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Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
Criticality in graviational microlensing is an everyday issue because that is what generates microlensing signals which may be of photon-challenged compact objects such as black holes or planetary systems ET calls home. The criticality of…
In this paper, we introduce a novel approach to fine-grained cross-view geo-localization. Our method aligns a warped ground image with a corresponding GPS-tagged satellite image covering the same area using homography estimation. We first…
Several central problems in quantum information theory (such as measurement compatibility and quantum steering) can be rephrased as membership in the minimal matrix convex set corresponding to special polytopes (such as the hypercube or its…
We introduce new linear mathematical formulations to calculate the focal length of a camera in an active platform. Through mathematical derivations, we show that the focal lengths in each direction can be estimated using only one point…
In this work, we present a camera geopositioning system based on matching a query image against a database with panoramic images. For matching, our system uses memory vectors aggregated from global image descriptors based on convolutional…
We describe a special case of structure from motion where the camera rotates on a sphere. The camera's optical axis lies perpendicular to the sphere's surface. In this case, the camera's pose is minimally represented by three rotation…
Automatic calibration of multi-camera systems, namely the accurate estimation of spatial extrinsic parameters, is fundamental for 3D reconstruction, panoramic perception, and multi-view data fusion. Existing methods typically rely on…
We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…
The familiar tools of Fourier analysis and Fisher matrices are applied to derive the uncertainties on photometric, astrometric, and weak-lensing measurements of stars and galaxies in real astronomical images. Many effects or functions that…
Deep approaches to predict monocular depth and ego-motion have grown in recent years due to their ability to produce dense depth from monocular images. The main idea behind them is to optimize the photometric consistency over image…
Most well-established and widely used color difference (CD) metrics are handcrafted and subject-calibrated against uniformly colored patches, which do not generalize well to photographic images characterized by natural scene complexities.…
We consider the classical camera pose estimation problem that arises in many computer vision applications, in which we are given n 2D-3D correspondences between points in the scene and points in the camera image (some of which are incorrect…
A fundamental question in computer vision is whether a set of point pairs is the image of a scene that lies in front of two cameras. Such a scene and the cameras together are known as a chiral reconstruction of the point pairs. In this…
Camera calibration is an essential process in photogrammetry, serving as a crucial link between the 2D image coordinate system and the 3D world coordinate system. However, when observations are conducted through refractive interfaces, the…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
Given a finite family of compact subsets of the complex plane we propose a certificate of mutual non-overlapping with respect to area measure. The criterion is stated as a couple of positivity conditions imposed on a four argument…
This paper proposes a novel algorithm of discovering the structure of a kaleidoscopic imaging system that consists of multiple planar mirrors and a camera. The kaleidoscopic imaging system can be recognized as the virtual multi-camera…
We prove that the algebraic set of pairs of matrices with a diagonal commutator over a field of positive prime characteristic, its irreducible components, and their intersection are $F$-pure when the size of matrices is equal to 3.…
We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate…