We present a spatio-temporal perspective on category-agnostic 3D lifting of 2D keypoints over a temporal se-quence. Our approach differs from existing state-of-the-art methods that are either: (i) object-agnostic, but can only operate on individual frames, or (ii) can model space-time dependencies, but are only designed to work with a single object category. Our approach is grounded in two core prin-ciples. First, general information about similar objects can be leveraged to achieve better performance when there is little object-specific training data. Second, a temporally-proximate context window is advantageous for achieving consistency throughout a sequence. These two principles allow us to outperform current state-of-the-art methods on per-frame and per-sequence metrics for a variety of animal categories. Lastly, we release a new synthetic dataset con-taining 3D skeletons and motion sequences for a variety of animal categories.

Neural fields encode continuous multidimensional signals as neural networks, enabling diverse applications in computer vision, robotics, and geometry. While Adam is effective for stochastic optimization, it often requires long training times. To address this, we explore alternative optimization techniques to accelerate training without sacrificing accuracy. Traditional second-order methods like L-BFGS are unsuitable for stochastic settings. We propose a theoretical framework for training neural fields with curvatureaware diagonal preconditioners, demonstrating their effectiveness across tasks such as image reconstruction, shape modeling, and Neural Radiance Fields (NeRF)1.

The test-time optimization of scene flow—using a coordinate network as a neural prior [27]—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.

Coordinate networks are widely used in computer vision due to their ability to represent signals as compressed, continuous entities. However, training these networks with first-order optimizers can be slow, hindering their use in real-time applications. Recent works have opted for shallow voxel-based representations to achieve faster training, but this sacrifices memory efficiency. This work proposes a solution that leverages second-order optimization methods to significantly reduce training times for coordinate networks while maintaining their compressibility. Experiments demonstrate the effectiveness of this approach on various signal modalities, such as audio, images, videos, shape and neural radiance fields (NeRF).

The role of quantization within implicit/coordinate neural networks is still not fully understood. We note that using a canonical fixed quantization scheme during training produces poor performance at low bit-rates due to the network weight distributions changing over the course of training. In this work, we show that a non-uniform quantization of neural weights can lead to significant improvements. Specifically, we demonstrate that a clustered quantization enables improved reconstruction. Finally, by characterising a trade-off between quantization and network capacity, we demonstrate that it is possible (while memory inefficient) to reconstruct signals using binary neural networks. We demonstrate our findings experimentally on 2D image reconstruction and 3D radiance fields; and show that simple quantization methods and architecture search can achieve compression of NeRF to less than 16kb with minimal loss in performance (323x smaller than the original NeRF).

Under mild conditions on the noise level of the measurements, rotation averaging satisfies strong duality, which enables global solutions to be obtained via semidefinite programming (SDP) relaxation. However, generic solvers for SDP are rather slow in practice, even on rotation averaging instances of moderate size, thus developing specialised algorithms is vital. In this paper, we present a fast algorithm that achieves global optimality called rotation coordinate descent (RCD). Unlike block coordinate descent (BCD) which solves SDP by updating the semidefinite matrix in a row-by-row fashion, RCD directly maintains and updates all valid rotations throughout the iterations. This obviates the need to store a large dense semidefinite matrix. We mathematically prove the convergence of our algorithm and empirically show its superior efficiency over state-of-the-art global methods on a variety of problem configurations. Maintaining valid rotations also facilitates incorporating local optimisation routines for further speed-ups. Moreover, our algorithm is simple to implement1.

Planar markers are useful in robotics and computer vision for mapping and localisation. Given a detected marker in an image, a frequent task is to estimate the 6DOF pose of the marker relative to the camera, which is an instance of planar pose estimation (PPE). Although there are mature techniques, PPE suffers from a fundamental ambiguity problem, in that there can be more than one plausible pose solutions for a PPE instance. Especially when localisation of the marker corners is noisy, it is often difficult to disambiguate the pose solutions based on reprojection error alone. Previous methods choose between the possible solutions using a heuristic criterion, or simply ignore ambiguous markers.We propose to resolve the ambiguities by examining the consistencies of a set of markers across multiple views. Our specific contributions include a novel rotation averaging formulation that incorporates long-range dependencies between possible marker orientation solutions that arise from PPE ambiguities. We analyse the combinatorial complexity of the problem, and develop a novel lifted algorithm to effectively resolve marker pose ambiguities, without discarding any marker observations. Results on real and synthetic data show that our method is able to handle highly ambiguous inputs, and provides more accurate and/or complete marker-based mapping and localisation.

We tackle the INS/GPS sensor fusion problem for pose estimation, particularly in the common setting where the INS components (IMU and magnetometer) function at much higher frequencies than GPS, and where the magnetometer and GPS are prone to giving erroneous measurements (outliers) due to magnetic disturbances and glitches. Our main contribution is a novel non-linear optimization framework that (1) fuses pre-integrated IMU and magnetometer measurements with GPS, in a manner that respects the manifold structure of the state space; and (2) supports the usage of robust norms and efficient large scale optimization to effectively mitigate the effects of outliers. Through extensive experiments, we demonstrate the superior accuracy and robustness of our approach over filtering methods (which are customarily applied in the target setting) with minimal impact to computational efficiency. Our work further illustrates the strength of optimization approaches in state estimation problems and paves the way for their adoption in the control and navigation communities.