InfraRed Thermography (IRT), a non-invasive, non-contact, and non-destructive testing (NDT) technique, has become an established tool in the assessment of a building’s behavior and energy performance. However, the inherent low spatial resolution of thermal infrared (TIR) cameras has led recent work to fuse thermographic and geometric data to generate accurate 3D representations of buildings encapsulating temperature information. Whilst existing data fusion methods have relied on sensors in fixed relative orientation (RO), the co-registration of independent TIR and RGB blocks using ground control points (GCPs), or the reprojection of TIR images onto additional geometric or parametric models, approaches that directly match multi-modal images remain limited. In principle, if multi-modal tie points were available, it would be possible to directly align the RGB block with the TIR block; however, such matching is extremely challenging due to the substantial differences in radiometric properties. The main contribution of this paper is to demonstrate the applicability of off-the-shelf deep learning-based image matching algorithms, originally trained on mono-modal datasets, to multi-modal matching tasks for InfraRed Thermography 3D-Data Fusion (IRT-3DDF). We conduct a comparative evaluation of the principal algorithms developed in recent years, with particular emphasis on 3D accuracy and computational efficiency, under the hypothesis that, owing to the inherently local nature of the problem they address, these algorithms can generalize from a mono-modal training domain to a multi-modal application domain. The results are benchmarked against existing hand-crafted open-source multi-modal reference methods. Importantly, the proposed method is fully-automatic, obviating the need for sensor pre-calibration, manual co-registration, or associated positioning information. Results demonstrate that DL-based image matching, using pre-trained neural networks outside of their expected training domain, provides a viable approach for IRT-3DDF capable of co-registering blocks of multi-modal images across varying scales, settings, sensors, and subjects. Our results indicate accuracy in 3D is up to seven times better than multi-modal hand-crafted algorithms, while hand-crafted mono-modal methods fail to co-register images in their entirety.

We prove that curve shortening flow on the round sphere displays sharp chord-arc improvement, precisely as in the planar setting (Andrews and Bryan, Comm. Anal. Geom., 2011). As in the planar case, the sharp estimate implies control on the curvature, resulting in a direct and efficient proof that simple spherical curves either contract to round points (in finite time) or converge to great circles (in infinite time).

The determination of precise and reliable interior (IO) and relative (RO) orientation parameters for thermal infrared (TIR) cameras is critical for their subsequent use in photogrammetric processes. Although 2D calibration boards have become the predominant approach for TIR geometric calibration, these targets are susceptible to projective coupling and often introduce error through manual construction methods, necessitating the development of 3D targets tailored to TIR geometric calibration. Therefore, this paper evaluates TIR geometric calibration results obtained from 2D board and 3D field calibration approaches, documenting the construction, observation, and calculation of IO and RO parameters. This includes a comparative analysis of values derived from three popular commercial software packages commonly used for geometric calibration: MathWorks’ MATLAB, Agisoft Metashape, and Photometrix’s Australis. Furthermore, to assess the validity of derived parameters, two InfraRed Thermography 3D-Data Fusion (IRT-3DDF) methods are developed to model historic building façades and medieval frescoes. The results demonstrate the success of the proposed 3D field calibration targets for the calculation of both IO and RO parameters tailored to photogrammetric data fusion. Additionally, a novel combined TIR-RGB bundle block adjustment approach demonstrates the success of applying ‘out-of-the-box’ deep-learning neural networks for multi-modal image matching and thermal modelling. Considerations for the development of TIR geometric calibration approaches and the evolution of proposed IRT-3DDF methods are provided for future work.

We consider the evolution of hypersurfaces on the unit sphere $\mathbb{S}^{n+1}$ by smooth functions of the Weingarten map. We introduce the notion of `quasi-ancient' solutions for flows that do not admit non-trivial, convex, ancient solutions. Such solutions are somewhat analogous to ancient solutions for flows such as the mean curvature flow, or 1-homogeneous flows. The techniques presented here allow us to prove that any convex, quasi-ancient solution of a curvature flow which satisfies a backwards in time uniform bound on mean curvature must be stationary or a family of shrinking geodesic spheres. The main tools are geometric, employing the maximum principle, a rigidity result in the sphere and an Alexandrov reflection argument. We emphasize that no homogeneity or convexity/concavity restrictions are placed on the speed, though we do also offer a short classification proof for several such restricted cases.

