David Boyle

LG
h-index3
21papers
316citations
Novelty51%
AI Score45

21 Papers

ROFeb 22, 2023
Constrained Reinforcement Learning using Distributional Representation for Trustworthy Quadrotor UAV Tracking Control

Yanran Wang, David Boyle

Simultaneously accurate and reliable tracking control for quadrotors in complex dynamic environments is challenging. As aerodynamics derived from drag forces and moment variations are chaotic and difficult to precisely identify, most current quadrotor tracking systems treat them as simple `disturbances' in conventional control approaches. We propose a novel, interpretable trajectory tracker integrating a Distributional Reinforcement Learning disturbance estimator for unknown aerodynamic effects with a Stochastic Model Predictive Controller (SMPC). The proposed estimator `Constrained Distributional Reinforced disturbance estimator' (ConsDRED) accurately identifies uncertainties between true and estimated values of aerodynamic effects. Simplified Affine Disturbance Feedback is used for control parameterization to guarantee convexity, which we then integrate with a SMPC. We theoretically guarantee that ConsDRED achieves at least an optimal global convergence rate and a certain sublinear rate if constraints are violated with an error decreases as the width and the layer of neural network increase. To demonstrate practicality, we show convergent training in simulation and real-world experiments, and empirically verify that ConsDRED is less sensitive to hyperparameter settings compared with canonical constrained RL approaches. We demonstrate our system improves accumulative tracking errors by at least 70% compared with the recent art. Importantly, the proposed framework, ConsDRED-SMPC, balances the tradeoff between pursuing high performance and obeying conservative constraints for practical implementations.

SYMay 14, 2022
Interpretable Stochastic Model Predictive Control using Distributional Reinforced Estimation for Quadrotor Tracking Systems

Yanran Wang, James O'Keeffe, Qiuchen Qian et al.

This paper presents a novel trajectory tracker for autonomous quadrotor navigation in dynamic and complex environments. The proposed framework integrates a distributional Reinforcement Learning (RL) estimator for unknown aerodynamic effects into a Stochastic Model Predictive Controller (SMPC) for trajectory tracking. Aerodynamic effects derived from drag forces and moment variations are difficult to model directly and accurately. Most current quadrotor tracking systems therefore treat them as simple `disturbances' in conventional control approaches. We propose Quantile-approximation-based Distributional Reinforced-disturbance-estimator, an aerodynamic disturbance estimator, to accurately identify disturbances, i.e., uncertainties between the true and estimated values of aerodynamic effects. Simplified Affine Disturbance Feedback is employed for control parameterization to guarantee convexity, which we then integrate with a SMPC to achieve sufficient and non-conservative control signals. We demonstrate our system to improve the cumulative tracking errors by at least 66% with unknown and diverse aerodynamic forces compared with recent state-of-the-art. Concerning traditional Reinforcement Learning's non-interpretability, we provide convergence and stability guarantees of Distributional RL and SMPC, respectively, with non-zero mean disturbances.

LGJul 13, 2023
Probabilistic Constrained Reinforcement Learning with Formal Interpretability

Yanran Wang, Qiuchen Qian, David Boyle

Reinforcement learning can provide effective reasoning for sequential decision-making problems with variable dynamics. Such reasoning in practical implementation, however, poses a persistent challenge in interpreting the reward function and the corresponding optimal policy. Consequently, representing sequential decision-making problems as probabilistic inference can have considerable value, as, in principle, the inference offers diverse and powerful mathematical tools to infer the stochastic dynamics whilst suggesting a probabilistic interpretation of policy optimization. In this study, we propose a novel Adaptive Wasserstein Variational Optimization, namely AWaVO, to tackle these interpretability challenges. Our approach uses formal methods to achieve the interpretability for convergence guarantee, training transparency, and intrinsic decision-interpretation. To demonstrate its practicality, we showcase guaranteed interpretability with an optimal global convergence rate in simulation and in practical quadrotor tasks. In comparison with state-of-the-art benchmarks including TRPO-IPO, PCPO and CRPO, we empirically verify that AWaVO offers a reasonable trade-off between high performance and sufficient interpretability.

