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	Inverse function - Wikipedia, the free encyclopedia
		In mathematics, an inverse function is in simple terms a function which "does the reverse" of a given function.
		If f is a real-valued function, then for f to have a valid inverse, it must pass the horizontal line test, that is a horizontal line y = k placed on the graph of f must pass through f exactly once for all real k.
		is also used for the (set valued) function associating to an element or a subset of the codomain, the inverse image of this subset (or element, seen as a singleton).
	en.wikipedia.org /wiki/Inverse_function (527 words)

	Image sub-sampling apparatus - Patent 5565925
		The present invention relates to an image sub-sampling apparatus, and in particular, to an image sub-sampling apparatus for use in an operation to receive and to reproduce an image encoded according to a discrete cosine transformation and a linear quantization for decoding the image.
		Heretofore, data represented by image signals to be transmitted or to be stored on a storage medium such as a memory card or a magnetic disk is commonly compressed to have a reduced data capacity in consideration of a limited capacity of the storage device or the like.
		Moreover, the data inversely quantized by the circuit 21 is fed to the circuit 24 to undergo an inverse discrete cosine transformation, thereby generating a restored image signal S.sub.1.
	www.freepatentsonline.com /5565925.html (2092 words)

	Image (mathematics) - Wikipedia, the free encyclopedia
		In mathematics, the image of an element x in a set X under the function f : X → Y, denoted by f(x), is the unique y in Y that is associated with x.
		The image of a subset A ⊆ X under f is the subset of Y defined by
		With this definition, the image f becomes a function whose domain is the set of all subsets of X (also known as the power set of X) and whose codomain is the power set of Y.
	en.wikipedia.org /wiki/Inverse_image (469 words)

	Image (mathematics) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-09-07)
		The image of a (A set whose members are members of another set; a set contained within another set) subset A &sube; X under f is the subset of Y defined by
		With this definition, the image f becomes a function whose domain is the set of all subsets of X (also known as the (additional info and facts about power set) power set of X) and whose codomain is the power set of Y.
		The results relating images and preimages to the algebra of (A junction where one street or road crosses another) intersection and (The state of being joined or united or linked) union work for any collections of subsets, not just for pairs of subsets.
	www.absoluteastronomy.com /encyclopedia/i/im/image_(mathematics).htm (493 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		However, when image data which has been coded based on blocks is restored, the restored image is considerably deteriorated, causing blocking artifacts near block boundaries, corner outliers at cross points of blocks, and ringing noise near the image edge.
		When an image is highly compressed, the block-based coding induces the well-known blocking artifacts near the block boundary, corner outliers at the cross points of the blocks, and ringing noise near the image edge.
		a decoder 20, which is a general decoder, decodes block-based image data and an image data post-processing apparatus 10 for reducing quantization effect occurring when the decoder 20 decodes an image, includes a semaphore extractor 100, a deblocking filter 110, a corner outlier compensator 120 and a deringing filter 130.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=99/22509.990506&ELEMENT_SET=DECL (7221 words)

	An Intuitive Explanation of Fourier Theory
		Every point on the input image radiates an expanding cone of rays towards the lens, but since the image is at the focus of the lens, those rays will be refracted into a parallel beam that illuminates the entire image at the ground-glass screen.
		Conversely, parallel rays from the entire input image are focused onto the single central point of the Fourier image, where it defines the central DC term by the average brightness of the input image.
		After performing the inverse transform on this image we see the effect of high-pass filtering, which is to preserve all of the sharp crisp edges from the original, but it loses the larger regions of dark and bright.
	cns-alumni.bu.edu /~slehar/fourier/fourier.html (1958 words)

	Image Defocusing - contd. (Site not responding. Last check: 2007-09-07)
		The results shown below are the restored images of the blurred image above using inverse filtering with HI at a = 30, and a = 28.
		Unless the exact distortion is known, inverse filtering proves to be a difficult method of image restoration.
		The inverse filter, HI with a = 30 was used, and the Wiener filter with K =.0045 was implemented.
	www.owlnet.rice.edu /~elec431/projects95/lords/page2.html (505 words)

	55:148 Dig. Image Proc. Chapter 4, Part 4
		The original image is obtained from the degraded one by a transformation inverse to the degradation.
		The undegraded image F is derived from its degraded version G. This equation shows that inverse filtration works well for images that are not corrupted by noise.
		S_{gg} is the spectral density of the degraded image
	www.icaen.uiowa.edu /~dip/LECTURE/PreProcessing4.html (1365 words)

	WTN
		Next, the transformed image is converted, using the SPRSIN function, to row-indexed sparse storage format retaining only elements with an absolute magnitude greater than or equal to a specified threshold.
		The image on the left is the original 256 by 256 image.
		The size of the compressed image's data file is 26.6% of the size of the original image's data file.
	www.astro.princeton.edu /~esirko/idl_html_help/W44.html (420 words)