An important set of theorems in geometric analysis consists of constant rank theorems for a wide variety of curvature problems. In this paper, for geometric curvature problems in compact and non-compact settings, we provide new proofs which are both elementary and short. Moreover, we employ our method to obtain constant rank theorems for homogeneous and non-homogeneous curvature equations in new geometric settings. One of the essential ingredients for our method is a generalization of a differential inequality in a viscosity sense satisfied by the smallest eigenvalue of a linear map Brendle et al. (Acta Math 219:1–16, 2017) to the one for the subtrace. The viscosity approach provides a concise way to work around the well known technical hurdle that eigenvalues are only Lipschitz in general. This paves the way for a simple induction argument.

We provide a curvature flow approach to the regular Christoffel-Minkowski problem. The speed of our curvature flow is of an entropy preserving type and contains a global term.

Comprehensive documentation is the foundation of effective conservation, repair and maintenance (CRM) practices for architectural heritage. In order to diagnose historic buildings and inform decision making, a combination of multi-disciplinary surveys is fundamental to understanding a building’s heritage and performance. Infrared thermography (IRT), a non-contact, non-invasive and non-destructive imaging technique, allows both qualitative and quantitative assessments of temperature to be undertaken. However, the inherent low spatial resolution of thermal imaging has led recent work to fuse thermographic and geometric data for the accurate 3D documentation of architectural heritage. This paper maps the scope of this emerging field to understand the application of IRT and 3D-data fusion (IRT-3DDF) for architectural heritage. A scoping review is undertaken to systematically map the current literature and determine research gaps and future trends. Results indicate that the increasing availability of thermal cameras and advances in photogrammetric software are enabling thermal models to be generated successfully for the diagnosis and holistic management of architectural heritage. In addition, it is evident that IRT-3DDF provides several opportunities for additional data integration, historic building information modelling (H-BIM) and temporal analysis of historic buildings. Future developments are needed to transform IRT-3DDF findings into actionable insights and to apply IRT-3DDF to pressing climate-related challenges, such as energy efficiency, retrofitting and thermal comfort assessments.

We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if they exist, solve the regular Orlicz–Minkowski problems. As an application, we obtain old and new existence results for the regular even Orlicz–Minkowski problems; the corresponding $$L_p$$ version is the even $$L_p$$ -Minkowski problem for $$p>-n-1$$ . Moreover, employing a parabolic approximation method, we give new proofs of some of the existence results for the general Orlicz–Minkowski problems; the $$L_p$$ versions are the even $$L_p$$ -Minkowski problem for $$p>0$$ and the $$L_p$$ -Minkowski problem for $$p>1$$ . In the final section, we use a curvature flow with no global term to solve a class of $$L_p$$ -Christoffel–Minkowski type problems.

This short note is a mostly expository article examining negatively curved three-manifolds. We look at some rigidity properties related to isometric embeddings into Minkowski space. We also review the Cross Curvature Flow (XCF) as a tool to study the space of negatively curved metrics on hyperbolic three-manifolds, the largest and least understood class of model geometries in Thurston's Geometrisation. The relationship between integrability and embedability yields interesting insights, and we show that solutions with fixed Einstein volume are precisely the integrable solutions, answering a question posed by Chow and Hamilton when they introduced the XCF.

We employ curvature flows without global terms to seek strictly convex, spacelike solutions of a broad class of elliptic prescribed curvature equations in the simply connected Riemannian spaceforms and the Lorentzian de Sitter space, where the prescribed function may depend on the position and the normal vector. In particular, in the Euclidean space we solve a class of prescribed curvature measure problems, intermediate L-p-Alelcsandrov and dual Minkowski problems as well as their counterparts, namely the L-p-Christoffel-Minkowski type problems. In some cases we do not impose any condition on the anisotropy except positivity, and in the remaining cases our condition resembles the constant rank theorem/convexity principle due to Caffarelli et al. (2007). Our approach does not rely on monotone entropy functionals and it is suitable to treat curvature problems that do not possess variational structures. (C) 2020 Elsevier Ltd. All rights reserved.

We obtain Harnack estimates for a class of curvature flows in Riemannian manifolds of constant non-negative sectional curvature as well as in the Lorentzian Minkowski and de Sitter spaces. Furthermore, we prove a Harnack estimate with a bonus term for mean curvature flow in locally symmetric Riemannian Einstein manifold of non-negative sectional curvature. Using a concept of "duality" for strictly convex hypersurfaces, we also obtain a new type of inequalities, so-called "pseudo"-Harnack inequalities, for expanding flows in the sphere and in the hyperbolic space.

We consider the evolution of hypersurfaces on the unit sphere $\mathbb{S}^{n+1}$ by their mean curvature. We prove a differential Harnack inequality for any weakly convex solution to the mean curvature flow. As an application, by applying an Aleksandrov reflection argument, we classify convex, ancient solutions of the mean curvature flow on the sphere.

We prove differential Harnack inequalities for flows of strictly convex hypersurfaces by powers p, 0 < p < 1, of the mean curvature in Einstein manifolds with a positive lower bound on the sectional curvature. We assume that this lower bound is sufficiently large compared to the derivatives of the curvature tensor of the ambient space and that the mean curvature of the initial hypersurface is sufficiently large compared to the ambient geometry. We also obtain some new Harnack inequalities for more general curvature flows in the sphere, as well as a monotonicity estimate for the mean curvature flow in non-negatively curved, locally symmetric spaces.

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.

We study long-time existence and asymptotic behaviour for a class of anisotropic, expanding curvature flows. For this we adapt new curvature estimates, which were developed by Guan, Ren and Wang to treat some stationary prescribed curvature problems. As an application we give a unified flow approach to the existence of smooth, even $L_p$-Minkowski problems in $\mathbb{R}^{n+1}$ for $p>-n-1.$

We prove Harnack inequalities for hypersurfaces flowing on the unit sphere by $p$-powers of a strictly monotone, 1-homogeneous, convex, curvature function $f$, $0<p\leq 1.$ If $f$ is the mean curvature, we obtain stronger Harnack inequalities.

Building Information Modelling (BIM) is a new process that is spreading in the Architecture, Engineering and Construction field. It allows the creation of virtual building models, which can be linked to numerical data, texts, images, and other types of information. Building components, such as walls, floors, etc. are modelled as “smart objects”, i.e. they are defined by numerical parameters, such as dimensions, and are embedded with other kinds of information, such as building materials and properties. Stored data are accessible and modifiable by all different professionals involved in the same project. The BIM process has been developed for new buildings, and it allows to plan and manage the whole building life-cycle. BIM for built heritage has started to be researched recently, and its use is still not widespread. Indeed, built heritage is characterised by complex morphology and non-homogeneous features, which clash with BIM’s standardised procedures. Moreover, to date, BIM does not allow fully automated procedures to model heritage buildings. This review focuses on the survey and digitisation phases, which can be seen as the initial phases of application of BIM in conservation projects. It also briefly covers the modelling stage. Here we present the main methodologies developed for BIM for built heritage. Issues about digitisation are also highlighted, principally in connection with the unavailability of automated processes. During the last 10 years, research has led to promising results; for example, videogame interfaces have been used to simulate virtual 3D tours that display in a single interface the 3D model and the database containing metadata, and new software plug-ins have been developed, to easily create “smart objects”. Nevertheless, further research is needed to establish how BIM can support the practice of building conservation. There is a gap in BIM’s information holding capacities, namely the storage of cultural and historical documentation, as well as monitored and simulated data relevant for preventive conservation. Future work should focus on the development of new tools that will be able to store and share all the relevant metadata.

Understanding and protecting cultural heritage involves the detection and long-term documentation of archaeological remains alongside the spatio-temporal analysis of their landscape evolution. Archive aerial photography can illuminate traces of ancient features which typically appear with different brightness values from their surrounding environment, but are not always well defined. This research investigates the implementation of the Structure-from-Motion - Multi-View Stereo image matching approach with an image enhancement algorithm to derive three epochs of orthomosaics and digital surface models from visible and near infrared historic aerial photography. The enhancement algorithm uses decorrelation stretching to improve the contrast of the orthomosaics so as archaeological features are better detected. Results include 2D / 3D locations of detected archaeological traces stored into a geodatabase for further archaeological interpretation and correlation with benchmark observations. The study also discusses the merits and difficulties of the process involved. This research is based on a European-wide project, entitled “Cultural Heritage Through Time”, and the case study research was carried out as a component of the project in the UK.

Diachronic studies are central to cultural heritage research for the investigation of change, from landscape to architectural scales. Temporal analyses and multi-temporal 3D reconstruction are fundamental for maintaining and safeguarding all forms of cultural heritage. Such studies form the basis for any kind of decision regarding intervention on cultural heritage, helping assess the risks and issues involved. This article introduces a European-wide project, entitled "Cultural Heritage Through Time", and the case study research carried out as a component of the project in the UK. The paper outlines the initial stages of the case study of landscape change at three locations on Hadrian's Wall, namely Beckfoot Roman Fort, Birdoswald Roman Fort and Corbridge Roman Station, all once part of the Roman Empire's north-west frontier. The main aim of the case study is to integrate heterogeneous information derived from a range of sources to help inform understanding of temporal aspects of landscape change. In particular, the study sites are at risk from natural hazards, notably erosion and flooding. The paper focuses on data collection and collation aspects, including an extensive archive search and field survey, as well as the methodology and preliminary data processing.

‘Cultural heritage is the lasting remains of our cultural tradition … a representation of our history and our identity; our affiliation to the past, to our present, and the future for the next gene...