arXiv subjects

Andrew Markham

Publications and source records attributed to Andrew Markham.

At least 73 records · Page 4Linked to original sources

arXiv2021

Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their ability to provide mesh-free solutions of differential equations and their ability to carry out forward and inverse modelling within the same optimisation problem. Whilst promising, a key limitation to date is that PINNs have struggled to accurately and efficiently solve problems with large domains and/or multi-scale solutions, which is crucial for their real-world application. Multiple significant and related factors contribute to this issue, including the increasing complexity of the underlying PINN optimisation problem as the problem size grows and the spectral bias of neural networks. In this work we propose a new, scalable approach for solving large problems relating to differential equations called Finite Basis PINNs (FBPINNs). FBPINNs are inspired by classical finite element methods, where the solution of the differential equation is expressed as the sum of a finite set of basis functions with compact support. In FBPINNs neural networks are used to learn these basis functions, which are defined over small, overlapping subdomains. FBINNs are designed to address the spectral bias of neural networks by using separate input normalisation over each subdomain, and reduce the complexity of the underlying optimisation problem by using many smaller neural networks in a parallel divide-and-conquer approach. Our numerical experiments show that FBPINNs are effective in solving both small and larger, multi-scale problems, outperforming standard PINNs in both accuracy and computational resources required, potentially paving the way to the application of PINNs on large, real-world problems.

physics.comp-ph↗

arXiv2021

Learning Semantic Segmentation of Large-Scale Point Clouds with Random Sampling

We study the problem of efficient semantic segmentation of large-scale 3D point clouds. By relying on expensive sampling techniques or computationally heavy pre/post-processing steps, most existing approaches are only able to be trained and operate over small-scale point clouds. In this paper, we introduce RandLA-Net, an efficient and lightweight neural architecture to directly infer per-point semantics for large-scale point clouds. The key to our approach is to use random point sampling instead of more complex point selection approaches. Although remarkably computation and memory efficient, random sampling can discard key features by chance. To overcome this, we introduce a novel local feature aggregation module to progressively increase the receptive field for each 3D point, thereby effectively preserving geometric details. Comparative experiments show that our RandLA-Net can process 1 million points in a single pass up to 200x faster than existing approaches. Moreover, extensive experiments on five large-scale point cloud datasets, including Semantic3D, SemanticKITTI, Toronto3D, NPM3D and S3DIS, demonstrate the state-of-the-art semantic segmentation performance of our RandLA-Net.

cs.CV↗

arXiv2021

SpinNet: Learning a General Surface Descriptor for 3D Point Cloud Registration

Extracting robust and general 3D local features is key to downstream tasks such as point cloud registration and reconstruction. Existing learning-based local descriptors are either sensitive to rotation transformations, or rely on classical handcrafted features which are neither general nor representative. In this paper, we introduce a new, yet conceptually simple, neural architecture, termed SpinNet, to extract local features which are rotationally invariant whilst sufficiently informative to enable accurate registration. A Spatial Point Transformer is first introduced to map the input local surface into a carefully designed cylindrical space, enabling end-to-end optimization with SO(2) equivariant representation. A Neural Feature Extractor which leverages the powerful point-based and 3D cylindrical convolutional neural layers is then utilized to derive a compact and representative descriptor for matching. Extensive experiments on both indoor and outdoor datasets demonstrate that SpinNet outperforms existing state-of-the-art techniques by a large margin. More critically, it has the best generalization ability across unseen scenarios with different sensor modalities. The code is available at https://github.com/QingyongHu/SpinNet.

cs.CV↗

arXiv2021

Towards Semantic Segmentation of Urban-Scale 3D Point Clouds: A Dataset, Benchmarks and Challenges

