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Jinc Function
A sombrero function (sometimes called besinc function or jinc function) is the 2-dimensional polar coordinate analog of the sinc function, and is so-called because it is shaped like a sombrero hat. This function is frequently used in image processing. It can be defined through the Bessel function, Bessel function of the first kind ( J_1) where . \operatorname (\rho) = \frac. The normalization factor makes . Sometimes the factor is omitted, giving the following alternative definition: \operatorname (\rho) = \frac. The factor of 2 is also often omitted, giving yet another definition and causing the function maximum to be 0.5: \operatorname (\rho) = \frac. The Fourier transform of the 2D circle function (\operatorname(\rho)) is a sombrero function. Thus a sombrero function also appears in the intensity profile of far-field diffraction through a circular aperture, known as an Airy disk. References {{reflist, refs= {{cite book , title = Theory of Remote Image Formation , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sombrero Function 3d
In English, a , ; ) is a type of wide-brimmed Mexican men's hat used to shield the face and eyes from the sun. It usually has a high, pointed crown; an extra-wide brim (broad enough to cast a shadow over the head, neck, and shoulders of the wearer) that is slightly upturned at the edge; and a chin strap to hold it in place. In Mexico, this hat type is known as a ('charro hat', referring to the traditional Mexican horsemen). In Spanish, any hat is considered a sombrero. Design Sombreros, like cowboy hats, were designed in response to the demands of the physical environment. High crowns provide insulation, and wide brims provide shade. Hot and sunny climates inspire such tall-crowned, wide-brimmed designs, and hats with one or both of these features have evolved again and again in history and across cultures. For example, the Greek petasos of two millennia ago, and the traditional conical hat widespread in different regions of Asiainto modern timesincorporate such heat-miti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polar Coordinate
In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two 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 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 intuitive to model using polar coordinates. The polar coordinate system is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sinc Function
In mathematics, physics and engineering, the sinc function ( ), denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatorname(x) = \frac. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa(''x''). In digital signal processing and information theory, the normalized sinc function is commonly defined for by \operatorname(x) = \frac. In either case, the value at is defined to be the limiting value \operatorname(0) := \lim_\frac = 1 for all real (the limit can be proven using the squeeze theorem). The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of ). As a further useful property, the zeros of the normalized sinc function are the nonzero integer values of . The normalized sinc function is the Fourier transform of the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sombrero
In English, a , ; ) is a type of wide-brimmed Mexican men's hat used to shield the face and eyes from the sun. It usually has a high, pointed crown; an extra-wide brim (broad enough to cast a shadow over the head, neck, and shoulders of the wearer) that is slightly upturned at the edge; and a chin strap to hold it in place. In Mexico, this hat type is known as a ('charro hat', referring to the traditional Mexican horsemen). In Spanish, any hat is considered a sombrero. Design Sombreros, like cowboy hats, were designed in response to the demands of the physical environment. High crowns provide insulation, and wide brims provide shade. Hot and sunny climates inspire such tall-crowned, wide-brimmed designs, and hats with one or both of these features have evolved again and again in history and across cultures. For example, the Greek petasos of two millennia ago, and the traditional conical hat widespread in different regions of Asiainto modern timesincorporate such heat-mit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Image Processing
An image or picture is a visual representation. An image can be two-dimensional, such as a drawing, painting, or photograph, or three-dimensional, such as a carving or sculpture. Images may be displayed through other media, including a projection on a surface, activation of electronic signals, or digital displays; they can also be reproduced through mechanical means, such as photography, printmaking, or photocopying. Images can also be animated through digital or physical processes. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term ''image'' (or ''optical image'') refers specifically to the reproduction of an object formed by light waves coming from the object. A ''volatile image'' exists or is perceived only for a short period. This may be a reflection of an object by a mirror, a projection of a camera obscura, or a scene displayed on a cathode-ray tube. A ''fixed image'', also called a hard copy, is one that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mexican Hat Wavelet
In mathematics and numerical analysis, the Ricker wavelet, Mexican hat wavelet, or Marr wavelet (for David Marr (neuroscientist), David Marr) :\psi(t) = \frac \left(1 - \left(\frac\right)^2 \right) e^ is the negative normalizing constant, normalized second derivative of a Gaussian function, i.e., up to scale and normalization, the second Hermite function. It is a special case of the family of continuous wavelets (wavelets used in a continuous wavelet transform) known as Hermitian wavelets. The Ricker wavelet is frequently employed to model seismic data, and as a broad-spectrum source term in computational electrodynamics. : \psi(x,y) = \frac\left(1-\frac \left(\frac\right)\right) e^ The multidimensional generalization of this wavelet is called the Laplacian of Gaussian function. In practice, this wavelet is sometimes approximated by the difference of Gaussians (DoG) function, because the DoG is separable and can therefore save considerable computation time in two or more dimens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