MAMar 29, 2023
Multi-Agent Reinforcement Learning with Action Masking for UAV-enabled Mobile Communications

Danish Rizvi, David Boyle

Unmanned Aerial Vehicles (UAVs) are increasingly used as aerial base stations to provide ad hoc communications infrastructure. Building upon prior research efforts which consider either static nodes, 2D trajectories or single UAV systems, this paper focuses on the use of multiple UAVs for providing wireless communication to mobile users in the absence of terrestrial communications infrastructure. In particular, we jointly optimize UAV 3D trajectory and NOMA power allocation to maximize system throughput. Firstly, a weighted K-means-based clustering algorithm establishes UAV-user associations at regular intervals. The efficacy of training a novel Shared Deep Q-Network (SDQN) with action masking is then explored. Unlike training each UAV separately using DQN, the SDQN reduces training time by using the experiences of multiple UAVs instead of a single agent. We also show that SDQN can be used to train a multi-agent system with differing action spaces. Simulation results confirm that: 1) training a shared DQN outperforms a conventional DQN in terms of maximum system throughput (+20%) and training time (-10%); 2) it can converge for agents with different action spaces, yielding a 9% increase in throughput compared to mutual learning algorithms; and 3) combining NOMA with an SDQN architecture enables the network to achieve a better sum rate compared with existing baseline schemes.

ROJul 17, 2024
Is That Rain? Understanding Effects on Visual Odometry Performance for Autonomous UAVs and Efficient DNN-based Rain Classification at the Edge

Andrea Albanese, Yanran Wang, Davide Brunelli et al.

The development of safe and reliable autonomous unmanned aerial vehicles relies on the ability of the system to recognise and adapt to changes in the local environment based on sensor inputs. State-of-the-art local tracking and trajectory planning are typically performed using camera sensor input to the flight control algorithm, but the extent to which environmental disturbances like rain affect the performance of these systems is largely unknown. In this paper, we first describe the development of an open dataset comprising ~335k images to examine these effects for seven different classes of precipitation conditions and show that a worst-case average tracking error of 1.5 m is possible for a state-of-the-art visual odometry system (VINS-Fusion). We then use the dataset to train a set of deep neural network models suited to mobile and constrained deployment scenarios to determine the extent to which it may be possible to efficiently and accurately classify these `rainy' conditions. The most lightweight of these models (MobileNetV3 small) can achieve an accuracy of 90% with a memory footprint of just 1.28 MB and a frame rate of 93 FPS, which is suitable for deployment in resource-constrained and latency-sensitive systems. We demonstrate a classification latency in the order of milliseconds using typical flight computer hardware. Accordingly, such a model can feed into the disturbance estimation component of an autonomous flight controller. In addition, data from unmanned aerial vehicles with the ability to accurately determine environmental conditions in real time may contribute to developing more granular timely localised weather forecasting.

LGMar 4
Hybrid Belief Reinforcement Learning for Efficient Coordinated Spatial Exploration

Danish Rizvi, David Boyle

Coordinating multiple autonomous agents to explore and serve spatially heterogeneous demand requires jointly learning unknown spatial patterns and planning trajectories that maximize task performance. Pure model-based approaches provide structured uncertainty estimates but lack adaptive policy learning, while deep reinforcement learning often suffers from poor sample efficiency when spatial priors are absent. This paper presents a hybrid belief-reinforcement learning (HBRL) framework to address this gap. In the first phase, agents construct spatial beliefs using a Log-Gaussian Cox Process (LGCP) and execute information-driven trajectories guided by a Pathwise Mutual Information (PathMI) planner with multi-step lookahead. In the second phase, trajectory control is transferred to a Soft Actor-Critic (SAC) agent, warm-started through dual-channel knowledge transfer: belief state initialization supplies spatial uncertainty, and replay buffer seeding provides demonstration trajectories generated during LGCP exploration. A variance-normalized overlap penalty enables coordinated coverage through shared belief state, permitting cooperative sensing in high-uncertainty regions while discouraging redundant coverage in well-explored areas. The framework is evaluated on a multi-UAV wireless service provisioning task. Results show 10.8% higher cumulative reward and 38% faster convergence over baselines, with ablation studies confirming that dual-channel transfer outperforms either channel alone.

HCNov 10, 2020Code
OnionBot: A System for Collaborative Computational Cooking

Bennet Cobley, David Boyle

An unsolved challenge in cooking automation is designing for shared kitchen workspaces. In particular, robots struggle with dexterity in the unstructured and dynamic kitchen environment. We propose that human-machine collaboration can be achieved without robotic manipulation. We describe a novel system design using computer vision to inform intelligent cooking interventions. This human-centered approach does not require actuators and promotes dynamic, natural collaboration. We show that automation that assists user-led actions can offer meaningful cooking assistance and can generate the image databases needed for fully autonomous robotic systems of the future. We provide an open source implementation of our work and encourage the research community to build upon it.

