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We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
We develop an algorithm capable of imaging a three-dimensional object given a collection of two-dimensional images of that object that are significantly influenced by the curvature of the Ewald sphere. These two-dimensional images cannot be…
We present an inverse method for designing a three-dimensional imaging system comprising of freeform optical surfaces. We impose an imaging condition on the optical map and combine it with the law of conservation of energy to conclude that…
Data visualizations summarize high-dimensional distributions in two or three dimensions. Dimensionality reduction entails a loss of information, and what is preserved differs between methods. Existing methods preserve the local or the…
This paper is aimed at presenting a systematic survey of the existing now different formulations for the problem of projection of the origin of the Euclidean space onto the convex polyhedron (PPOCP). In the present paper, there are…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
Steganography is the task of concealing a message within a medium such that the presence of the hidden message cannot be detected. Beyond the standard scope of private-key steganography, steganography is also potentially interesting from…
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
The Cartesian coordinate system is the most commonly used system in computer visualization. This is due to its ease of use and processing speed. However, it is not always suitable for a given problem. Angular measures often allow us to…
Using spherical mirrors in place of wide-angle cameras allows for cost-effective monitoring of manufacturing processes in hazardous environment, where a camera would normally not operate. This includes environments of high heat, vacuum and…
Directionality in a holographic screen may be useful for projecting images to be seen in complete horizontal parallax. The continuous sequence of views from an object may be transferred from the object and enlarged at the screen giving the…
We present some properties of a Cauchy family of distributions on the sphere, which is a spherical extension of the wrapped Cauchy family on the circle. The spherical Cauchy family is closed under the M\"obius transformation on the sphere…
In this work we study the identification of spatial correlation in distributions of 2D scalar fields, presented across different forms of visual displays. We study simple visual displays that directly show color-mapped scalar fields, namely…
This paper investigates several distinct attempts to generalize in higher dimension the standard 2-dimensional phyllotaxy set construction. We first recall known contructions for these sets on $2D$ manifolds of constant curvature (the…
Mirror adapters can match a camera and a projector to the task of producing and visualizing a stereo pair. The imaging digital technology can benefit on the traditional optical technology of the last century to get more compact and…
Inferring the 3D shape of an object from an RGB image has shown impressive results, however, existing methods rely primarily on recognizing the most similar 3D model from the training set to solve the problem. These methods suffer from poor…
Projections are constructed in the rotation algebra that are orthogonal to their Fourier transform and which are fixed under the flip automorphism. Such projections are expected in a construction of an inductive limit structure for the…
We introduce TetSphere Splatting, a Lagrangian geometry representation designed for high-quality 3D shape modeling. TetSphere splatting leverages an underused yet powerful geometric primitive -- volumetric tetrahedral meshes. It represents…
3D reconstruction plays an increasingly important role in modern photogrammetric systems. Conventional satellite or aerial-based remote sensing (RS) platforms can provide the necessary data sources for the 3D reconstruction of large-scale…
This paper develops the theory behind the bispectrum, a concept that is well established in statistical signal processing but not, until recently, extended to computer vision as a source of frequency-domain invariants. Recent papers on…