An essential prerequisite for unleashing the potential of supervised deep learning algorithms in the area of 3D scene understanding is the availability of large-scale and richly annotated datasets. However, publicly available datasets are either in relative small spatial scales or have limited semantic annotations due to the expensive cost of data acquisition and data annotation, which severely limits the development of fine-grained semantic understanding in the context of 3D point clouds. In this paper, we present an urban-scale photogrammetric point cloud dataset with nearly three billion richly annotated points, which is three times the number of labeled points than the existing largest photogrammetric point cloud dataset. Our dataset consists of large areas from three UK cities, covering about 7.6 km^2 of the city landscape. In the dataset, each 3D point is labeled as one of 13 semantic classes. We extensively evaluate the performance of state-of-the-art algorithms on our dataset and provide a comprehensive analysis of the results. In particular, we identify several key challenges towards urban-scale point cloud understanding. The dataset is available at https://github.com/QingyongHu/SensatUrban.

cs.CV↗

arXiv2021

RadarLoc: Learning to Relocalize in FMCW Radar

Relocalization is a fundamental task in the field of robotics and computer vision. There is considerable work in the field of deep camera relocalization, which directly estimates poses from raw images. However, learning-based methods have not yet been applied to the radar sensory data. In this work, we investigate how to exploit deep learning to predict global poses from Emerging Frequency-Modulated Continuous Wave (FMCW) radar scans. Specifically, we propose a novel end-to-end neural network with self-attention, termed RadarLoc, which is able to estimate 6-DoF global poses directly. We also propose to improve the localization performance by utilizing geometric constraints between radar scans. We validate our approach on the recently released challenging outdoor dataset Oxford Radar RobotCar. Comprehensive experiments demonstrate that the proposed method outperforms radar-based localization and deep camera relocalization methods by a significant margin.

cs.RO↗

arXiv2020

3-D Motion Capture of an Unmodified Drone with Single-chip Millimeter Wave Radar

Accurate motion capture of aerial robots in 3-D is a key enabler for autonomous operation in indoor environments such as warehouses or factories, as well as driving forward research in these areas. The most commonly used solutions at present are optical motion capture (e.g. VICON) and Ultrawideband (UWB), but these are costly and cumbersome to deploy, due to their requirement of multiple cameras/sensors spaced around the tracking area. They also require the drone to be modified to carry an active or passive marker. In this work, we present an inexpensive system that can be rapidly installed, based on single-chip millimeter wave (mmWave) radar. Importantly, the drone does not need to be modified or equipped with any markers, as we exploit the Doppler signals from the rotating propellers. Furthermore, 3-D tracking is possible from a single point, greatly simplifying deployment. We develop a novel deep neural network and demonstrate decimeter level 3-D tracking at 10Hz, achieving better performance than classical baselines. Our hope is that this low-cost system will act to catalyse inexpensive drone research and increased autonomy.

cs.RO↗

arXiv2020

Demo Abstract: Indoor Positioning System in Visually-Degraded Environments with Millimetre-Wave Radar and Inertial Sensors

Positional estimation is of great importance in the public safety sector. Emergency responders such as fire fighters, medical rescue teams, and the police will all benefit from a resilient positioning system to deliver safe and effective emergency services. Unfortunately, satellite navigation (e.g., GPS) offers limited coverage in indoor environments. It is also not possible to rely on infrastructure based solutions. To this end, wearable sensor-aided navigation techniques, such as those based on camera and Inertial Measurement Units (IMU), have recently emerged recently as an accurate, infrastructure-free solution. Together with an increase in the computational capabilities of mobile devices, motion estimation can be performed in real-time. In this demonstration, we present a real-time indoor positioning system which fuses millimetre-wave (mmWave) radar and IMU data via deep sensor fusion. We employ mmWave radar rather than an RGB camera as it provides better robustness to visual degradation (e.g., smoke, darkness, etc.) while at the same time requiring lower computational resources to enable runtime computation. We implemented the sensor system on a handheld device and a mobile computer running at 10 FPS to track a user inside an apartment. Good accuracy and resilience were exhibited even in poorly illuminated scenes.

