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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) 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 in three views given their intrinsic parameters and encodes the relative pose of the cameras up to global scale, totalling 11 independent elements or degrees of freedom. The reduced degrees of freedom allow for fewer correspondences to fit the model, at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Vision
Computer vision is an 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 acquiring, processing, 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 scientific discipline of computer vision is concerned with the theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics (stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics (electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), general relativity ( stress–energy tensor, cur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa. Properties meaningful for projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix and translations (the affine transformations). The first issue for geometers is what kind of geometry is adequate for a novel situation. It is not possible to refer to angles in projective geometry as it is in Euclidean geometry, because angle is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pose (computer Vision)
In the fields of computing and computer vision, pose (or spatial pose) represents the position and orientation of an object, usually in three dimensions. Poses are often stored internally as transformation matrices. The term “pose” is largely synonymous with the term “transform”, but a transform may often include scale, whereas pose does not. In computer vision, the pose of an object is often estimated from camera input by the process of ''pose estimation''. This information can then be used, for example, to allow a robot to manipulate an object or to avoid moving into the object based on its perceived position and orientation in the environment. Pose estimation The specific task of determining the pose of an object in an image (or stereo images, image sequence) is referred to as ''pose estimation''. The pose estimation problem can be solved in different ways depending on the image sensor configuration, and choice of methodology. Three classes of methodologies can be di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 defines ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Camera Matrix
In computer vision a camera matrix or (camera) projection matrix is a 3 \times 4 matrix which describes the mapping of a pinhole camera from 3D points in the world to 2D points in an image. Let \mathbf be a representation of a 3D point in homogeneous coordinates (a 4-dimensional vector), and let \mathbf be a representation of the image of this point in the pinhole camera (a 3-dimensional vector). Then the following relation holds : \mathbf \sim \mathbf \, \mathbf where \mathbf is the camera matrix and the \, \sim sign implies that the left and right hand sides are equal except for a multiplication by a non-zero scalar k \neq 0: : \mathbf = k \, \mathbf \, \mathbf . Since the camera matrix \mathbf is involved in the mapping between elements of two projective spaces, it too can be regarded as a projective element. This means that it has only 11 degrees of freedom since any multiplication by a non-zero scalar results in an equivalent camera matrix. Derivation Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross Product
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product). If two vectors have the same direction or have the exact opposite direction from each other (that is, they are ''not'' linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendic ... [...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 ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java (programming Language)
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers ''write once, run anywhere'' ( WORA), meaning that compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are typically compiled to bytecode that can run on any Java virtual machine (JVM) regardless of the underlying computer architecture. The syntax of Java is similar to C and C++, but has fewer low-level facilities than either of them. The Java runtime provides dynamic capabilities (such as reflection and runtime code modification) that are typically not available in traditional compiled languages. , Java was one of the most popular programming languages in use according to GitHub, particularly for client–server web applications, with a reported 9 million developers. Java was originally developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry In Computer Vision
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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