Moreover, from the definitive transformation of intercepts on the generators of Af, it is clear that the only points of Q at which a line can meet its image are the points of Aj.

For example, JPEG compression uses a variant of the Fourier transformation ( discrete cosine transform ) of small square pieces of a digital image.

* The kernel of a representation ρ of a group G is defined as the normal subgroup of G whose image under ρ is the identity transformation:

Eliphas Levi's image of " Baphomet " serves as an example of the transformation of the Devil into a benevolent fertility deity and provided the prototype for Murray's horned god.

When asked by Constantia ( Emperor Constantine's sister ) for an image of Jesus, Eusebius denied the request, replying that " To depict purely the human form of Christ before its transformation, on the other hand, is to break the commandment of God and to fall into pagan error ".

The rank is also the dimension of the image of the linear transformation that is multiplication by A.

An image of a fern which exhibits affine transformation | affine self-similarity

Supposing we exclude the degenerate case where ABCD has zero area, there is a unique such affine transformation T. Drawing out a whole grid of parallelograms based on ABCD, the image T ( P ) of any point P is determined by noting that T ( A ) = A ′, T applied to the line segment AB is A ′ B ′, T applied to the line segment AC is A ′ C ′, and T respects scalar multiples of vectors based at A.

A special case is a homothetic transformation or central similarity: it neither involves rotation nor taking the mirror image.

In heterodyne systems, output noise power includes spurious contributions from image-frequency transformation, but the portion attributable to thermal noise in the input termination at standard noise temperature includes only that which appears in the output via the principal frequency transformation of the system and excludes that which appears via the image frequency transformation.

If this object is a class of transformations ( such as " isomorphism " or " permutation "), it implies the equivalence of objects one of which is the image of the other under such a transformation.

To compute the transformation of image coordinates required for the distortion, e. g. the algorithm of Beier and Neely can be used.

Another example of MISD is pipelined image processing where every image pixel is piped through several hardware units performing several steps of image transformation.

If the world file describes an image that is rotated from the axis of the target projection, however, then A, D, B and E must be derived from the required affine transformation ( see below ).

* such that the new coordinates of the image of each point are the same as the old coordinates of the original point ( the formulas for the mapping are the inverse of those for the coordinate transformation )

* such that the old coordinates of the image of each point are the same as the new coordinates of the original point ( the formulas for the mapping are the same as those for the coordinate transformation )

To complete her image transformation, she also cropped her hair short in the style of other female flyers.

If one considers the matrix as a linear transformation from R < sup > n </ sup > to R < sup > m </ sup >, then the column space of the matrix equals the image of this linear transformation.

The column space of a matrix is the image or range of the corresponding matrix transformation.

An electrostatic system suffers generally from image plane curvature leading to defocusing in the peripheral image region if a flat viewing screen ( or interstage coupler ) is utilized, while a magnetic system requires accurate adjustment of the solenoid, which is heavy and bulky.

Settled phosphors, as generally used in image intensifiers, have low optical contact with the substrate surface, hence Af shall be assumed.

This assumption is justified if a poor image on the focusing screen remains stationary when the aperture is diminished ; in practice, this generally occurs.

Complementarians generally believe that the husband and wife are of equal worth before God, since both are created in God's image, but that husbands and wives have different functions and responsibilities that are based on gender with the husband always being the senior authority figure.

Progressive-scan camcorders generally produce a slightly sharper image.

Many flags are dyed through and through to be inexpensive to manufacture, such that the reverse side is the mirror image of the obverse ( front ) side, generally the side displayed when the flag is flying from the observer's point of view from left, the side of the pole, to right.

Comparable images from Western Christianity are generally not described as " icons ", although " iconic " may be used to describe a static style of devotional image.

Consequently it is generally not possible to distinguish a Christian use of a given image on an object of that period from a non-Christian use.

Another criticism of image veneration is found in the non-canonical 2nd-century Acts of John ( generally considered a gnostic work ), in which the Apostle John discovers that one of his followers has had a portrait made of him, and is venerating it:

The Eastern Orthodox view of the origin of icons is generally quite different from that of most secular scholars and from some in contemporary Roman Catholic circles: " The Orthodox Church maintains and teaches that the sacred image has existed from the beginning of Christianity ", Léonid Ouspensky has written.

Chinese vegetarian restaurants are generally decorated with her image, and she appears in most Buddhist vegetarian pamphlets and magazines.