	Texture mapping in Matlab
		That is map a billboard image in 3-space through a camera onto the image plane by working from the image-plane coordinates to the texture (billboard) coodinates.
		The skewed image is the resulting shape after the rectangular surface is rotated in space and projected into the image plane.
		These coordinates are a result of rotating a camera around the rectangular surface and computing the resulting image in the image plane (as done in the last homework, expect that this time only the four corners of the rectangle are manipulated).
	www.cs.unc.edu /~dorianm/academics/comp235/texturemap (518 words)

	Function (mathematics) [Definition] (Site not responding. Last check: 2007-09-07)
		The preimageIn mathematics, the image of an element x in a set X under the function f : X → Y, denoted by f(x), is the unique y in Y that is associated with x.
		The image of a subset A ⊆; X under f is the subset of Y defined by...
		See also inverse imageIn mathematics, the image of an element x in a set X under the function f : X → Y, denoted by f(x), is the unique y in Y that is associated with x.
	www.wikimirror.com /Function_(mathematics) (8343 words)

	Introduction to the Fourier Transform
		The images are a pure horizontal cosine of 8 cycles and a pure vertical cosine of 32 cycles.
		The images displayed are horizontal cosines of 8 cycles, differing only by the fact that one is shifted laterally from the other by 1/2 cycle (or by PI in phase).
		These images are all scaled differently and the comparison is only qualitative, but it can be seen that the windowed image FT is much closer to the true FT and eliminates many of the edge effects.
	www.cs.unm.edu /~brayer/vision/fourier.html (2405 words)

	6.4. Topology and Continuity
		The inverse image of every open set under f is the intersection of D with an open set.
		The inverse image of every closed set under f is the intersection of D with a closed set.
		Now we know that the inverse images of open sets are open, and the inverse images of closed sets are closed whenever f is continuous.
	web01.shu.edu /projects/reals/cont/topcont.html (814 words)

	Inversion: Reflection in a Circle
		From (1) it is obvious that if A' is the inverse of A, then A is the inverse of A', so that the points are said to be symmetric in the circle, or to be reflections of each other.
		A' is said to be the inverse image of A with respect to, or in, the given circle.
		The center of inversion is often [Coxeter] left over as a point with no inverse image, but sometimes [Courant] is said to be mapped to the point at infinity.
	www.cut-the-knot.org /Curriculum/Geometry/SymmetryInCircle.shtml (476 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		The forward wavelet transform is repeated on on the downside image (=the DC image) appearing in the upper left corner until only 1 pixel is left.
		On this wavelet image a series of backward wavelet transforms are applied until an image of the original size is reached.
		This process is repeated until an exact reconstruction of the original image is obtained and displayed on the bottom left.
	www.geocities.com /Athens/Agora/3027/work/jpeg2000/jpeg2Dem.html (429 words)

	c24g2 images.doc (Site not responding. Last check: 2007-09-07)
		IMAGES (Original implementation by Bernard R. Brooks, 1983) CHARMM has a general image support system that allows the simulation of almost any crystal and also finite point groups (such as dimers and tertamers...).
		Rereading an image transformation file without the INIT keyword is useful when crystal parameters are to be modified, but the patching data is to be retained.
		Image Centering There is a set of commands that allow for the centering of selected part of the PSF during an image update.
	www.psc.edu /general/software/packages/charmm/c24g2/images.html (2409 words)

	Inversion in the Incircle
		The inverse images of the side lines of a triangle in its incircle are three circles of equal radii that concur at the incenter.
		The circle through their second points of intersection is none other than the inverse image of the circumcircle.
		It is a curious fact that the inverse image of the circumcircle in the incircle is the 9-point circle of
	www.cut-the-knot.com /Curriculum/Geometry/ThreeEqualCircles.shtml (361 words)

	EE 610 Image Processing (Site not responding. Last check: 2007-09-07)
		For your software for Wiener filtering to be meaningful, (a) the SNR of the Wiener filtered image should be higher than the SNR for the noisy and blurred image, and (b) the SNR of the Wiener filtered image should be higher than the pseudo-inverse filtered image.
		Generate a motion blurred image, where the motion blurring is assumed to be uniform and in the horizontal direction.
		This image will be used in a subsequent assignment for de-blurring of images blurred due to motion.
	poisson.ecse.rpi.edu /~anand/projects/image_processing_ipgrp20/aman/hw4.html (599 words)

