for shapes with complex deformations and helps perform shape comparisons, transformations, and generating new shapes efficiently. It also works across different resolutions and reduces processing time from over 10 minutes to under 3 seconds.
What this means in practice
- •For 3d animation teams: Generate and manipulate complex animated 3D characters with nonrigid shape changes more accurately and quickly.
- •For medical imaging engineers: Enhance analysis of changing anatomical shapes over time by speeding up shape comparison and deformation tracking in 3D/4D scans.
Authors
Awais Nizamani, Hamid Laga, Guanjin Wang, Farid Boussaid, Mohammed Bennamoun, Anuj Srivastava
Abstract
We introduce NeuralSRNF, a novel framework for the statistical shape analysis and generation of genus-zero 3D and 4D objects that undergo nonrigid deformations. Traditional methods rely on complex and computationally expensive nonlinear elastic metrics that measure bending and stretching. Recent advances in elastic shape analysis achieve computational efficiency by mapping input 3D shapes to the space of Square Root Normal Fields (SRNFs) where the L2 metric approximates the partial elastic metric, significantly facilitating the process of computing geodesics and summary statistics. SRNFs, however, are not invertible, and the numerical algorithms used to map SRNFs back to the original space of surfaces remain computationally very expensive and often lead to approximate results. This paper addresses this fundamental SRNF inversion problem using a novel neural representation, termed NeuralSRNF. Unlike the commonly used numerical SRNF, NeuralSRNF is (1) continuous, and thus resolution-agnostic, enabling full functional shape analysis, (2) more accurate, and (3) computationally more efficient as it can compute inverse SRNF maps along a geodesic path in less than 3 s compared to over 10 min for the numerical SRNF. We demonstrate, using various datasets, the utility and efficiency of the proposed NeuralSRNF in multiple elastic 3D and 4D shape analysis tasks such as geodesic computation, deformation transfer, statistical summaries computation, and 3D shape generation. We show that it outperforms competing methods on most evaluated datasets and metrics by a wide margin in both accuracy and computational efficiency. The source code and additional results are available at https://awaisnizamani16.github.io/awais/NeuralSRNF/.