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Fundamental Matrix (computer Vision)
In computer vision, the fundamental matrix \mathbf is a 3×3 matrix which relates corresponding points in stereo images. In epipolar geometry, with homogeneous image coordinates, x and x′, of corresponding points in a stereo image pair, Fx describes a line (an epipolar line) on which the corresponding point x′ on the other image must lie. That means, for all pairs of corresponding points holds : \mathbf'^ \mathbf = 0. Being of rank two and determined only up to scale, the fundamental matrix can be estimated given at least seven point correspondences. Its seven parameters represent the only geometric information about cameras that can be obtained through point correspondences alone. The term "fundamental matrix" was coined by QT Luong in his influential PhD thesis. It is sometimes also referred to as the "bifocal tensor". As a tensor it is a two-point tensor in that it is a bilinear form relating points in distinct coordinate systems. The above relation which defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epipolar Geometry
Epipolar geometry is the geometry of stereo vision. When two cameras view a 3D scene from two distinct positions, there are a number of geometric relations between the 3D points and their projections onto the 2D images that lead to constraints between the image points. These relations are derived based on the assumption that the cameras can be approximated by the pinhole camera model. Definitions The figure below depicts two pinhole cameras looking at point X. In real cameras, the image plane is actually behind the focal center, and produces an image that is symmetric about the focal center of the lens. Here, however, the problem is simplified by placing a ''virtual image plane'' in front of the focal center i.e. optical center of each camera lens to produce an image not transformed by the symmetry. OL and OR represent the centers of symmetry of the two cameras lenses. X represents the point of interest in both cameras. Points xL and xR are the projections of point X onto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epipolar Line
Epipolar geometry is the geometry of stereo vision. When two cameras view a 3D scene from two distinct positions, there are a number of geometric relations between the 3D points and their projections onto the 2D images that lead to constraints between the image points. These relations are derived based on the assumption that the cameras can be approximated by the pinhole camera model. Definitions The figure below depicts two pinhole cameras looking at point X. In real cameras, the image plane is actually behind the focal center, and produces an image that is symmetric about the focal center of the lens. Here, however, the problem is simplified by placing a ''virtual image plane'' in front of the focal center i.e. optical center of each camera lens to produce an image not transformed by the symmetry. OL and OR represent the centers of symmetry of the two cameras lenses. X represents the point of interest in both cameras. Points xL and xR are the projections of point X onto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epipolar Geometry
Epipolar geometry is the geometry of stereo vision. When two cameras view a 3D scene from two distinct positions, there are a number of geometric relations between the 3D points and their projections onto the 2D images that lead to constraints between the image points. These relations are derived based on the assumption that the cameras can be approximated by the pinhole camera model. Definitions The figure below depicts two pinhole cameras looking at point X. In real cameras, the image plane is actually behind the focal center, and produces an image that is symmetric about the focal center of the lens. Here, however, the problem is simplified by placing a ''virtual image plane'' in front of the focal center i.e. optical center of each camera lens to produce an image not transformed by the symmetry. OL and OR represent the centers of symmetry of the two cameras lenses. X represents the point of interest in both cameras. Points xL and xR are the projections of point X onto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Vision
Computer vision is an Interdisciplinarity, interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to understand and automate tasks that the human visual system can do. Computer vision tasks include methods for image sensor, acquiring, Image processing, processing, Image analysis, analyzing and understanding digital images, and extraction of high-dimensional data from the real world in order to produce numerical or symbolic information, e.g. in the forms of decisions. Understanding in this context means the transformation of visual images (the input of the retina) into descriptions of the world that make sense to thought processes and can elicit appropriate action. This image understanding can be seen as the disentangling of symbolic information from image data using models constructed with the aid of geometry, physics, statistics, and learning theory. The scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pushbroom Sensor
A push broom scanner, also known as an along-track scanner, is a device for obtaining images with spectroscopic sensors. The scanners are regularly used for passive remote sensing from space, and in spectral analysis on production lines, for example with near-infrared spectroscopy used to identify contaminated food and feed. The moving scanner line in a traditional photocopier (or a scanner or facsimile machine) is also a familiar, everyday example of a push broom scanner. Push broom scanners and the whisk broom scanners variant (also known as across-track scanners) are often contrasted with staring arrays (such as in a digital camera), which image objects without scanning, and are more familiar to most people. In orbital push broom sensors, a line of sensors arranged perpendicular to the flight direction of the spacecraft is used. Different areas of the surface are imaged as the spacecraft flies forward. A push broom scanner can gather more light than a whisk broom scanner becau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
