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Recent work on the intrinsic image of humans starts to consider the visibility of incident illumination and encodes the light transfer function by spherical harmonics. In this paper, we show that such a light transfer function can be…
We present a novel approach of modelling surface light scattering in the context of freeform optical design. The model relies on energy conservation and optimal transport theory. For isotropic scattering in cylindrically or rotationally…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
Intraoperative shape reconstruction of organs from endoscopic camera images is a complex yet indispensable technique for image-guided surgery. To address the uncertainty in reconstructing entire shapes from single-viewpoint occluded images,…
Purpose: Visual 3D scene reconstruction can support colonoscopy navigation. It can help in recognising which portions of the colon have been visualised and characterising the size and shape of polyps. This is still a very challenging…
The displacement of star images by atmospheric refraction observed by an Earth-bound telescope is dominated by a familiar term proportional to the product of the tangent of the zenith angle by the refractivity at the ground. The manuscript…
Reconstructing soft tissues from stereo endoscope videos is an essential prerequisite for many medical applications. Previous methods struggle to produce high-quality geometry and appearance due to their inadequate representations of 3D…
It is common in Physiological Optics to fit the corneal and the lens surfaces to conic-based surfaces (usually ellipse-based surfaces), obtaining their characteristic radius of curvature and asphericity. Here we show that the variation in…
Many modern imaging and remote sensing applications require reconstructing a function from spherical averages (mean values). Examples include photoacoustic tomography, ultrasound imaging or SONAR. Several formulas of the back-projection…
The most common problem in data reconstruction is to fit a function based on the observations of some sample (guiding) points. This paper provides a methodological point of view of digital-discrete surface reconstruction. We explain our…
In this paper, we study the problem of reproducing the world lighting from a single image of an object covered with random specular microfacets on the surface. We show that such reflectors can be interpreted as a randomized mapping from the…
We consider tessellations of the Euclidean $(d-1)$-sphere by $(d-2)$-dimensional great subspheres or, equivalently, tessellations of Euclidean $d$-space by hyperplanes through the origin; these we call conical tessellations. For random…
In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…
In Euclidean space, we investigate surfaces whose mean curvature $H$ satisfies the equation $H=\alpha\langle N,\mathbf{x}\rangle+\lambda$, where $N$ is the Gauss map, $\mathbf{x}$ is the position vector and $\alpha$ and $\lambda$ are two…
Cervical cancer is a malignant tumor that seriously threatens women's health, and is one of the most common that affects women worldwide. For its early detection, colposcopic images of the cervix are used for searching for possible injuries…
In our recent works we have used meromorphic differentials on Riemann surfaces all of whose periods are real to study the geometry of the moduli spaces of Riemann surfaces. In this paper we survey the relevant constructions and show how…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface…
Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…
We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…