cs.CV↗

arXiv2020

milliEgo: Single-chip mmWave Radar Aided Egomotion Estimation via Deep Sensor Fusion

Robust and accurate trajectory estimation of mobile agents such as people and robots is a key requirement for providing spatial awareness for emerging capabilities such as augmented reality or autonomous interaction. Although currently dominated by optical techniques e.g., visual-inertial odometry, these suffer from challenges with scene illumination or featureless surfaces. As an alternative, we propose milliEgo, a novel deep-learning approach to robust egomotion estimation which exploits the capabilities of low-cost mmWave radar. Although mmWave radar has a fundamental advantage over monocular cameras of being metric i.e., providing absolute scale or depth, current single chip solutions have limited and sparse imaging resolution, making existing point-cloud registration techniques brittle. We propose a new architecture that is optimized for solving this challenging pose transformation problem. Secondly, to robustly fuse mmWave pose estimates with additional sensors, e.g. inertial or visual sensors we introduce a mixed attention approach to deep fusion. Through extensive experiments, we demonstrate our proposed system is able to achieve 1.3% 3D error drift and generalizes well to unseen environments. We also show that the neural architecture can be made highly efficient and suitable for real-time embedded applications.

cs.RO↗

arXiv2020

SelfVIO: Self-Supervised Deep Monocular Visual-Inertial Odometry and Depth Estimation

In the last decade, numerous supervised deep learning approaches requiring large amounts of labeled data have been proposed for visual-inertial odometry (VIO) and depth map estimation. To overcome the data limitation, self-supervised learning has emerged as a promising alternative, exploiting constraints such as geometric and photometric consistency in the scene. In this study, we introduce a novel self-supervised deep learning-based VIO and depth map recovery approach (SelfVIO) using adversarial training and self-adaptive visual-inertial sensor fusion. SelfVIO learns to jointly estimate 6 degrees-of-freedom (6-DoF) ego-motion and a depth map of the scene from unlabeled monocular RGB image sequences and inertial measurement unit (IMU) readings. The proposed approach is able to perform VIO without the need for IMU intrinsic parameters and/or the extrinsic calibration between the IMU and the camera. estimation and single-view depth recovery network. We provide comprehensive quantitative and qualitative evaluations of the proposed framework comparing its performance with state-of-the-art VIO, VO, and visual simultaneous localization and mapping (VSLAM) approaches on the KITTI, EuRoC and Cityscapes datasets. Detailed comparisons prove that SelfVIO outperforms state-of-the-art VIO approaches in terms of pose estimation and depth recovery, making it a promising approach among existing methods in the literature.

cs.CV↗

arXiv2020

A Survey on Deep Learning for Localization and Mapping: Towards the Age of Spatial Machine Intelligence

Deep learning based localization and mapping has recently attracted significant attention. Instead of creating hand-designed algorithms through exploitation of physical models or geometric theories, deep learning based solutions provide an alternative to solve the problem in a data-driven way. Benefiting from ever-increasing volumes of data and computational power, these methods are fast evolving into a new area that offers accurate and robust systems to track motion and estimate scenes and their structure for real-world applications. In this work, we provide a comprehensive survey, and propose a new taxonomy for localization and mapping using deep learning. We also discuss the limitations of current models, and indicate possible future directions. A wide range of topics are covered, from learning odometry estimation, mapping, to global localization and simultaneous localization and mapping (SLAM). We revisit the problem of perceiving self-motion and scene understanding with on-board sensors, and show how to solve it by integrating these modules into a prospective spatial machine intelligence system (SMIS). It is our hope that this work can connect emerging works from robotics, computer vision and machine learning communities, and serve as a guide for future researchers to apply deep learning to tackle localization and mapping problems.

