The test-time optimization of scene flow - using a coordinate network as a neural prior - has gained popularity due to its simplicity, lack of dataset bias, and state-of-the-art performance. We observe, however, that although coordinate networks capture general motions by implicitly regularizing the scene flow predictions to be spatially smooth, the neural prior by itself is unable to identify the underlying multi-body rigid motions present in real-world data. To address this, we show that multi-body rigidity can be achieved without the cumbersome and brittle strategy of constraining the $SE(3)$ parameters of each rigid body as done in previous works. This is achieved by regularizing the scene flow optimization to encourage isometry in flow predictions for rigid bodies. This strategy enables multi-body rigidity in scene flow while maintaining a continuous flow field, hence allowing dense long-term scene flow integration across a sequence of point clouds. We conduct extensive experiments on real-world datasets and demonstrate that our approach outperforms the state-of-the-art in 3D scene flow and long-term point-wise 4D trajectory prediction. The code is available at: \href{https://github.com/kavisha725/MBNSF}{https://github.com/kavisha725/MBNSF}.

翻译：场景流的测试时优化——使用坐标网络作为神经先验——因其简单性、无数据集偏差以及最先进的性能而日益受到关注。然而，我们观察到，尽管坐标网络通过隐式正则化使场景流预测在空间上平滑来捕捉一般运动，但神经先验本身无法识别现实数据中存在的潜在多体刚体运动。为此，我们展示了无需像先前工作中那样采用繁琐且脆弱的约束每个刚体$SE(3)$参数的策略，即可实现多体刚体性。这是通过正则化场景流优化以鼓励刚体的流预测具有等距性来实现的。该策略在保持连续流场的同时实现了场景流中的多体刚体性，从而能够跨点云序列进行密集的长期场景流积分。我们在真实数据集上进行了广泛实验，结果表明我们的方法在3D场景流和长期逐点4D轨迹预测方面优于现有技术。代码可在以下地址获取：\href{https://github.com/kavisha725/MBNSF}{https://github.com/kavisha725/MBNSF}。