Andrew J. Davison

Aalok Patwardhan, Riku Murai, Andrew J. Davison

Precise coordinated planning over a forward time window enables safe and highly efficient motion when many robots must work together in tight spaces, but this would normally require centralised control of all devices which is difficult to scale. We demonstrate GBP Planning, a new purely distributed technique based on Gaussian Belief Propagation for multi-robot planning problems, formulated by a generic factor graph defining dynamics and collision constraints over a forward time window. In simulations, we show that our method allows high performance collaborative planning where robots are able to cross each other in busy, intricate scenarios. They maintain shorter, quicker and smoother trajectories than alternative distributed planning techniques even in cases of communication failure. We encourage the reader to view the accompanying video demonstration at https://youtu.be/8VSrEUjH610.

Seth Nabarro, Mark van der Wilk, Andrew J Davison

We propose an approach to do learning in Gaussian factor graphs. We treat all relevant quantities (inputs, outputs, parameters, latents) as random variables in a graphical model, and view both training and prediction as inference problems with different observed nodes. Our experiments show that these problems can be efficiently solved with belief propagation (BP), whose updates are inherently local, presenting exciting opportunities for distributed and asynchronous training. Our approach can be scaled to deep networks and provides a natural means to do continual learning: use the BP-estimated parameter marginals of the current task as parameter priors for the next. On a video denoising task we demonstrate the benefit of learnable parameters over a classical factor graph approach and we show encouraging performance of deep factor graphs for continual image classification.

Hidenobu Matsuki, Riku Murai, Paul H. J. Kelly et al.

We present the first application of 3D Gaussian Splatting in monocular SLAM, the most fundamental but the hardest setup for Visual SLAM. Our method, which runs live at 3fps, utilises Gaussians as the only 3D representation, unifying the required representation for accurate, efficient tracking, mapping, and high-quality rendering. Designed for challenging monocular settings, our approach is seamlessly extendable to RGB-D SLAM when an external depth sensor is available. Several innovations are required to continuously reconstruct 3D scenes with high fidelity from a live camera. First, to move beyond the original 3DGS algorithm, which requires accurate poses from an offline Structure from Motion (SfM) system, we formulate camera tracking for 3DGS using direct optimisation against the 3D Gaussians, and show that this enables fast and robust tracking with a wide basin of convergence. Second, by utilising the explicit nature of the Gaussians, we introduce geometric verification and regularisation to handle the ambiguities occurring in incremental 3D dense reconstruction. Finally, we introduce a full SLAM system which not only achieves state-of-the-art results in novel view synthesis and trajectory estimation but also reconstruction of tiny and even transparent objects.

Riku Murai, Eric Dexheimer, Andrew J. Davison

We present a real-time monocular dense SLAM system designed bottom-up from MASt3R, a two-view 3D reconstruction and matching prior. Equipped with this strong prior, our system is robust on in-the-wild video sequences despite making no assumption on a fixed or parametric camera model beyond a unique camera centre. We introduce efficient methods for pointmap matching, camera tracking and local fusion, graph construction and loop closure, and second-order global optimisation. With known calibration, a simple modification to the system achieves state-of-the-art performance across various benchmarks. Altogether, we propose a plug-and-play monocular SLAM system capable of producing globally-consistent poses and dense geometry while operating at 15 FPS.

Aalok Patwardhan, Callum Rhodes, Gwangbin Bae et al. · cambridge

Camera rotation estimation from a single image is a challenging task, often requiring depth data and/or camera intrinsics, which are generally not available for in-the-wild videos. Although external sensors such as inertial measurement units (IMUs) can help, they often suffer from drift and are not applicable in non-inertial reference frames. We present U-ARE-ME, an algorithm that estimates camera rotation along with uncertainty from uncalibrated RGB images. Using a Manhattan World assumption, our method leverages the per-pixel geometric priors encoded in single-image surface normal predictions and performs optimisation over the SO(3) manifold. Given a sequence of images, we can use the per-frame rotation estimates and their uncertainty to perform multi-frame optimisation, achieving robustness and temporal consistency. Our experiments demonstrate that U-ARE-ME performs comparably to RGB-D methods and is more robust than sparse feature-based SLAM methods. We encourage the reader to view the accompanying video at https://callum-rhodes.github.io/U-ARE-ME for a visual overview of our method.

