Centre for Mathematical Imaging Techniques (CMIT)
- CMIT Research Seminar 2024/25 -
Semester 2 2024/25 (current)
19 February 2025 14:00-15:00 UK time. Online.
Orkun Furat (Ulm University, Germany).
Title. Reconstructing 3D microstructures from 2D image data by combining generative AI and stochastic geometry
Abstract. This talk introduces a computational method for generating digital twins of the 3D morphology of (functional) materials through stochastic geometry models, calibrated by means of 2D image data. By means of systematic variations of model parameters a wide spectrum of structural scenarios can be investigated, such that the corresponding digital twins can be exploited as geometry input for numerical simulations of macroscopic effective properties [1,2,3]. For calibrating models that can generate virtual 3D microstructures by stochastic simulation, generative adversarial networks (GANs) have gained an increased popularity [4]. While GANs offer a data-driven approach for modeling complex 3D morphologies, the systematic variation of model parameters for generating diverse structural scenarios can be difficult. In contrast to this, relatively simple models of stochastic geometry (e.g., based on Gaussian random fields) allow parameter-driven structure variations, but can fall short in mimicking complex morphologies. Still, these “simple models” can be used to construct more advanced parametric stochastic geometry models (like excursion sets of more general random fields, or random tessellations induced by marked point processes). However, with increasing model complexity the calibration of model parameters to image data can become increasingly difficult. Combining GANs with advanced stochastic geometry models can overcome these limitations and, in addition, allows for the calibration of model parameters solely based on 2D image data of planar sections through the 3D structure [5]. These parametric hybrid models are flexible enough to stochastically model complex 3D morphologies, enabling the systematic exploration of different structures. Moreover, by combining stochastic and numerical simulations, the impact of morphological descriptors on macroscopic effective properties can be investigated and quantitative structure-property relationships can be established. Thus, the presented method, allows for the generation of a wide spectrum of virtual 3D morphologies, that can be used for identifying structures with optimized functional properties.
(The talk is based on joint work with Sabrina Weber, Lukas Fuchs, Volker Schmidt.)
References
[1] B. Prifling et al. (2021). Front. in Mater. 8 (2021), 786502.
[2] O. Furat et al. (2021). npj Comput. Mater. 7, 105.
[3] E. Schlautmann et al. (2023). Adv. Energy Mater. 13, 2302309.
[4] S. Kench and S.J. Cooper (2021). Nat. Mach. Intell. 3, 299-305.
[5] L. Fuchs et al. (2025). Commun. Mater. 6, 4.
Semester 1 2024/25
16 December 2024 15:30-16:30 UK time. In-Person and online (Math Building, Room 104).
Ronald Lui (The Chinese University of Hong Kong, HK).
Title. Shape Prior Segmentation Guided by Harmonic Beltrami Signature
Abstract This talk presents a novel image segmentation method that incorporates the Harmonic Beltrami Signature (HBS) as shape prior knowledge. The HBS represents 2D simply-connected shapes that are invariant to translation, rotation, and scaling. By leveraging the HBS, the proposed method enables direct shape similarity measurement using the L^2 distance between signatures, while also encoding shapes robustly against perturbations. The method integrates the HBS into a baseline Beltrami coefficient segmentation framework. It utilizes reference shape boundaries and computes corresponding HBS as prior knowledge. This HBS prior guides the segmentation of partially damaged or occluded objects towards the reference shape(s), ensuring their similarity. Experimental results on synthetic and natural images validate these benefits, and comparisons with baseline segmentation models show significant improvements. This work is supported by HKRGC GRF (Project ID: 14307622).
Semester 2 2023/24
28 February 2024 15:00-16:00 UK time. In-Person and online (Math Building, Room 104).
Maciej Buze (UK).
Title. Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport
Abstract. The microstructure of metals and foams is often modelled using power diagrams, a general class of tessellations which includes the well-known Voronoi diagrams. While power diagram-based approaches can generate complex microstructures in a matter of seconds and require a relatively small number of parameters, the idealised grains they produce are inherently unrealistic - they have flat boundaries and any spatial anisotropy they possess is solely determined by the relative location of seed points of neighbouring grains and not by the preferred growth directions of each grain.
