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Pinhole Camera Model
The pinhole camera model describes the mathematical relationship between the coordinates of a point in three-dimensional space and its projection onto the image plane of an ''ideal'' pinhole camera, where the camera aperture is described as a point and no lenses are used to focus light. The model does not include, for example, geometric distortions or blurring of unfocused objects caused by lenses and finite sized apertures. It also does not take into account that most practical cameras have only discrete image coordinates. This means that the pinhole camera model can only be used as a first order approximation of the mapping from a 3D scene to a 2D image. Its validity depends on the quality of the camera and, in general, decreases from the center of the image to the edges as lens distortion effects increase. Some of the effects that the pinhole camera model does not take into account can be compensated, for example by applying suitable coordinate transformations on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Similar Triangles
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other. For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other. This is because two ellipses can have different width to height ratios, two rectangles can have different length to breadth ratios, and two i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectilinear Lens
In photography, a rectilinear lens is a photographic lens that yields images where straight features, such as the edges of walls of buildings, appear with straight lines, as opposed to being curved. In other words, it is a lens with little or no barrel or pincushion distortion. At particularly wide angles, however, the rectilinear perspective will cause objects to appear increasingly stretched and enlarged as they near the edge of the frame. These types of lenses are often used to create forced perspective effects. The most famous example is the Rapid Rectilinear Lens developed by John Henry Dallmeyer in 1866. It allowed distortionless photos to be taken quickly for the first time, and was a standard lens design for 60 years. As of 2020, the Laowa 9mm f/5.6 lens is the world's widest rectilinear lens for full frame cameras. The vast majority of video and still cameras use lenses that produce nearly rectilinear images. A popular alternative type of lens is a fisheye lens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pinhole Camera
A pinhole camera is a simple camera without a lens but with a tiny aperture (the so-called ''Pinhole (optics), pinhole'')—effectively a light-proof box with a small hole in one side. Light from a scene passes through the aperture and projects an inverted image on the opposite side of the box, which is known as the camera obscura effect. The size of the images depends on the distance between the object and the pinhole. A Worldwide Pinhole Photography Day is observed on the last Sunday of April, every year. History Camera obscura The camera obscura or pinhole image is a natural optical phenomenon. Early known descriptions are found in the Chinese Mozi (book), Mozi writings (circa 500 BCE) and the Aristotelian ''Problems (Aristotle), Problems'' (circa 300 BCE – 600 CE). Ibn al-Haytham (965–1039), an Physics in the medieval Islamic world, Arab physicist also known as Alhazen, described the camera obscura effect. Over the centuries others started to experiment with it, main ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ibn Al-Haytham
Ḥasan Ibn al-Haytham (Latinization of names, Latinized as Alhazen; ; full name ; ) was a medieval Mathematics in medieval Islam, mathematician, Astronomy in the medieval Islamic world, astronomer, and Physics in the medieval Islamic world, physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the principal Arab mathematicians and, without any doubt, the best physicist.") , ("Ibn al-Ḥaytam was an eminent eleventh-century Arab optician, geometer, arithmetician, algebraist, astronomer, and engineer."), ("Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics.") Referred to as "the father of modern optics", he made significant contributions to the principles of optics and visual perception in particular. His most influential work is titled ''Book of Optics, Kit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exit Pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only ray (optics), rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a optical telescope, telescope or compound microscope, this image is the image of the Objective (optics), objective element(s) as produced by the eyepiece. The size and shape of this disc is crucial to the instrument's performance, because the observer's eye can see light only if it passes through the aperture. The term ''exit pupil'' is also sometimes used to refer to the diameter of the virtual aperture. Older literature on optics sometimes refers to the exit pupil as the ''Ramsden disc'', named after English instrument-maker Jesse Ramsden. Visual instruments To use an optical instrument, the entrance pupil of the viewer's eye (the image of the pupil, anatomical pupil as seen through the cornea) must be aligned with and be of similar size to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entrance Pupil
In an optical system, the entrance pupil is the optical image of the physical aperture stop, as 'seen' through the optical elements in front of the stop. The corresponding image of the aperture stop as seen through the optical elements behind it is called the ''exit pupil''. The entrance pupil defines the cone of rays that can enter and pass through the optical system. Rays that fall outside of the entrance pupil will not pass through the system. If there is no lens in front of the aperture (as in a pinhole camera), the entrance pupil's location and size are identical to those of the aperture. Optical elements in front of the aperture will produce a magnified or diminished image of the aperture that is displaced from the aperture location. The entrance pupil is usually a virtual image: it lies behind the first optical surface of the system. The entrance pupil is a useful concept for determining the size of the cone of rays that an optical system will accept. Once the size ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collinearity Equation
The collinearity equations are a set of two equations, used in photogrammetry and computer stereo vision, to relate coordinates in a sensor plane (in two dimensions) to object coordinates (in three dimensions). The equations originate from the Projection (mathematics), central projection of a point of the 3D modeling, object through the Cardinal point (optics)#Principal planes and points, optical centre of the pinhole camera, camera to the image on the sensor plane. Definition Let x, y, and z refer to a coordinate system with the x- and y-axis in the sensor plane. Denote the coordinates of the point P on the object by x_P,y_P,z_P, the coordinates of the image point of P on the sensor plane by ''x'' and ''y'' and the coordinates of the projection (optical) centre by x_0,y_0,z_0. As a consequence of the projection method there is the same fixed ratio \lambda between x-x_0 and x_0-x_P, y-y_0 and y_0-y_P, and the distance of the projection centre to the sensor plane z_0=c and z ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Camera Resectioning
Camera resectioning is the process of estimating the parameters of a pinhole camera model approximating the camera that produced a given photograph or video; it determines which incoming light ray is associated with each pixel on the resulting image. Basically, the process determines the pose of the pinhole camera. Usually, the camera parameters are represented in a 3 × 4 projection matrix called the '' camera matrix''. The extrinsic parameters define the camera '' pose'' (position and orientation) while the intrinsic parameters specify the camera image format (focal length, pixel size, and image origin). This process is often called geometric camera calibration or simply camera calibration, although that term may also refer to photometric camera calibration or be restricted for the estimation of the intrinsic parameters only. Exterior orientation and interior orientation refer to the determination of only the extrinsic and intrinsic parameters, respectively. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Space
In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines. This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, ''point'' and ''line'' are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Camera Matrix
In computer vision 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 ... a camera matrix or (camera) projection matrix is a 3 \times 4 matrix (mathematics), 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 Modulo (mathematics), except for a multiplication by a non-zero scalar k \neq 0: : \mathbf = k \, \mathbf \, \mathbf . Since th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Coordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work , are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix. They are also used in fundamental elliptic curve cryptography algorithms. If homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point. Since homogeneous coordinates are also given to points at infini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