INRIA
The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name ''Institut de recherche en informatique et en automatique'' (IRIA) in 1967 at Rocquencourt near Paris, part of Plan Calcul. Its first site was the historical premises of SHAPE (central command of NATO military forces), which is still used as Inria's main headquarters. In 1980, IRIA became INRIA. Since 2011, it has been styled ''Inria''. Inria is a Public Scientific and Technical Research Establishment (EPST) under the double supervision of the French Ministry of National Education, Advanced Instruction and Research and the Ministry of Economy, Finance and Industry. Administrative status Inria has 9 research centers distributed across France (in Bordeaux, Grenoble-Inovallée, Lille, Lyon, Nancy, Paris- Rocquencourt, Rennes, Saclay, and Sophia Antipolis) and one center ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levenberg–Marquardt Algorithm
In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting. The LMA interpolates between the Gauss–Newton algorithm (GNA) and the method of gradient descent. The LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be slower than the GNA. LMA can also be viewed as Gauss–Newton using a trust region approach. The algorithm was first published in 1944 by Kenneth Levenberg, while working at the Frankford Army Arsenal. It was rediscovered in 1963 by Donald Marquardt, who worked as a statistician at DuPont, and independently by Girard, Wynne and Morrison. The LMA is used in many software applications for solvin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Statistics
Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution. For example, robust methods work well for mixtures of two normal distributions with different standard deviations; under this model, non-robust methods like a t-test work poorly. Introduction Robust statistics seek to provide methods that emulate popular statistical methods, but which are not unduly affected by outliers or other small departures from model assumptions. In statistics, classical estimation methods rely heavily on assumptions which are often not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marc Pollefeys
Marc Pollefeys from the ETH Zurich, Zurich, Switzerland was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2012 ''for contributions to three-dimensional computer vision''. He was named to the 2022 class of ACM Fellow ACM or A.C.M. may refer to: Aviation * AGM-129 ACM, 1990–2012 USAF cruise missile * Air chief marshal * Air combat manoeuvring or dogfighting * Air cycle machine * Arica Airport (Colombia) (IATA: ACM), in Arica, Amazonas, Colombia Computing ...s, "for contributions to geometric computer vision and applications to AR/VR/MR, robotics, and autonomous vehicles". References External links ETH Zurich Bio Fellow Members of the IEEE Fellows of the Association for Computing Machinery Living people Year of birth missing (living people) Place of birth missing (living people) Academic staff of ETH Zurich {{Switzerland-engineer-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eight-point Algorithm
The eight-point algorithm is an algorithm used in computer vision to estimate the essential matrix or the fundamental matrix related to a stereo camera pair from a set of corresponding image points. It was introduced by Christopher Longuet-Higgins in 1981 for the case of the essential matrix. In theory, this algorithm can be used also for the fundamental matrix, but in practice the normalized eight-point algorithm, described by Richard Hartley in 1997, is better suited for this case. The algorithm's name derives from the fact that it estimates the essential matrix or the fundamental matrix from a set of eight (or more) corresponding image points. However, variations of the algorithm can be used for fewer than eight points. Coplanarity constraint One may express the epipolar geometry of two cameras and a point in space with an algebraic equation. Observe that, no matter where the point P is in space, the vectors \overline, \overline and \overline belong to the same plane ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trifocal Tensor
In computer vision, the trifocal tensor (also tritensor) is a 3×3×3 array of numbers (i.e., a tensor) that incorporates all projective geometric relationships among three views. It relates the coordinates of corresponding points or lines in three views, being independent of the scene structure and depending only on the relative motion (i.e., pose Human positions refer to the different physical configurations that the human body can take. There are several synonyms that refer to human positioning, often used interchangeably, but having specific nuances of meaning. *''Position'' is a gen ...) among the three views and their intrinsic calibration parameters. Hence, the trifocal tensor can be considered as the generalization of the fundamental matrix in three views. It is noted that despite the tensor being made up of 27 elements, only 18 of them are actually independent. There is also a so-called calibrated trifocal tensor, which relates the coordinates of points and lines i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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