Related papers: Catenary and Mercator projection
In this paper we observe that information theoretical concepts are valuable tools for extracting information from images and, in particular, information on image symmetries. It is shown that the problem of detecting reflectional and…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
When light travels through scattering media, speckles (spatially random distribution of fluctuated intensities) are formed due to the interference of light travelling along different optical paths, preventing the perception of structure,…
This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general instances, the boundary of the image is given by two highly…
Light field cameras can capture both spatial and angular information of light rays, enabling 3D reconstruction by a single exposure. The geometry of 3D reconstruction is affected by intrinsic parameters of a light field camera…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
We show that many topological and geometrical properties of complex projective space can be understood just by looking at a suitably constructed picture. The idea is to view CP^n as a set of flat tori parametrized by the positive octant of…
Wavefront shaping is a powerful technique that can be used to focus light through scattering media, which can be important for imaging through scattering samples such as tissue. The method is based on the assumption that the field at the…
We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and…
We develop an inversion technique of annual scattered light curves to sketch a two-dimensional albedo map of exoplanets in face-on orbits. As a test-bed for future observations of extrasolar terrestrial planets, we apply this mapping…
This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
This paper quantifies an error source that limits the accuracy of lidar scan matching, particularly for voxel-based methods. Lidar scan matching, which is used in dead reckoning (also known as lidar odometry) and mapping, computes the…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Projection Mapping (PM) is a technology that projects images onto the surfaces of physical objects, allowing multiple users to share an augmented reality experience without special devices. However, its practical use has been constrained by…
Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove…
Magic windows (or mirrors) consist of optical devices with a surface deformation or thickness distribution devised in such a way to form a desired image. The associated image intensity distribution has been shown to be related to the…
Matrix scaling is a classical problem with a wide range of applications. It is known that the Sinkhorn algorithm for matrix scaling is interpreted as alternating e-projections from the viewpoint of classical information geometry. Recently,…
Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…
A rectangulation is a tiling of a rectangle by a finite number of rectangles. The rectangulation is called generic if no four of its rectangles share a single corner. We initiate the enumeration of generic rectangulations up to…