LGJan 28, 2025
Inducing, Detecting and Characterising Neural Modules: A Pipeline for Functional Interpretability in Reinforcement Learning

Anna Soligo, Pietro Ferraro, David Boyle

Interpretability is crucial for ensuring RL systems align with human values. However, it remains challenging to achieve in complex decision making domains. Existing methods frequently attempt interpretability at the level of fundamental model units, such as neurons or decision nodes: an approach which scales poorly to large models. Here, we instead propose an approach to interpretability at the level of functional modularity. We show how encouraging sparsity and locality in network weights leads to the emergence of functional modules in RL policy networks. To detect these modules, we develop an extended Louvain algorithm which uses a novel `correlation alignment' metric to overcome the limitations of standard network analysis techniques when applied to neural network architectures. Applying these methods to 2D and 3D MiniGrid environments reveals the consistent emergence of distinct navigational modules for different axes, and we further demonstrate how these functions can be validated through direct interventions on network weights prior to inference.

SPAug 30, 2025
Dual Actor DDPG for Airborne STAR-RIS Assisted Communications

Danish Rizvi, David Boyle

This study departs from the prevailing assumption of independent Transmission and Reflection Coefficients (TRC) in Airborne Simultaneous Transmit and Reflect Reconfigurable Intelligent Surface (STAR-RIS) research. Instead, we explore a novel multi-user downlink communication system that leverages a UAV-mounted STAR-RIS (Aerial-STAR) incorporating a coupled TRC phase shift model. Our key contributions include the joint optimization of UAV trajectory, active beamforming vectors at the base station, and passive RIS TRCs to enhance communication efficiency, while considering UAV energy constraints. We design the TRC as a combination of discrete and continuous actions, and propose a novel Dual Actor Deep Deterministic Policy Gradient (DA-DDPG) algorithm. The algorithm relies on two separate actor networks for high-dimensional hybrid action space. We also propose a novel harmonic mean index (HFI)-based reward function to ensure communication fairness amongst users. For comprehensive analysis, we study the impact of RIS size on UAV aerodynamics showing that it increases drag and energy demand. Simulation results demonstrate that the proposed DA-DDPG algorithm outperforms conventional DDPG and DQN-based solutions by 24% and 97%, respectively, in accumulated reward. Three-dimensional UAV trajectory optimization achieves 28% higher communication efficiency compared to two-dimensional and altitude optimization. The HFI based reward function provides 41% lower QoS denial rates as compared to other benchmarks. The mobile Aerial-STAR system shows superior performance over fixed deployed counterparts, with the coupled phase STAR-RIS outperforming dual Transmit/Reflect RIS and conventional RIS setups. These findings highlight the potential of Aerial-STAR systems and the effectiveness of our proposed DA-DDPG approach in optimizing their performance.

ROFeb 24, 2022
KinoJGM: A framework for efficient and accurate quadrotor trajectory generation and tracking in dynamic environments

Yanran Wang, James O'Keeffe, Qiuchen Qian et al.

Unmapped areas and aerodynamic disturbances render autonomous navigation with quadrotors extremely challenging. To fly safely and efficiently, trajectory planners and trackers must be able to navigate unknown environments with unpredictable aerodynamic effects in real-time. When encountering aerodynamic effects such as strong winds, most current approaches to quadrotor trajectory planning and tracking will not attempt to deviate from a determined plan, even if it is risky, in the hope that any aerodynamic disturbances can be resisted by a robust controller. This paper presents a novel systematic trajectory planning and tracking framework for autonomous quadrotors. We propose a Kinodynamic Jump Space Search (Kino-JSS) to generate a safe and efficient route in unknown environments with aerodynamic disturbances. A real-time Gaussian Process is employed to model the effects of aerodynamic disturbances, which we then integrate with a Model Predictive Controller to achieve efficient and accurate trajectory optimization and tracking. We demonstrate our system to improve the efficiency of trajectory generation in unknown environments by up to 75\% in the cases tested, compared with recent state-of-the-art. We also demonstrate that our system improves the accuracy of tracking in selected environments with unpredictable aerodynamic effects.