Curved boundaries and control over the anisotropy of individual grains can be achieved by employing anisotropic power diagrams (APDs), with several promising APD-based approaches explored in recent years by various authors. One obstacle in the wider adoption of APDs as a practical tool for modelling the microstructure of metals is the computational cost of generating them. Known efficient methods for generating power diagrams do not translate to the anisotropic setup and known techniques for generating APDs are drastically slower - while the usual runtime to generate a power diagram with grains of given volumes is (tens of) seconds, for APDs it ranges from (tens of) minutes to (tens of) hours.
In this talk I will begin by providing a brief overview of (anisotropic) power diagram methods in geometric modelling of polycrystalline materials and subsequently present a novel approach to generating APDs with prescribed statistical properties, in which we combine semi-discrete optimal transport techniques with modern GPU-oriented computational tools, originally developed for the Sinkhorn algorithm. Our method succeeds in bringing the runtime to generate optimal APDs down to (tens of) seconds, which is fast enough to be used, e.g. in computational homogenisation.
I will finish by showcasing the speed and the versatility of our method with several examples, including ones based on Electron Backscatter Diffraction (EBSD) measurements provided by our industrial partner, Tata Steel.
This is joint work with David Bourne (Heriot-Watt), Jean Feydy (Inria Paris), Steve Roper (Glasgow) and Karo Sedighiani (Tata Steel).
Semester 1 2023/24
6 December 2023 10:00-11:00 UK time. Online on Zoom (link will be announced by email)
Zhicheng Wang (CN).
Title. Solution multiplicity and effects of data and eddy viscosity on Navier-Stokes solutions inferred by physics-informed neural networks
Abstract. Physics-informed neural networks (PINNs) have emerged as a new simulation paradigm for fluid flows and are especially effective for inverse and hybrid problems. However, vanilla PINNs often fail in forward problems, especially at high Reynolds (Re) number flows. Herein, we study systematically the classical lid-driven cavity flow at Re=2,000, 3,000 and 5,000. We observe that vanilla PINNs obtain two classes of solutions, one class that agrees with direct numerical simulations (DNS), and another that is an unstable solution to the Navier-Stokes equations and not physically realizable. We attribute this solution multiplicity to singularities and unbounded vorticity, and we propose regularization methods that restore a unique solution within 1\% difference from the DNS solution. In particular, we introduce a parameterized entropy-viscosity method as artificial eddy viscosity and identify suitable parameters that drive the PINNs solution towards the DNS solution. Furthermore, we solve the inverse problem by subsampling the DNS solution, and identify a new eddy viscosity distribution that leads to velocity and pressure fields almost identical to their DNS counterparts. Surprisingly, a single measurement at a random point suffices to obtain a unique PINNs DNS-like solution even without artificial viscosity, which suggests possible pathways in simulating high Reynolds number turbulent flows using vanilla PINNs.
1 December 2023 14:00-15:00 UK time. Online on Zoom (link will be announced by email)
Paolo Dulio (Department of Mathematics, Polytechnic University of Milan, IT).
Title. Convex Ghosts in Discrete Tomography
Abstract. In Computerized Axial Tomography, the problem of reconstructing an unknown object from X-ray projections is considered.
The original theoretical model bases on the inversion of the Radon transform, but, in view of application, several items must be refined. Among them, the necessary constraint of using only a finite number of projections leads to the lost of injectivity of the Radon transform. This introduces ghosts in the tomographic problem, namely, non trivial images having zero projections along all the considered directions.
As a consequence, uniqueness of reconstruction can never be ensured, even from a theoretical point of view, without assuming some kind of prior knowledge, so to understand the structure of the space of ghosts.