	WIENER FILTERING
		The inverse filtering is a restoration technique for deconvolution, i.e., when the image is blurred by a known lowpass filter, it is possible to recover the image by inverse filtering or generalized inverse filtering.
		The disadvantage of this implementation is that when the inverse filter is singular, we have to use the generalized inverse filtering.
		Notice that the restored image is improved in terms of the visual performance, but the MSEs don't indicate this, the reason of which is that MSE is not a good metric for deconvolution.
	www.owlnet.rice.edu /~elec539/Projects99/BACH/proj2/wiener.html (502 words)

	ipedia.com: Inverse image Article (Site not responding. Last check: 2007-09-07)
		An inverse image in mathematics is defined in the following way: Consider a function f which maps from some set A to some set B. Let C be a subset of B, then the inverse image of C under the function...
		Consider a function f which maps from some set A to some set B. Let C be a subset of B, then the inverse image of C under the function f, written f
		Then the inverse image of C consists of the numbers 1, 2 and 3, since only these numbers have a square less than 10, namely 1, 4 and 9.
	www.ipedia.com /inverse_image.html (206 words)

	ELE 585 - Digital Image Processing - Lab #7 (Site not responding. Last check: 2007-09-07)
		We take the 2D fft of the 20 x 20 filter kernel, zero padded to that it's the same size as the blurred image, and perform the inverse filtering in the frequency domain on the both the high-precision 64-bit and the 8-bit blurred images.
		We can see that the inverse filter tends to greatly amplify high frequency noise, and as a result the deblurred version of the quantized image is unrecognizable.
		The results of such inverse filtering are shown below for the blurred image and the quantized blurred image.
	www.ele.uri.edu /~hansenj/projects/ele585/lab7 (350 words)

	MACS 458 Assignments (Site not responding. Last check: 2007-09-07)
		We define the inverse image of B to be g(B) = {x in S: f(x) belongs to B}.
		Does a function have to have an inverse (ie be 1-1 and onto) inorder to have an inverse image?
		For the general case (not the particular example above) prove that for any subsets A and B of T, g(A intersect B) = g(A) intersect g(B) where g is the inverse image defined above.
	www.mines.edu /fs_home/runderwo/teaching/macs358_projects.html (214 words)

	Salt and Pepper
		Noise in an image are small, unwanted random pixels in areas where the surrounding majority of pixels are a different value, i.e.
		As can be seen in the second image, erosion was successful in eliminating the salt noise, but amplified the pepper noise, and further damaged the original image.
		A quick comparison between the original noisy image and the final restored image confirms that virtually all noise has been eliminated, while little damage was inflicted upon the structure of the image.
	www.eece.unm.edu /ivpcl/Classes/Morphology_Gui/Salt_and_Pepper/salt_and_pepper.html (658 words)

	absfity
		This task generates the output inverse sensitivity image required by the Routine Science Data Processing (RSDP) system.
		Image containing the wavelengths for which the output inverse sensitivity file is to be generated.
		Name of the input template image header used to construct the output inverse sensitivity image.
	stsdas.stsci.edu /cgi-bin/gethelp.cgi?absfity (378 words)

	[No title]
		The image of the equator under the stereographic projection is a circle centered at the South Pole whose radius is twice that of the equator.
		While it is not surprising that the image a circle reflected in a mirror is again a circle, it is surprising that the inverse of a circle is also a circle in spite of the distortions of the circular inversion map.
		The inverse of an extended circle with respect to another extended circle is an extended circle.
	www.plu.edu /~dornerbc/teaching/math321/jrnycmpn/chapt2/chapter2.htm (1032 words)

	Maps between Schemes
		An inverse specified by polynomials or rational functions on Y can be given as G. When an inverse is not given F is allowed to be a sequence of sequences of polynomials or rational functions.
		The image of the blowup of p as a point of X is returned as a third value.
		The closure of the image f(X) where X is a subscheme of the domain of the map of schemes f.
	www.umich.edu /~gpcc/scs/magma/text1020.htm (5798 words)

	[No title]
		Is 1 an inverse image of b?No, 3 is not an inverse image of a.
		Yes, 1 is an inverse image of b.
		of c?Inverse image of b = {1, 3, 5}.
	www.cc.gatech.edu /classes/AY2005/cs1050b_spring/HW6Solutions.doc (1167 words)

	The Wavelet Digest :: View topic - Question: Inverse image halftoning using wavelets
		I am doing a work about tecniques to do inverse halftoning of an image.
		I am interested in the use of wavelets, and I have read an article from the IEEE, called "Inverse halftoning using wavelets".
		As I would like to program with Matlab, it would be a big help if somebody could give me some information, about how to use wavelets with the matlab, and how to implement the method explained in the article that I have read with the software matlab.
	www.wavelet.org /phpBB2/viewtopic.php?t=5288&view=next (111 words)

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