cs.CV↗

arXiv2020

Solving the wave equation with physics-informed deep learning

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale, propagating and oscillatory nature of its solutions, and it is unclear how well they perform in this setting. We use a deep neural network to learn solutions of the wave equation, using the wave equation and a boundary condition as direct constraints in the loss function when training the network. We test the approach by solving the 2D acoustic wave equation for spatially-varying velocity models of increasing complexity, including homogeneous, layered and Earth-realistic models, and find the network is able to accurately simulate the wavefield across these cases. By using the physics constraint in the loss function the network is able to solve for the wavefield far outside of its boundary training data, offering a way to reduce the generalisation issues of existing deep learning approaches. We extend the approach for the Earth-realistic case by conditioning the network on the source location and find that it is able to generalise over this initial condition, removing the need to retrain the network for each solution. In contrast to traditional numerical simulation this approach is very efficient when computing arbitrary space-time points in the wavefield, as once trained the network carries out inference in a single step without needing to compute the entire wavefield. We discuss the potential applications, limitations and further research directions of this work.

physics.comp-ph↗

arXiv2020

See Through Smoke: Robust Indoor Mapping with Low-cost mmWave Radar

This paper presents the design, implementation and evaluation of milliMap, a single-chip millimetre wave (mmWave) radar based indoor mapping system targetted towards low-visibility environments to assist in emergency response. A unique feature of milliMap is that it only leverages a low-cost, off-the-shelf mmWave radar, but can reconstruct a dense grid map with accuracy comparable to lidar, as well as providing semantic annotations of objects on the map. milliMap makes two key technical contributions. First, it autonomously overcomes the sparsity and multi-path noise of mmWave signals by combining cross-modal supervision from a co-located lidar during training and the strong geometric priors of indoor spaces. Second, it takes the spectral response of mmWave reflections as features to robustly identify different types of objects e.g. doors, walls etc. Extensive experiments in different indoor environments show that milliMap can achieve a map reconstruction error less than 0.2m and classify key semantics with an accuracy around 90%, whilst operating through dense smoke.

eess.SP↗

arXiv2020

RandLA-Net: Efficient Semantic Segmentation of Large-Scale Point Clouds

We study the problem of efficient semantic segmentation for large-scale 3D point clouds. By relying on expensive sampling techniques or computationally heavy pre/post-processing steps, most existing approaches are only able to be trained and operate over small-scale point clouds. In this paper, we introduce RandLA-Net, an efficient and lightweight neural architecture to directly infer per-point semantics for large-scale point clouds. The key to our approach is to use random point sampling instead of more complex point selection approaches. Although remarkably computation and memory efficient, random sampling can discard key features by chance. To overcome this, we introduce a novel local feature aggregation module to progressively increase the receptive field for each 3D point, thereby effectively preserving geometric details. Extensive experiments show that our RandLA-Net can process 1 million points in a single pass with up to 200X faster than existing approaches. Moreover, our RandLA-Net clearly surpasses state-of-the-art approaches for semantic segmentation on two large-scale benchmarks Semantic3D and SemanticKITTI.

cs.CV↗

arXiv2020

FootSLAM meets Adaptive Thresholding

Calibration of the zero-velocity detection threshold is an essential prerequisite for zero-velocity-aided inertial navigation. However, the literature is lacking a self-contained calibration method, suitable for large-scale use in unprepared environments without map information or pre-deployed infrastructure. In this paper, the calibration of the zero-velocity detection threshold is formulated as a maximum likelihood problem. The likelihood function is approximated using estimation quantities readily available from the FootSLAM algorithm. Thus, we obtain a method for adaptive thresholding that does not require map information, measurements from supplementary sensors, or user input. Experimental evaluations are conducted using data with different gait speeds, sensor placements, and walking trajectories. The proposed calibration method is shown to outperform fixed-threshold zero-velocity detectors and a benchmark using a speed-based threshold classifier.