In this view, I will focus on the extra information that the set to be reconstructed has some kind of convexity, pointing out properties of the cross-ratio associated to the involved ghosts. In particular, I will present results obtained when only horizontal and vertical convexity is assumed, and how the corresponding ghosts can be numerically characterized in terms of integer sequences.
25 October 2023 10:00-11:00 UK time. Online on Zoom (link will be announced by email)
Luying Gui (School of Mathematics and Statistics, Nanjing University of Science and Technology, CN).
Title. Histopathology image analysis of pancreatic ductal adenocarcinoma based on
Unsupervised and weakly-supervised learning algorithms.
Abstract. Histopathology images are considered the most reliable method for detecting and diagnosing cancer. However, analyzing these images is a complex task that requires a great deal of expertise. Pathologists need to search for useful information in huge pathology images to diagnose diseases in clinical applications. Additionally, analyzing pathology images can predict disease trends and prognosis.
The development of deep neural networks has brought many breakthroughs in automated histopathology image analysis. However, these methods rely heavily on the availability of a large number of pixel-level labels, which is a labor-intensive and time-consuming task. To overcome these challenges, we investigated algorithms for histopathology image analysis using unlabeled or a small number of coarse-grained labels. We applied these algorithms to analyze histopathological images of pancreatic ductal adenocarcinoma (PDAC).
Our experimental results demonstrate that these weakly-supervised and unsupervised-based algorithms accurately segment the components of the pathology images, thus laying the foundation for further image analysis and prognosis prediction studies.
17 October 2023 11:00-12:00 UK time. In-Person and online (Math Building, Room 303). Joint CMIT-RCMM seminar talk.
Federico Sabina (Universidad Nacional Autónoma de México, MX).
Title. Towards asymptotic modeling of seismic surface metabarriers: Transient
scattering of a Rayleigh wave by a cluster of subwavelength resonators.
Abstract. A seismic metabarrier (intended for surface waves mitigation effect) is
modeled as a cluster of single-degree-of-freedom resonator units deposited on the
surface of an isotropic homogeneous elastic half-space. It is assumed that each
resonator has a frictionless rigid base of diameter much smaller than the wavelength
of an incoming surface wave. The slow-motions asymptotic method is applied for
constructing the first-order asymptotic model of multiple time-dependent
scattering of a pulsed Rayleigh wave with respect to the vertical displacements of
the resonators (including their rigid bases and inertial elements) and the
normal contact forces (time-dependent integral characteristics of the contact reactions
beneath the resonator bases). Both the stationary and transient multiple scattering
scenarios are considered. The variation of the amplitude reduction factor due to
the model parameters variation is studied in detail.
Past Semesters
Semester 2, 2022/23
- 15 February 2023 14:00-15:00 UK time. In-Person (Math Building, Room 103).
Alex Frangi (University of Leeds, UK).
Title. Computational Precision Imaging and Medicine in Regulatory Science
Abstract. Traditional medical device product development life cycle begins with pre-clinical development. In laboratories, bench/in-vitro experiments establish plausibility for treatment efficacy. Then in-vivo animal models with different species provide guidance on medical device efficacy/safety for humans. With success in both in-vitro/in-vivo studies, scientists can propose clinical trials testing whether the product is made available for humans. Clinical trials are often divided into four phases. Phase 3 involves testing on many people, which is costly, long, and sometimes implausible (e.g., paediatric patients, rare diseases, and underrepresented ethnic groups). When medical devices fail at later stages, financial losses can be catastrophic Predicting low-frequency side effects has been difficult because such side effects may not become apparent until the treatment is adopted by many patients. Statistics on marketed medical device highlight increased serious adverse effects on patients (#serious-events/$bn-medical device-spend increased +8%p.a. in 2001-2009 and led to expensive recall/compensation cases. The appearance of severe side effects in Phase-3 trials often causes development to stop, for ethical/economic reasons. In recent years, medical devices also failed in Phase 3 because of a lack of efficacy rather than safety. With success rates declining and clinical trial costs rising, innovation stagnating and clinical trials in US/UK moving abroad where costs are lower, but patient profiles may differ. One reason for failure is that traditional trials aim to establish efficacy/safety for *most* subjects rather than *individual* subjects, so efficacy is determined by a statistic of central tendency for the trial. Traditional trials do not adapt treatment to covariates of subjects, so so-called Precision Medicine becomes elusive. Many reports have pointed to this broken/slow innovation system and its impact on societal costs and suboptimal healthcare. However, radical changes to this innovation process are still to be developed.
