Related papers: Stereoscopic visualization in curved spacetime: se…
Photons emitted by light sources in the neighbourhood of a black hole can wind several times around it before fleeing towards the observer. For spherically symmetric black holes, two infinite sequences of images are created for any given…
Stereoscopic projection mapping (PM) allows a user to see a three-dimensional (3D) computer-generated (CG) object floating over physical surfaces of arbitrary shapes around us using projected imagery. However, the current stereoscopic PM…
Monocular and stereo visions are cost-effective solutions for 3D human localization in the context of self-driving cars or social robots. However, they are usually developed independently and have their respective strengths and limitations.…
This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build…
Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…
The use of time--like geodesics to measure temporal distances is better justified than the use of space--like geodesics for a measurement of spatial distances. We give examples where a ''spatial distance'' cannot be appropriately determined…
We proposed viewpoint-tolerant shared depth perception without individual tracking by leveraging human cognitive compensation in universally 3D rendered images on a wall-sized display. While traditional 3D perception-enabled display systems…
The concept of time-space defined in an earlier paper of the author is a certain generalization of the so-called space-time. In this paper we introduce the concept of time-space manifolds. In the homogeneous case, a time-space manifold is a…
I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE…
Despite the popularisation of machine learning models, more often than not, they still operate as black boxes with no insight into what is happening inside the model. There exist a few methods that allow to visualise and explain why a model…
The method of maximum entropy is used to model curved physical space in terms of points defined with a finite resolution. Such a blurred space is automatically endowed with a metric given by information geometry. The corresponding…
Fine holes are an important structural component of industrial components, and their inner surface quality is closely related to their function.In order to detect the quality of the inner surface of the fine hole,a special optical…
We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of…
Depth estimation is a critical topic for robotics and vision-related tasks. In monocular depth estimation, in comparison with supervised learning that requires expensive ground truth labeling, self-supervised methods possess great potential…
We consider the problem of determination of a volume of some bounded space-like hypersurfaces in the case of spherically symmetric spacetimes. In the case when the hypersurfaces is cut or bounded by a light-like hypersurface the problem may…
The visual distortion effects visible to an observer traveling around and descending to the surface of an extremely compact star are described. Specifically, trips to a ``normal" neutron star, a black hole, and an ultracompact neutron star…
We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…
The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric…
We consider the standard relativistic geometrically thin and optically thick accretion disc around a distorted static black hole and a distorted naked singularity. The distortion is the result of the existence of a static axisymmetric…
Virtual-reality simulations of curved space are most effective and most fun when presented as a game (for example, curved-space billiards), so the user not only has something to see in the curved space, but also has something fun to do…