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Homographies -- a mathematical formalism for relating image points across different camera viewpoints -- are at the foundations of geometric methods in computer vision and are used in geometric camera calibration, image registration, and…

A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…

Relative pose estimation using point correspondences (PC) is a widely used technique. A minimal configuration of six PCs is required for two views of generalized cameras. In this paper, we present several minimal solvers that use six PCs to…

The problem of self-calibration of two cameras from a given fundamental matrix is one of the basic problems in geometric computer vision. Under the assumption of known principal points and square pixels, the well-known Bougnoux formula…

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…

Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…

Many robotics and mapping systems contain multiple sensors to perceive the environment. Extrinsic parameter calibration, the identification of the position and rotation transform between the frames of the different sensors, is critical to…

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…

Let $\Pi$ be a polar space of type $\textsf{D}_{n}$. Denote by ${\mathcal G}_{\delta}(\Pi)$, $\delta\in \{+,-\}$ the associated half-spin Grassmannians and write $\Gamma_{\delta}(\Pi)$ for the corresponding half-spin Grassmann graphs. In…

The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…

Several Scientific and engineering applications require merging of sampled images for complex perception development. In most cases, for such requirements, images are merged at intensity level. Even though it gives fairly good perception of…

Offline camera calibration techniques typically employ parametric or generic camera models. Selecting parametric models relies heavily on user experience, and an inappropriate camera model can significantly affect calibration accuracy.…

We give an explicit construction of any simply-connected superconformal surface $\phi\colon M^2\to \R^4$ in Euclidean space in terms of a pair of conjugate minimal surfaces $g,h\colon M^2\to\R^4$. That $\phi$ is superconformal means that…

Spectral embedding provides a framework for solving perceptual organization problems, including image segmentation and figure/ground organization. From an affinity matrix describing pairwise relationships between pixels, it clusters pixels…

Camera calibration is a process of paramount importance in computer vision applications that require accurate quantitative measurements. The popular method developed by Zhang relies on the use of a large number of images of a planar grid of…

We address the problem of optical decalibration in mobile stereo camera setups, especially in context of autonomous vehicles. In real world conditions, an optical system is subject to various sources of anticipated and unanticipated…

Template matching is a fundamental task in computer vision and has been studied for decades. It plays an essential role in manufacturing industry for estimating the poses of different parts, facilitating downstream tasks such as robotic…

Many underwater applications rely on vision sensors and require proper camera calibration, i.e. knowing the incoming light ray for each pixel in the image. While for the ideal pinhole camera model all viewing rays intersect in a single 3D…

Camera calibration is a first and fundamental step in various computer vision applications. Despite being an active field of research, Zhang's method remains widely used for camera calibration due to its implementation in popular toolboxes.…

To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…