In this talk, I will overview our progress in the INSILEX Programme. We envision a paradigm shift in medical device innovation where quantitative sciences are exploited to carefully engineer medical device designs, explicitly optimise clinical outcomes, and thoroughly test side effects before being marketed. In-silico clinical trials (ISCT) are essentially computer-based medical device trials performed on populations of virtual patients. They use computer models/simulations to conceive, develop and assess devices with the intended clinical outcome explicitly optimised from the outset (a-priori) instead of tested on humans (a-posteriori). This will include testing for potential risks to patients (side effects) exhaustively exploring in-silico for medical device failure modes and operational uncertainties before being tested in human clinical trials. Advanced computer modelling will prove useful to predict how a device behaves when deployed across the general population or when used in new scenarios outreaching the primary prescriptions (device repurposing), helping to help the widest possible target patient group without unintended consequences of side effects and device interactions.
INSILEX is underpinned by Computational Medicine, an emerging discipline devoted to developing quantitative approaches for understanding the mechanisms, diagnoses, and treatment of human disease through the systematic application of mathematics, engineering, and computational science. Dealing with the extraordinary multi-scale complexity and variability intrinsic to human biological systems and health data demands radically new approaches compared to methods for manufactured systems.
Within this framework, INSILEX extensively uses medical image computing, a mature field challenged by the progress made across all medical imaging technologies and more recent breakthroughs in biological imaging. The cross-fertilisation between medical image analysis, medical imaging physics and technology, and domain knowledge from medicine and biology has spurred a truly interdisciplinary effort that stretched outside the original boundaries of the disciplines that gave birth to this field and created stimulating and enriching synergies. We advocate for "Precision Imaging", not as a new discipline but a distinct emphasis in medical imaging, unifying the efforts behind mechanistic and phenomenological model-based imaging. Precision Imaging is characterised by being descriptive, predictive, and integrative. It captures three main directions in the effort to deal with the information deluge in imaging sciences and thus achieve wisdom from data, information, and knowledge. Precision imaging can lead to carefully and mechanistically engineered imaging biomarkers and the use of medical imaging-based computational modelling and simulation for improved regulatory science and innovation of medical products. This talk summarises and formalises our vision of Precision Imaging for Precision Medicine and highlights connections with past research and our current focus on large-scale computational phenomics and in silico clinical trials.
Selected References:
- Frangi AF, Taylor ZA, Gooya A. Precision Imaging: more descriptive, predictive and integrative imaging. Med Image Anal. 2016 Oct;33:27-32.
- Sarrami-Foroushani A, Lassila T, MacRaild M, Asquith J, Roes KCB, Byrne JV, Frangi AF. In-silico trial of intracranial flow diverters replicates and expands insights from conventional clinical trials. Nat Commun. 2021 Jun 23;12(1):3861. doi: 10.1038/s41467-021-23998-w.
- Abadi E, Segars WP, Tsui BMW, Kinahan PE, Bottenus N, Frangi AF, Maidment A, Lo J, Samei E. Virtual clinical trials in medical imaging: a review. J Med Imaging (Bellingham). 2020 Jul;7(4):042805. doi: 10.1117/1.JMI.7.4.042805.
- 1 March 2023 13:00-14:00 UK time. Online (via Zoom).
Joost Batenburg (Leiden University, The Netherlands).
Title. Towards an intelligent CT-scanner
Abstract. Computed Tomography (CT) is a powerful technique for creating images of the interior of an object in a non-invasive manner. Current workflows for CT are mostly sequential: the computations and analysis of the data take place after the scan is finished. In this talk I will discuss recent developments in turning CT imaging into an interactive process, and discuss how this paves the way for developing “intelligent” CT-systems that can interact with the operator to achieve more informative data acquisition.
- 8 March 2023 14:00-15:00 UK time. Online (via Zoom).
Yeonjong Shin (Korea Advanced Institute of Science and Technology, South Korea).
Title. Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications
Abstract. Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become an emerging field, Scientific Machine Learning (SciML). Many ML techniques, however, are very complex and sophisticated, commonly requiring many trial-and-error and tricks. These result in a lack of robustness and interpretability, which are critical factors for scientific applications. This talk centers around mathematical approaches for SciML, promoting trustworthiness. The first part is about how to embed physics into neural networks (NNs). I will present a general framework for designing NNs that obey the first and second laws of thermodynamics. The framework not only provides flexible ways of leveraging available physics information but also results in expressive NN architectures. The second part is about the training of NNs, one of the biggest challenges in ML. I will present an efficient training method for NNs - Active Neuron Least Squares (ANLS). ANLS is developed from the insight gained from the analysis of gradient descent training.
- 3 May 2023 10:00-11:00 UK time. Online (via Zoom).
Lui Lok Ming (The Chinese University of Hong Kong, Hong Kong).
Title. From Computational Quasiconformal Geometry to Deep Learning for Imaging
Abstract. Computational Quasiconformal (CQC) Geometry studies the deformation pattern between shapes. It has found important applications in imaging science, such as image registration, image analysis and image segmentation. With the advance of deep learning techniques, the incorporation of CQC theories to deep neural networks can further improve the performance for these imaging tasks in both efficiency and accuracy. In this talk, I will give an overview on how CQC and deep learning can play an important role in image processing. This work is supported by HKRGC GRF.
- 5 May 2023 14:00-15:00 UK time. In-Person (Math Building, Room 103).
Arijit Patra (UCB Pharma).
Title. Artificial Intelligence and Toxicologic Pathology and drug development
Bio. Dr Arijit Patra is a Senior Principal Scientist at UCB, based in London. He holds a PhD in machine learning for healthcare imaging from the University of Oxford, where he was a Rhodes Scholar. Prior to that, he completed a dual degree in Mechanical Engineering from the Indian Institute of Technology (IIT) at Kharagpur, India. He has also been associated with AstraZeneca, Shell, Microsoft Research and CSIR-South Africa at various points in his career and has been actively involved in the AI4SG (AI for Social Good) community. He has authored several publications around machine learning and medical imaging and is a reviewer for multiple peer reviewed venues such as NeurIPS, ICML, MICCAI and several journals.
- 10 May 2023 14:00-15:00 UK time. Online (via Zoom).
Jan Modersitzki (Universität zu Lübeck, Germany).
Title. Mathematical Models for Correspondence Problems
Abstract. Correspondence problems are among the most difficult challenges in image processing, especially in biomedical fields. We illustrate this with examples that show the complexity of the task. In the absence of ground-truth data, mathematical modeling of the problem is particularly important. The talk presents a variational approach and discusses important components such as distance measures and regularization. One focus is the efficient optimisation and the associated differentiability of the components.
Semester 1, 2022/23
- 9 November 2022 12:00-13:00 UK time. Online (via Zoom).
Chenglong Bao (Tsinghua University, China).
Title. Learning Robust Imaging Models without Paired Data
Abstract. The observations in practical imaging systems always contain complex noise such that classical approaches are difficult to obtain satisfactory results. In recent years, deep neural networks directly learned a map between the noisy and clean images based on the training on paired data. Despite its promising results in various tasks, collecting the training data is difficult and time-consuming in practice. In this talk, in the unpaired data regime, we will discuss our recent progress for building AI-aided robust models and their applications in image processing. Leveraging the Bayesian inference framework, our model combines classical mathematical modeling and deep neural networks to improve interpretability. Experimental results on various real datasets validate the advantages of the proposed methods.
- 16 November 2022 13:00-14:00 UK time. Online (via Zoom).