HCFeb 23, 2022
Open5x: Accessible 5-axis 3D printing and conformal slicing

Freddie Hong, Steve Hodges, Connor Myant et al.

The common layer-by-layer deposition of regular, 3-axis 3D printing simplifies both the fabrication process and the 3D printer's mechanical design. However, the resulting 3D printed objects have some unfavourable characteristics including visible layers, uneven structural strength and support material. To overcome these, researchers have employed robotic arms and multi-axis CNCs to deposit materials in conformal layers. Conformal deposition improves the quality of the 3D printed parts through support-less printing and curved layer deposition. However, such multi-axis 3D printing is inaccessible to many individuals due to high costs and technical complexities. Furthermore, the limited GUI support for conformal slicers creates an additional barrier for users. To open multi-axis 3D printing up to more makers and researchers, we present a cheap and accessible way to upgrade a regular 3D printer to 5 axes. We have also developed a GUI-based conformal slicer, integrated within a popular CAD package. Together, these deliver an accessible workflow for designing, simulating and creating conformally-printed 3D models.

LGFeb 16, 2022
Towards Battery-Free Machine Learning and Inference in Underwater Environments

Yuchen Zhao, Sayed Saad Afzal, Waleed Akbar et al.

This paper is motivated by a simple question: Can we design and build battery-free devices capable of machine learning and inference in underwater environments? An affirmative answer to this question would have significant implications for a new generation of underwater sensing and monitoring applications for environmental monitoring, scientific exploration, and climate/weather prediction. To answer this question, we explore the feasibility of bridging advances from the past decade in two fields: battery-free networking and low-power machine learning. Our exploration demonstrates that it is indeed possible to enable battery-free inference in underwater environments. We designed a device that can harvest energy from underwater sound, power up an ultra-low-power microcontroller and on-board sensor, perform local inference on sensed measurements using a lightweight Deep Neural Network, and communicate the inference result via backscatter to a receiver. We tested our prototype in an emulated marine bioacoustics application, demonstrating the potential to recognize underwater animal sounds without batteries. Through this exploration, we highlight the challenges and opportunities for making underwater battery-free inference and machine learning ubiquitous.

CRJul 21, 2021
A Tandem Framework Balancing Privacy and Security for Voice User Interfaces

Ranya Aloufi, Hamed Haddadi, David Boyle

Speech synthesis, voice cloning, and voice conversion techniques present severe privacy and security threats to users of voice user interfaces (VUIs). These techniques transform one or more elements of a speech signal, e.g., identity and emotion, while preserving linguistic information. Adversaries may use advanced transformation tools to trigger a spoofing attack using fraudulent biometrics for a legitimate speaker. Conversely, such techniques have been used to generate privacy-transformed speech by suppressing personally identifiable attributes in the voice signals, achieving anonymization. Prior works have studied the security and privacy vectors in parallel, and thus it raises alarm that if a benign user can achieve privacy by a transformation, it also means that a malicious user can break security by bypassing the anti-spoofing mechanism. In this paper, we take a step towards balancing two seemingly conflicting requirements: security and privacy. It remains unclear what the vulnerabilities in one domain imply for the other, and what dynamic interactions exist between them. A better understanding of these aspects is crucial for assessing and mitigating vulnerabilities inherent with VUIs and building effective defenses. In this paper,(i) we investigate the applicability of the current voice anonymization methods by deploying a tandem framework that jointly combines anti-spoofing and authentication models, and evaluate the performance of these methods;(ii) examining analytical and empirical evidence, we reveal a duality between the two mechanisms as they offer different ways to achieve the same objective, and we show that leveraging one vector significantly amplifies the effectiveness of the other;(iii) we demonstrate that to effectively defend from potential attacks against VUIs, it is necessary to investigate the attacks from multiple complementary perspectives(security and privacy).

HCApr 26, 2021
Vacuum-formed 3D printed electronics: fabrication of thin, rigid and free-form interactive surfaces

Freddie Hong, Luca Tendera, Connor Myant et al.

