Related papers: Ambiguities in a Problem in Planar Geodesy
Recent theoretical developments in astronomical aperture synthesis have revealed the existence of integer-ambiguity problems. Those problems, which appear in the self-calibration procedures of radio imaging, have been shown to be similar to…
Uncertainty relations for light pulses found in [Phys. Rev. A {\bf 86}, 022118 (2012)] were derived in the three-dimensional case which emphasized the localization in a volume. Here we derive the uncertainty relation for light beams in the…
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
6D object pose estimation aims to infer the relative pose between the object and the camera using a single image or multiple images. Most works have focused on predicting the object pose without associated uncertainty under occlusion and…
We consider the problem of classification of points sampled from an unknown probability measure on a Euclidean space. We study the question of querying the class label at a very small number of judiciously chosen points so as to be able to…
A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation…
There are several remarkable points, defined for polygons and multisets of points in the plane, called centers (such as the centroid). To make possible their study, there exists a formal definition for the concept of center in both cases.…
The author proposes a new geometry in this book. The author named this new geometry Intercenter Geometry. Intercenter Geometry is different from traditional Euclidean geometry and analytic geometry (coordinate geometry). The idea of…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
This paper studies the problem of identifying directions of axial symmetry in multivariate distributions. Theoretical results are derived on how the measure or cardinality of the set of symmetry directions relates to spherical symmetry. The…
Under study is the new class of geometrical extremal problems in which it is required to achieve the best result in the presence of conflicting goals; e.g., given the surface area of a convex body $\mathfrak x$, we try to maximize the…
We analyze the complexity of fitting a variety, coming from a class of varieties, to a configuration of points in $\Bbb C^n$. The complexity measure, called the algebraic complexity, computes the Euclidean Distance Degree (EDdegree) of a…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
Choose a polynomial in three variables with not more than three or four monomials of moderate degree. Take simple coefficients as 1 and -1. Then draw a picture of the solution variety in real three space using a ray-tracing program like…
A point visibility graph is a graph induced by a set of points in the plane, where every vertex corresponds to a point, and two vertices are adjacent whenever the two corresponding points are visible from each other, that is, the open…
A radial probability measure is a probability measure with a density (with respect to the Lebesgue measure) which depends only on the distances to the origin. Consider the Euclidean space enhanced with a radial probability measure. A…
It is a fact of our existence, that no matter where we are, we most often find ourselves either hearing, seeing, talking, or even engaged in design related activities. Despite this reality, the notion of 'design', and in particular…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
This article evaluates how creative uses of machine learning can address three adjacent terms: ambiguity, uncertainty and indeterminacy. Through the progression of these concepts it reflects on increasing ambitions for machine learning as a…
We prove explicit bounds on the number of lattice points on or near a convex curve in terms of geometric invariants such as length, curvature, and affine arclength. In several of our results we obtain the best possible constants. Our…