Wenjia Bai (Imperial College London, UK).
Title. Modelling the Shape for 100,000 Hearts
Abstract. Understanding the variation of cardiac shape and function plays an essential role in medical imaging and cardiovascular research. In recent years, the emerging of population-level imaging studies and fast development of machine learning research provide us with both new data and new tools to investigate this question. In this talk, I will present our recent work on robust medical image segmentation and cardiac shape modelling and discuss potential future directions.
- 30 November 2022 17:00-18:00 UK time. Online (via Zoom).
Amanda Howard (Pacific Northwest National Laboratory, USA).
Title. Multifidelity approaches for machine learning
Abstract. In this talk, I will discuss two approaches to multifidelity machine learning: physics informed Gaussian process regression and multifidelity Deep Operator Networks (DeepONets.) In both cases, there is a need for fast and accurate models using only limited high fidelity data. In the Physics-informed CoKriging (CoPhIK) machine learning method we use a fast, but inaccurate physics-based model to constrain Gaussian process regression trained on a small amount of high fidelity experimental data. We demonstrate that the CoPhIK model shows good agreement with experimental results and significant improvements over existing physics-based models. We show that the proposed model is robust as it is not sensitive to the input parameters in the physics-based model. Additionally, we will discuss multifidelity DeepONets, with the ability to train operators using low fidelity noisy or low resolution data and a small amount of high fidelity data. Our approaches allow for accurate models when training with data alone is infeasible.
- 7 December 2022 15:00-16:00 UK time. In-Person. Math Building, Room 103. Online stream over the usual CMIT Zoom link.
David Bourne (Heriot-Watt University, UK).
Title. Optimal transport theory and geometric modelling of polycrystalline materials
Abstract. Over the last few years optimal transport theory has developed into a vibrant research area and found applications in PDEs, economics, image processing and data science. In this talk I will describe a new application to microstructure modelling. In particular, I will show how optimal transport theory can be used to generate geometric models (Representative Volume Elements) of polycrystalline materials. This is joint work with Piet Kok (Tata Steel Research and Development & Ghent University), Mason Pearce (Heriot-Watt University), Steve Roper (University of Glasgow) and Wil Spanjer (Tata Steel Research and Development).
- 14 December 2022 13:00-14:00 UK time. Online (via Zoom).
Hongkai Zhao (Duke University, USA).
Title. How much can one learn a PDE from a single solution data?
Abstract. In this presentation, we discuss a few basic questions for PDE learning from observed solution data. Using various types of PDEs as examples, we show 1) how large the data space spanned by all snapshots along a solution trajectory is, 2) if one can construct an arbitrary solution by superposition of snapshots of a single solution, and 3) identifiability of a differential operator from a single solution data on local patches.
- 19 December 2022 TBA UK time. In-Person.
Xiaohao Cai (University of Southampton, UK).
Title. Inference in Medical Imaging by Few-shot Learning with Subspace Feature Representations
Abstract. Unlike the fields e.g. visual scene recognition, where tremendous advances have taken place due to the availability of very large datasets to train deep neural networks, inference from medical images is often hampered by the fact that only small amounts of data may be available. When working with very small dataset problems, of the order of a few hundred items of data, the power of deep learning may still be exploited by using a model pre-trained on natural images as a feature extractor and carrying out classic pattern recognition techniques in this feature space, the so-called few-shot learning problem. In regimes where the dimension of this feature space is comparable to or even larger than the number of items of data, dimensionality reduction is a necessity and is often achieved by principal component analysis or singular value decomposition (PCA/SVD). Noting the inappropriateness of using SVD for this setting, in this talk, we explore two alternatives based on discriminant analysis (DA) and non-negative matrix factorization (NMF). Using 14 different datasets spanning 11 distinct disease types we demonstrate that at low dimensions, discriminant subspaces achieve significant improvements over SVD-based subspaces and the original feature space. We also show that at modest dimensions, NMF is a competitive alternative to SVD in this setting.