eess.SP↗

arXiv2020

Milli-RIO: Ego-Motion Estimation with Low-Cost Millimetre-Wave Radar

Robust indoor ego-motion estimation has attracted significant interest in the last decades due to the fast-growing demand for location-based services in indoor environments. Among various solutions, frequency-modulated continuous-wave (FMCW) radar sensors in millimeter-wave (MMWave) spectrum are gaining more prominence due to their intrinsic advantages such as penetration capability and high accuracy. Single-chip low-cost MMWave radar as an emerging technology provides an alternative and complementary solution for robust ego-motion estimation, making it feasible in resource-constrained platforms thanks to low-power consumption and easy system integration. In this paper, we introduce Milli-RIO, an MMWave radar-based solution making use of a single-chip low-cost radar and inertial measurement unit sensor to estimate six-degrees-of-freedom ego-motion of a moving radar. Detailed quantitative and qualitative evaluations prove that the proposed method achieves precisions on the order of few centimeters for indoor localization tasks.

eess.SP↗

arXiv2020

DeepPCO: End-to-End Point Cloud Odometry through Deep Parallel Neural Network

Odometry is of key importance for localization in the absence of a map. There is considerable work in the area of visual odometry (VO), and recent advances in deep learning have brought novel approaches to VO, which directly learn salient features from raw images. These learning-based approaches have led to more accurate and robust VO systems. However, they have not been well applied to point cloud data yet. In this work, we investigate how to exploit deep learning to estimate point cloud odometry (PCO), which may serve as a critical component in point cloud-based downstream tasks or learning-based systems. Specifically, we propose a novel end-to-end deep parallel neural network called DeepPCO, which can estimate the 6-DOF poses using consecutive point clouds. It consists of two parallel sub-networks to estimate 3-D translation and orientation respectively rather than a single neural network. We validate our approach on KITTI Visual Odometry/SLAM benchmark dataset with different baselines. Experiments demonstrate that the proposed approach achieves good performance in terms of pose accuracy.

cs.CV↗

arXiv2020

DeepTIO: A Deep Thermal-Inertial Odometry with Visual Hallucination

Visual odometry shows excellent performance in a wide range of environments. However, in visually-denied scenarios (e.g. heavy smoke or darkness), pose estimates degrade or even fail. Thermal cameras are commonly used for perception and inspection when the environment has low visibility. However, their use in odometry estimation is hampered by the lack of robust visual features. In part, this is as a result of the sensor measuring the ambient temperature profile rather than scene appearance and geometry. To overcome this issue, we propose a Deep Neural Network model for thermal-inertial odometry (DeepTIO) by incorporating a visual hallucination network to provide the thermal network with complementary information. The hallucination network is taught to predict fake visual features from thermal images by using Huber loss. We also employ selective fusion to attentively fuse the features from three different modalities, i.e thermal, hallucination, and inertial features. Extensive experiments are performed in hand-held and mobile robot data in benign and smoke-filled environments, showing the efficacy of the proposed model.

cs.CV↗

arXiv2020

Deep Learning based Pedestrian Inertial Navigation: Methods, Dataset and On-Device Inference

Modern inertial measurements units (IMUs) are small, cheap, energy efficient, and widely employed in smart devices and mobile robots. Exploiting inertial data for accurate and reliable pedestrian navigation supports is a key component for emerging Internet-of-Things applications and services. Recently, there has been a growing interest in applying deep neural networks (DNNs) to motion sensing and location estimation. However, the lack of sufficient labelled data for training and evaluating architecture benchmarks has limited the adoption of DNNs in IMU-based tasks. In this paper, we present and release the Oxford Inertial Odometry Dataset (OxIOD), a first-of-its-kind public dataset for deep learning based inertial navigation research, with fine-grained ground-truth on all sequences. Furthermore, to enable more efficient inference at the edge, we propose a novel lightweight framework to learn and reconstruct pedestrian trajectories from raw IMU data. Extensive experiments show the effectiveness of our dataset and methods in achieving accurate data-driven pedestrian inertial navigation on resource-constrained devices.

cs.RO↗