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Log-polar Coordinates
In mathematics, log-polar coordinates (or logarithmic polar coordinates) is a coordinate system in two dimensions, where a point is identified by two numbers, one for the logarithm of the distance to a certain point, and one for an angle. Log-polar coordinates are closely connected to polar coordinates, which are usually used to describe domains in the plane with some sort of rotational symmetry. In areas like Harmonic analysis, harmonic and complex analysis, the log-polar coordinates are more canonical than polar coordinates. Definition and coordinate transformations ''Log-polar coordinates'' in the plane consist of a pair of real numbers (ρ,θ), where ρ is the logarithm of the distance between a given point and the origin (mathematics), origin and θ is the angle between a line of reference (the ''x''-axis) and the line through the origin and the point. The angular coordinate is the same as for polar coordinates, while the radial coordinate is transformed according to the rule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Retinotopy
Retinotopy () is the mapping of visual input from the retina to neurons, particularly those neurons within the visual stream. For clarity, 'retinotopy' can be replaced with 'retinal mapping', and 'retinotopic' with 'retinally mapped'. Visual field maps (retinotopic maps) are found in many amphibian and mammalian species, though the specific size, number, and spatial arrangement of these maps can differ considerably. Sensory topographies can be found throughout the brain and are critical to the understanding of one's external environment. Moreover, the study of sensory topographies and retinotopy in particular has furthered our understanding of how neurons encode and organize sensory signals. Retinal mapping of the visual field is maintained through various points of the visual pathway including but not limited to the retina, the dorsal lateral geniculate nucleus, the optic tectum, the primary visual cortex (V1), and higher visual areas (V2-V4). Retinotopic maps in cortical ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eric L
The given name Eric, Erich, Erikk, Erik, Erick, Eirik, or Eiríkur is derived from the Old Norse name ''Eiríkr'' (or ''Eríkr'' in Old East Norse due to monophthongization). The first element, ''ei-'' may be derived from the older Proto-Norse language, Proto-Norse ''*wikt:Reconstruction:Proto-Germanic/ainaz, aina(z)'', meaning "one, alone, unique", ''as in the form'' ''Æ∆inrikr'' explicitly, but it could also be from ''*wikt:Reconstruction:Proto-Germanic/aiwaz, aiwa(z)'' "everlasting, eternity", as in the Gothic form ''Euric''. The second element ''-wikt:ríkr, ríkr'' stems either from Proto-Germanic language, Proto-Germanic ''*wikt:Reconstruction:Proto-Germanic/rīks, ríks'' "king, ruler" (cf. Gothic ''wikt:𐍂𐌴𐌹𐌺𐍃, reiks'') or the therefrom derived ''*wikt:Reconstruction:Proto-Germanic/rīkijaz, ríkijaz'' "kingly, powerful, rich, prince"; from the common Proto-Indo-European language, Proto-Indo-European root *wikt:Reconstruction:Proto-Indo-European/h₃r� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Coordinates
In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are * the radial distance along the line connecting the point to a fixed point called the origin; * the polar angle between this radial line and a given ''polar axis''; and * the azimuthal angle , which is the angle of rotation of the radial line around the polar axis. (See graphic regarding the "physics convention".) Once the radius is fixed, the three coordinates (''r'', ''θ'', ''φ''), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle) is called the ''reference plane'' (sometimes '' fundamental plane''). Terminology The radial distance from the fixed point of origin is also called the ''radius'', or ''radial line'', or ''radial coord ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylindrical Coordinates
A cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in a solid ball versus sphere surface)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces. In the literature the unadorned term "cylinder" could refer to either of these or to an even more specialized object, the '' right circular cylinder''. Types The definitions and results in this section are taken from the 1913 text ''Plane and Solid Geometry'' by George A. Wentworth and David Eugene Smith . A ' is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polar Coordinates
In mathematics, the polar coordinate system specifies a given point (mathematics), point in a plane (mathematics), plane by using a distance and an angle as its two coordinate system, coordinates. These are *the point's distance from a reference point called the ''pole'', and *the point's direction from the pole relative to the direction of the ''polar axis'', a ray (geometry), ray drawn from the pole. The distance from the pole is called the ''radial coordinate'', ''radial distance'' or simply ''radius'', and the angle is called the ''angular coordinate'', ''polar angle'', or ''azimuth''. The pole is analogous to the origin in a Cartesian coordinate system. Polar coordinates are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point in a plane, such as spirals. Planar physical systems with bodies moving around a central point, or phenomena originating from a central point, are often simpler and more in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Registration
Image registration is the process of transforming different sets of data into one coordinate system. Data may be multiple photographs, data from different sensors, times, depths, or viewpoints. It is used in computer vision, medical imaging, military automatic target recognition, and compiling and analyzing images and data from satellites. Registration is necessary in order to be able to compare or integrate the data obtained from these different measurements. Algorithm classification Intensity-based vs feature-based Image registration or image alignment algorithms can be classified into intensity-based and feature-based.A. Ardeshir Goshtasby2-D and 3-D Image Registration for Medical, Remote Sensing, and Industrial Applications Wiley Press, 2005. One of the images is referred to as the ''target'', ''fixed'' or ''sensed'' image and the others are referred to as the ''moving'' or ''source'' images. Image registration involves spatially transforming the source/moving image(s) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytical Function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions. A function is analytic if and only if for every x_0 in its domain, its Taylor series about x_0 converges to the function in some neighborhood of x_0 . This is stronger than merely being infinitely differentiable at x_0 , and therefore having a well-defined Taylor series; the Fabius function provides an example of a function that is infinitely differentiable but not analytic. Definitions Formally, a function f is ''real analytic'' on an open set D in the real line if for any x_0\in D one can write f(x) = \sum_^\infty a_ \left( x-x_0 \right)^ = a_0 + a_1 (x-x_0) + a_2 (x-x_0)^2 + \cdots in which the coefficients a_0, a_1, \dots are real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