Hidenobu Matsuki, Gwangbin Bae, Andrew J. Davison · cambridge

We propose the first 4D tracking and mapping method that jointly performs camera localization and non-rigid surface reconstruction via differentiable rendering. Our approach captures 4D scenes from an online stream of color images with depth measurements or predictions by jointly optimizing scene geometry, appearance, dynamics, and camera ego-motion. Although natural environments exhibit complex non-rigid motions, 4D-SLAM remains relatively underexplored due to its inherent challenges; even with 2.5D signals, the problem is ill-posed because of the high dimensionality of the optimization space. To overcome these challenges, we first introduce a SLAM method based on Gaussian surface primitives that leverages depth signals more effectively than 3D Gaussians, thereby achieving accurate surface reconstruction. To further model non-rigid deformations, we employ a warp-field represented by a multi-layer perceptron (MLP) and introduce a novel camera pose estimation technique along with surface regularization terms that facilitate spatio-temporal reconstruction. In addition to these algorithmic challenges, a significant hurdle in 4D SLAM research is the lack of reliable ground truth and evaluation protocols, primarily due to the difficulty of 4D capture using commodity sensors. To address this, we present a novel open synthetic dataset of everyday objects with diverse motions, leveraging large-scale object models and animation modeling. In summary, we open up the modern 4D-SLAM research by introducing a novel method and evaluation protocols grounded in modern vision and rendering techniques.

Riku Murai, Joseph Ortiz, Sajad Saeedi et al.

We show that a distributed network of robots or other devices which make measurements of each other can collaborate to globally localise via efficient ad-hoc peer to peer communication. Our Robot Web solution is based on Gaussian Belief Propagation on the fundamental non-linear factor graph describing the probabilistic structure of all of the observations robots make internally or of each other, and is flexible for any type of robot, motion or sensor. We define a simple and efficient communication protocol which can be implemented by the publishing and reading of web pages or other asynchronous communication technologies. We show in simulations with up to 1000 robots interacting in arbitrary patterns that our solution convergently achieves global accuracy as accurate as a centralised non-linear factor graph solver while operating with high distributed efficiency of computation and communication. Via the use of robust factors in GBP, our method is tolerant to a high percentage of faults in sensor measurements or dropped communication packets.

Andrew Davison

A common approach to solving prediction tasks on large networks, such as node classification or link prediction, begin by learning a Euclidean embedding of the nodes of the network, from which traditional machine learning methods can then be applied. This includes methods such as DeepWalk and node2vec, which learn embeddings by optimizing stochastic losses formed over subsamples of the graph at each iteration of stochastic gradient descent. In this paper, we study the effects of adding an $\ell_2$ penalty of the embedding vectors to the training loss of these types of methods. We prove that, under some exchangeability assumptions on the graph, this asymptotically leads to learning a graphon with a nuclear-norm-type penalty, and give guarantees for the asymptotic distribution of the learned embedding vectors. In particular, the exact form of the penalty depends on the choice of subsampling method used as part of stochastic gradient descent. We also illustrate empirically that concatenating node covariates to $\ell_2$ regularized node2vec embeddings leads to comparable, when not superior, performance to methods which incorporate node covariates and the network structure in a non-linear manner.

Andrew Davison, Morgane Austern

Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which algorithms developed for vector-valued data are applied. For large networks, embeddings are learned using stochastic gradient methods where the sub-sampling scheme can be freely chosen. Despite the strong empirical performance of such methods, they are not well understood theoretically. Our work encapsulates representation methods using a subsampling approach, such as node2vec, into a single unifying framework. We prove, under the assumption that the graph is exchangeable, that the distribution of the learned embedding vectors asymptotically decouples. Moreover, we characterize the asymptotic distribution and provided rates of convergence, in terms of the latent parameters, which includes the choice of loss function and the embedding dimension. This provides a theoretical foundation to understand what the embedding vectors represent and how well these methods perform on downstream tasks. Notably, we observe that typically used loss functions may lead to shortcomings, such as a lack of Fisher consistency.

Joseph Ortiz, Talfan Evans, Andrew J. Davison

In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), an approximate probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special case of loopy belief propagation, GBP updates rely only on local information and will converge independently of the message schedule. Our key argument is that, given recent trends in computing hardware, GBP has the right computational properties to act as a scalable distributed probabilistic inference framework for future machine learning systems.

Joseph Ortiz, Mark Pupilli, Stefan Leutenegger et al.

Graph processors such as Graphcore's Intelligence Processing Unit (IPU) are part of the major new wave of novel computer architecture for AI, and have a general design with massively parallel computation, distributed on-chip memory and very high inter-core communication bandwidth which allows breakthrough performance for message passing algorithms on arbitrary graphs. We show for the first time that the classical computer vision problem of bundle adjustment (BA) can be solved extremely fast on a graph processor using Gaussian Belief Propagation. Our simple but fully parallel implementation uses the 1216 cores on a single IPU chip to, for instance, solve a real BA problem with 125 keyframes and 1919 points in under 40ms, compared to 1450ms for the Ceres CPU library. Further code optimisation will surely increase this difference on static problems, but we argue that the real promise of graph processing is for flexible in-place optimisation of general, dynamically changing factor graphs representing Spatial AI problems. We give indications of this with experiments showing the ability of GBP to efficiently solve incremental SLAM problems, and deal with robust cost functions and different types of factors.