Vacuum-forming is a common manufacturing technique for constructing thin plastic shell products by pressing heated plastic sheets onto a mold using atmospheric pressure. Vacuum-forming is ubiquitous in packaging and casing products in industry spanning fast moving consumer goods to connected devices. Integrating advanced functionality, which may include sensing, computation and communication, within thin structures is desirable for various next-generation interactive devices. Hybrid additive manufacturing techniques like thermoforming are becoming popular for prototyping freeform electronics given its design flexibility, speed and cost-effectiveness. In this paper, we present a new hybrid method for constructing thin, rigid and free-form interconnected surfaces via fused deposition modelling (FDM) 3D printing and vacuum-forming. While 3D printing a mold for vacuum-forming has been explored by many, utilising 3D printing to construct sheet materials has remains unexplored. 3D printing the sheet material allows embedding conductive traces within thin layers of the substrate, which can be vacuum-formed but remain conductive and insulated. We characterise the behaviour of the vacuum-formed 3D printed sheet, analyse the electrical performance of 3D printed traces after vacuum-forming, and showcase a range of examples constructed using the technique. We demonstrate a new design interface specifically for designing conformal interconnects, which allows designers to draw conductive patterns in 3D and export pre-distorted sheet models ready to be 3D printed.

CLApr 1, 2021
Configurable Privacy-Preserving Automatic Speech Recognition

Ranya Aloufi, Hamed Haddadi, David Boyle

Voice assistive technologies have given rise to far-reaching privacy and security concerns. In this paper we investigate whether modular automatic speech recognition (ASR) can improve privacy in voice assistive systems by combining independently trained separation, recognition, and discretization modules to design configurable privacy-preserving ASR systems. We evaluate privacy concerns and the effects of applying various state-of-the-art techniques at each stage of the system, and report results using task-specific metrics (i.e. WER, ABX, and accuracy). We show that overlapping speech inputs to ASR systems present further privacy concerns, and how these may be mitigated using speech separation and optimization techniques. Our discretization module is shown to minimize paralinguistics privacy leakage from ASR acoustic models to levels commensurate with random guessing. We show that voice privacy can be configurable, and argue this presents new opportunities for privacy-preserving applications incorporating ASR.

ETNov 12, 2020
Thermoformed Circuit Boards: Fabrication of highly conductive freeform 3D printed circuit boards with heat bending

Freddie Hong, Connor Myant, David Boyle

Fabricating 3D printed electronics using desktop printers has become more accessible with recent developments in conductive thermoplastic filaments. Because of their high resistance and difficulties in printing traces in vertical directions, most applications are restricted to capacitive sensing. In this paper, we introduce Thermoformed Circuit Board (TCB), a novel approach that employs the thermoformability of the 3D printed plastics to construct various double-sided, rigid and highly conductive freeform circuit boards that can withstand high current applications through copper electroplating. To illustrate the capability of the TCB, we showcase a range of examples with various shapes, electrical characteristics and interaction mechanisms. We also demonstrate a new design tool extension to an existing CAD environment that allows users to parametrically draw the substrate and conductive trace, and export 3D printable files. TCB is an inexpensive and highly accessible fabrication technique intended to broaden HCI researcher participation.

CLNov 4, 2020
Paralinguistic Privacy Protection at the Edge

Ranya Aloufi, Hamed Haddadi, David Boyle

Voice user interfaces and digital assistants are rapidly entering our lives and becoming singular touch points spanning our devices. These always-on services capture and transmit our audio data to powerful cloud services for further processing and subsequent actions. Our voices and raw audio signals collected through these devices contain a host of sensitive paralinguistic information that is transmitted to service providers regardless of deliberate or false triggers. As our emotional patterns and sensitive attributes like our identity, gender, well-being, are easily inferred using deep acoustic models, we encounter a new generation of privacy risks by using these services. One approach to mitigate the risk of paralinguistic-based privacy breaches is to exploit a combination of cloud-based processing with privacy-preserving, on-device paralinguistic information learning and filtering before transmitting voice data. In this paper we introduce EDGY, a configurable, lightweight, disentangled representation learning framework that transforms and filters high-dimensional voice data to identify and contain sensitive attributes at the edge prior to offloading to the cloud. We evaluate EDGY's on-device performance and explore optimization techniques, including model quantization and knowledge distillation, to enable private, accurate and efficient representation learning on resource-constrained devices. Our results show that EDGY runs in tens of milliseconds with 0.2% relative improvement in "zero-shot" ABX score or minimal performance penalties of approximately 5.95% word error rate (WER) in learning linguistic representations from raw voice signals, using a CPU and a single-core ARM processor without specialized hardware.

ASJul 29, 2020
Privacy-preserving Voice Analysis via Disentangled Representations

Ranya Aloufi, Hamed Haddadi, David Boyle

Voice User Interfaces (VUIs) are increasingly popular and built into smartphones, home assistants, and Internet of Things (IoT) devices. Despite offering an always-on convenient user experience, VUIs raise new security and privacy concerns for their users. In this paper, we focus on attribute inference attacks in the speech domain, demonstrating the potential for an attacker to accurately infer a target user's sensitive and private attributes (e.g. their emotion, sex, or health status) from deep acoustic models. To defend against this class of attacks, we design, implement, and evaluate a user-configurable, privacy-aware framework for optimizing speech-related data sharing mechanisms. Our objective is to enable primary tasks such as speech recognition and user identification, while removing sensitive attributes in the raw speech data before sharing it with a cloud service provider. We leverage disentangled representation learning to explicitly learn independent factors in the raw data. Based on a user's preferences, a supervision signal informs the filtering out of invariant factors while retaining the factors reflected in the selected preference. Our experimental evaluation over five datasets shows that the proposed framework can effectively defend against attribute inference attacks by reducing their success rates to approximately that of guessing at random, while maintaining accuracy in excess of 99% for the tasks of interest. We conclude that negotiable privacy settings enabled by disentangled representations can bring new opportunities for privacy-preserving applications.

ASSep 18, 2019
Emotion Filtering at the Edge

Ranya Aloufi, Hamed Haddadi, David Boyle

Voice controlled devices and services have become very popular in the consumer IoT. Cloud-based speech analysis services extract information from voice inputs using speech recognition techniques. Services providers can thus build very accurate profiles of users' demographic categories, personal preferences, emotional states, etc., and may therefore significantly compromise their privacy. To address this problem, we have developed a privacy-preserving intermediate layer between users and cloud services to sanitize voice input directly at edge devices. We use CycleGAN-based speech conversion to remove sensitive information from raw voice input signals before regenerating neutralized signals for forwarding. We implement and evaluate our emotion filtering approach using a relatively cheap Raspberry Pi 4, and show that performance accuracy is not compromised at the edge. In fact, signals generated at the edge differ only slightly (~0.16%) from cloud-based approaches for speech recognition. Experimental evaluation of generated signals show that identification of the emotional state of a speaker can be reduced by ~91%.

CRAug 9, 2019
Emotionless: Privacy-Preserving Speech Analysis for Voice Assistants

Ranya Aloufi, Hamed Haddadi, David Boyle

Voice-enabled interactions provide more human-like experiences in many popular IoT systems. Cloud-based speech analysis services extract useful information from voice input using speech recognition techniques. The voice signal is a rich resource that discloses several possible states of a speaker, such as emotional state, confidence and stress levels, physical condition, age, gender, and personal traits. Service providers can build a very accurate profile of a user's demographic category, personal preferences, and may compromise privacy. To address this problem, a privacy-preserving intermediate layer between users and cloud services is proposed to sanitize the voice input. It aims to maintain utility while preserving user privacy. It achieves this by collecting real time speech data and analyzes the signal to ensure privacy protection prior to sharing of this data with services providers. Precisely, the sensitive representations are extracted from the raw signal by using transformation functions and then wrapped it via voice conversion technology. Experimental evaluation based on emotion recognition to assess the efficacy of the proposed method shows that identification of sensitive emotional state of the speaker is reduced by ~96 %.

CVNov 12, 2018
A new approach for pedestrian density estimation using moving sensors and computer vision

Eric K. Tokuda, Yitzchak Lockerman, Gabriel B. A. Ferreira et al.

An understanding of pedestrian dynamics is indispensable for numerous urban applications including the design of transportation networks and planing for business development. Pedestrian counting often requires utilizing manual or technical means to count individuals in each location of interest. However, such methods do not scale to the size of a city and a new approach to fill this gap is here proposed. In this project, we used a large dense dataset of images of New York City along with computer vision techniques to construct a spatio-temporal map of relative person density. Due to the limitations of state of the art computer vision methods, such automatic detection of person is inherently subject to errors. We model these errors as a probabilistic process, for which we provide theoretical analysis and thorough numerical simulations. We demonstrate that, within our assumptions, our methodology can supply a reasonable estimate of person densities and provide theoretical bounds for the resulting error.