Recent deep-learning-based techniques for the reconstruction of geometries from different input representations such as images and point clouds have been instrumental in advancing research in geometric machine learning. Most of these techniques rely on a triangular mesh representation for representing the geometry, with very recent attempts in using B-splines. While Non-Uniform Rational B-splines (NURBS) are the de facto standard in the CAD industry, minimal efforts have been made to bridge the gap between deep-learning frameworks and the NURBS representation for geometry. The backbone of modern deep learning techniques is the use of a fully automatic differentiable definition for each mathematical operation to enable backpropagation of losses while training. In order to integrate the NURBS representation of CAD models with deep learning methods, we propose a differentiable NURBS layer for evaluating the curve or surface given a set of NURBS parameters. We have developed a NURBS layer defining the forward and backward pass required for automatic differentiation. Our implementation is GPU accelerated and is directly integrated with PyTorch, a popular deep learning framework. We demonstrate the efficacy of our NURBS layer by automatically incorporating it with the stochastic gradient descent algorithm and performing CAD operations such as curve or surface fitting and surface offsetting. Further, we show its utility in deep learning applications such as point cloud reconstruction and structural modeling and analysis of shell structures such as heart valves. These examples show that our layer has better performance for certain deep learning frameworks and can be directly integrated with any CAD deep-learning framework that require the use of NURBS.
翻译:最近从图像和点云等不同输入表示法中重建地貌的深学习技术,从图像和点云等不同输入表示法中重建地貌的最近深层次技术,有助于推进对几何机器学习的研究。这些技术大多依靠三角网格表示来代表几何,最近试图使用B-Sprine。虽然非统一理性B-Sprine(NURBS)是CAD行业事实上的标准,但我们为缩小深层次学习框架与NURBS的几何代表法之间的距离,作出了极少的努力。现代深层次学习技术的骨干是使用完全自动的不同定义,使每个数学操作在培训期间能够对损失进行反演算。为了将CAD模型的NURBS代表制与深层次学习方法相结合,我们建议一个不同的NURBS层层结构,我们通过将Sloial-CLBS的精度和Sloial的精度分析,我们用S-CURBS的精度模型来进行更深层次的学习,我们用SlevyTrch的深度学习框架来进行更深层的学习。我们用CBS的精度和更深层的土壤的深度分析。我们用SLADLADR的精度的精度的精度的精度的精度的精度和深层的精度的精度的精度的精度和深层和深层的精度的精度,我们的精度的精度,我们的精度的精度和深层的精度和深层分析。我们用法的精度的精度的精度,我们的精度和深层的精度,让我们的精度,让我们的深度的深度的深度的深度的深度的深度的深度的精度和深层的深度的深度的深度的深度的深度的深度的深度的深度的深度的深度的深度的深度的深度的深度的深度的深度的演化的演化的演化的深度的深度的深度的深度的深度的深度的深度的深度的深度的演化的演化的演化的演化的演化,我们的演化的演化的深度的演化的演化的演化的精度,我们的深度的深度的深度的深度的深度的深度的深度的深度