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The Peirce quincuncial projection is a mapping of the surface of a sphere to the interior of a square. It is a conformal map except for four points on the equator. These points of non-conformality cause significant artifacts in photographic…
We propose a novel iterative method for optimally placing and orienting multiple cameras in a 3D scene. Sample applications include improving the accuracy of 3D reconstruction, maximizing the covered area for surveillance, or improving the…
In this work, we address the problem of refining the geometry of local image features from multiple views without known scene or camera geometry. Current approaches to local feature detection are inherently limited in their keypoint…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
Two-view triangulation is a problem of minimizing a quadratic polynomial under an equality constraint. We derive a polynomial that encodes the local minimizers of this problem using the theory of Lagrange multipliers. This offers a simpler…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
Pairwise translation directions are a key input to camera location estimation in global structure-from-motion. Existing estimators usually process each image pair independently, producing directions that may be locally plausible but…
In this paper, we introduce a moving object detection algorithm for fisheye cameras used in autonomous driving. We reformulate the three commonly used constraints in rectilinear images (epipolar, positive depth and positive height…
We consider the problem of direction finding using partly calibrated arrays, a distributed subarray with position errors between subarrays. The key challenge is to enhance angular resolution in the presence of position errors. To achieve…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
We address the problem of projecting a point onto a quadratic hypersurface, more specifically a central quadric. We show how this problem reduces to finding a given root of a scalar-valued nonlinear function. We completely characterize one…
Camera calibration is a crucial prerequisite in many applications of computer vision. In this paper, a new, geometry-based camera calibration technique is proposed, which resolves two main issues associated with the widely used Zhang's…
In this paper we present a visual servoing approach to the problem of object grasping and more generally, to the problem of aligning an end-effector with an object. First we extend the method proposed by Espiau et al. [1] to the case of a…
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…
3D human pose estimation has been a long-standing challenge in computer vision and graphics, where multi-view methods have significantly progressed but are limited by the tedious calibration processes. Existing multi-view methods are…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
We present a novel data set made up of omnidirectional video of multiple objects whose centroid positions are annotated automatically. Omnidirectional vision is an active field of research focused on the use of spherical imagery in video…
The structured light projection technique is a representative active method for 3-D reconstruction, but many researchers face challenges with the intricate projector calibration process. To address this complexity, we employs an additional…