Estimating integrals of functions forms the cornerstone of many general classes of problems such as optimisation, sampling and normalisation; these problems, in turn, are central tools for a plethora of applications across various fields such as computer graphics, computer vision and machine learning. The integrand, or function to be integrated, is complicated and rarely available in closed form. Its domain spans spaces of arbitrarily high dimensionality. Exact integration is hopeless and approximation is unavoidable in practice. An estimate of the integral is typically constructed using evaluations of the integrand at a number of sampled locations in the domain. The set of points where the function is sampled is often referred to collectively as a sampling pattern. For computer graphics applications, a modern animation feature film of length 1.5h typically involves the generation of a total of a few hundreds of trillions of high-dimensional samples that are mapped into light paths. Although a number of strategies have been proposed towards generating samples, measuring the quality of high-dimensional sampling patterns is an open problem. Sampling strategies are currently compared on a case-by-case basis by explicitly computing errors in the context of each application independently. The computation associated with measures such as discrepancy and Fourier analysis scale exponentially with dimensionality and are therefore not practicable for samples in high-dimensional domains. The proposed work seeks to quantify equidistribution of high-dimensional point sets using an alternative measure to discrepancy that is tractable. This project will establish mathematical connections between computational topology, stochastic geometry and error analysis for Monte Carlo integration. The goal is to develop a measure for assessing the quality of sampling-based estimators purely based on the samples used. The derived theory will be evaluated and applied on Monte Carlo rendering for Computer Graphics applications.

This proposal seeks to reconceptualise consumer value and business resilience in the UK's creative and visitor sectors and their value chain (from VFX companies, theatres and museums to festivals, catering and accommodation providers), collectively referred to as the experience economy. With a value of over £300bn, the health of the experience economy maintains the UK's status as the world's seventh most visited country and producer of quality creative experiences. Prior to the COVID-19 pandemic, many experience economy operators in the creative sector had begun experimenting with online content. Over the course of the pandemic, the range of these offers has expanded, opening up new audiences and sustaining existing ones. For many businesses, the digital or online 'experience' comprises mainly recorded and distributed content, usually provided free. Experiences are heavily dependent on evoking a sense of place. Therefore, at a time when access to physical places is restricted, there is a risk that online material fails to provide an effective proxy for the experience itself. While proving popular during the pandemic (see bibliography), existing products arguably offer limited additional experiential or business benefits. Convening expertise in experience design, post-production technology, games, visitor economy and place-making, this project will: - support experience providers in developing online and digital products which enhance their physical counterparts. - investigate modes of delivery and monetisation, as well as the policy instruments required to maintain adjacent place-based reputations and offers. - produce tools to support experience economy businesses' immediate post-COVID-19 regeneration, including scenario modelling, enabling a robust economic recovery.

Personalisation of media experiences for the individual is vital for audience engagement of young and old, allowing more meaningful encounters tailored to their interest, making them part of the story, and increasing accessibility. The goal of the BBC Prosperity Partnership is to realise a transformation to future personalised content creation and delivery at scale for the public at home or on the move. Evolution of mass-media audio-visual 'broadcast' content (news, sports, music, drama) has moved increasingly towards Internet delivery, which creates exciting potential for hyper-personalised media experiences delivered at scale to mass audiences. This radical new user-centred approach to media creation and delivery has the potential to disrupt the media landscape by directly engaging individuals at the centre of their experience, rather than predefining the content as with existing media formats (radio, TV, film). This will allow a new form of user-centred media experience which dynamically adapts to the individual, their location, the media content and producer storytelling intent, together with the platform/device and the network/compute resources available for rendering the content.The BBC Prosperity Partnership will position the BBC at the forefront of this 'Personalised Media' revolution enabling the creation and delivery of new services, and positioning the UK creative industry to lead future personalised media creation and intelligent network distribution to render personalised experiences for everyone anywhere. Realisation of personalised experiences at scale presents three fundamental research challenges: capture of object-based representations of the content to enable dynamic adaption for personalisation at the point of rendering; production to create personalised experiences which enhance the perceived quality of experience for each user; and delivery at scale with intelligent utilisation of the available network, edge and device resources for mass audiences. The BBC Prosperity Partnership will address the major technical and creative challenges to delivering user-centred personalised audience experiences at scale. Advances in audio-visual AI for machine understanding of captured content will enable the automatic transformation of captured 2D video streams to an object-based media (OBM) representation. OBM will allow adaptation for efficient production, delivery and personalisation of the media experience whilst maintaining the perceived quality of the captured video content. To deliver personalised experiences to audiences of millions requires transformation of media processing and distribution architectures into a hybrid and distributed low-latency computation platform, allowing flexible deployment of compute-intensive tasks across the network. This will achieve efficiency in terms of cost and energy use, while providing optimal quality of experience for the audience within the technical constraints of the system.

In redeveloping the EngD VEIV centre, we will be focussing on three themes in the area: - Vision & Imaging, covering the areas of computer-based interpretation of images. For example, object tracking in real-time video, or face detection and surface appearance capture. UCL now has a broad expertise in medical imaging (see description of CMIC), and also in tracking and interpretation of images (e.g. expertise of Julier and Prince who are on the management team). Previously we have supported several EngD projects in this area: e.g. Philips (structure from MRI), Sortex (object detection), Bodymetrics (body measurement from scanning data), where the innovation has been in higher-levels of interpretation of imaging data and derivation of measurements automatically. Two other projects highlight the rapidly developing imaging technology, with high-density sensors and high dynamic range imagery (e.g. BBC and Framestore). We have outline support from several companies for continuing in this area. - Media & Interfaces, covering real-time graphics and interactive interfaces. For example, the use of spatially immersive interfaces, or computer games technology. We have a growing relationship with a number of key games companies (EA, Sony, Eidos, Rebellion), where their concern or interest lies in the management of large sets of assets for complex games software. There is interest in tools for developing imagery (r.g. Arthropics, Geomerics). We also have interest in the online 3D social spaces from IBM and BT. A relatively recent development that we plan to exploit is the combination of real-time tracking, real-time graphics and ubiquitous sensing to create augmented reality systems. Interest has been expressed in this area from Selex and BAe. There is also a growing use of these technologies in the digital heritage area, which we have expertise in and want to expand. - Visualisation & Design, covering the generation and visualisation of computer models in support of decision-making processes. For example, the use of visualisation of geographic models, or generative modelling for architectural design. Great advances have been made in this area recently, with the popularity of online GIS tools such as Google Earth tied in to web services and the acceptance of the role of IT in complex design processes. We would highlight the areas of parameterised geometry (e.g. with Fosters and the ComplexMatters spin-out), studying pedestrian movements (with Buro Happold, Node Architects), visualisation of GIS data (e.g. ThinkLondon, Arup Geotechnical), and medical visualisation.These themes will be supported by broadening the engagement with other centres around UCL, including: the UCL Interaction Centre, the Centre for Medical Image Computing, the Chorley Institute and the Centre for Computational Science.The main value of the centre is that visual engineering requires cross-disciplinary training. This is possible with a normal PhD, but within the centre model inter-disciplinary training can embed the students' focussed research into a larger context. The centre model provides a programme structure and forums to ensure that opportunities and mechanisms for cross-disciplinary working are available. The centre also provides an essential role in providing some core training; though by its nature the programme must incorporate modules of teaching from a wide variety of departments that would otherwise be difficult to justify.