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: https://github.com/kavisha725/MBNSF.

翻译：场景流的测试时优化——利用坐标网络作为神经先验——因其简洁性、无数据集偏差以及最先进的性能而受到广泛关注。然而，我们观察到，尽管坐标网络通过隐式正则化场景流预测以实现空间平滑性来捕捉普遍运动，但神经先验本身无法识别现实世界数据中存在的潜在多体刚体运动。为解决此问题，我们证明：无需像先前工作那样采用约束每个刚体$SE(3)$参数的繁琐且脆弱的策略，即可实现多体刚体运动。这通过正则化场景流优化来鼓励刚体流预测的等距性得以实现。该策略在保持连续流场的同时实现场景流中的多体刚体运动，从而支持跨点云序列的密集长期场景流整合。我们在真实数据集上进行了大量实验，证明我们的方法在3D场景流和长期逐点4D轨迹预测方面优于现有最先进方法。代码见：https://github.com/kavisha725/MBNSF。