In the U. S., people generally prefer a more colorful facial image than in reality ( higher color saturation ).

In Japan, consumers generally prefer a less saturated image.

OS / 2 version 3. 0, released in 1994, was labelled as OS / 2 Warp to highlight the new performance benefits, and generally to freshen the product image.

In computer graphics, a raster graphics image, or bitmap, is a dot matrix data structure representing a generally rectangular grid of pixels, or points of color, viewable via a monitor, paper, or other display medium.

A bitmap corresponds bit-for-bit with an image displayed on a screen, generally in the same format used for storage in the display's video memory, or maybe as a device-independent bitmap.

Sleipnir is generally accepted as depicted on two 8th century Gotlandic image stones ; the Tjängvide image stone and the Ardre VIII image stone.

The electron beam is generally scanned in a raster scan pattern, and the beam's position is combined with the detected signal to produce an image.

As first mentioned in regard to earliest ZBD closed-core transformers, transformers are generally considered to be either core form or shell form in design depending on the type of magnetic circuit used in winding construction ( see image ).

The concept developed in Du " Cubisme " of observing a subject from different points in space and time simultaneously, i. e., the act of moving around an object to seize it from several successive angles fused into a single image (' multiple viewpoints ' or ' mobile perspective '), is now a generally recognized phenomenon of the Cubist style.

In order to form an image, the ground plane surface must generally have dimensions of at least a quarter-wavelength of the radio waves used.

High-end LCD televisions now feature up to 240 Hz refresh rate, which requires advanced digital processing to insert additional interpolated frames between the real images to smooth the image motion.

Displaying any other resolution either requires a video scaler, causing blurriness and jagged edges ; or running the display at native resolution using 1: 1 pixel mapping, causing the image either not to fill the screen ( letterboxed display ), or to run off the lower right edge of the screen.

Any tampering with the original image of a film, particularly to crop it to fit a television screen, implies a compromise of the original image, and the cropping of a widescreen image to a full screen image for standard televisions requires skill by a film editor to prevent undue loss of elements of the composition.

A high quality image requires a large number of different separations between telescopes.

Firmware in the camera, or a software in a raw converter program such as Adobe Camera Raw, interprets the raw data from the sensor to obtain a full color image, because the RGB color model requires three intensity values for each pixel: one each for the red, green, and blue ( other color models, when used, also require three or more values per pixel ).

HIPAA requires that backup copies of patient images be made in case of image loss from the PACS.

The JFIF standard requires samples to be sited " interstitially " — meaning the decoder can treat each component array as representing an array of equal-sized rectangular pixels sampled in their centers, with each array having the same exterior boundaries as the image.

To establish that it is an image of an independent moon requires many other assumptions that amount to begging the question.

A 640 × 480 image requires 37. 5 KiB of storage.

To maintain or re-display this image requires still more processing and consequential energy cost ( in contrast to printed output for instance ).

It is possible to create image maps by hand using a text editor, but doing so requires web designers to know how to code HTML as well as how to enumerate the coordinates of the areas they wish to place over the image.

Because creating image maps in a text editor requires much time and effort, many applications have been designed to allow web designers to create image maps quickly and easily, much as they would create shapes in a vector graphics editor.

Relatively insensitive film, with a correspondingly lower speed index requires more exposure to light to produce the same image density as a more sensitive film, and is thus commonly termed a slow film.

Proper service marketing requires creative visualization to effectively evoke a concrete image in the service consumer's mind.

( This is a little inaccurate: Deligne did later show that E ∩ E < sup >⊥</ sup > = 0 by using the hard Lefschetz theorem, this requires the Weil conjectures, and the proof of the Weil conjectures really has to use a slightly more complicated argument with E / E ∩ E < sup >⊥</ sup > rather than E .) An argument of Kazhdan and Margulis shows that the image of the monodromy group acting on E, given by the Picard – Lefschetz formula, is Zariski dense in a symplectic group and therefore has the same invariants, which are well known from classical invariant theory.

In contrast, BMP requires padding rows to 4-byte boundaries, while TIFF and PNG are metadata containers that do not place the image data or attributes at a fixed location within the file.

* The simpler circuitry required translates into fewer layers of material in the silicon chip meaning that tangential light requires less correction in order to traverse to the depth at which the photons result in signal, simplifying the need for lensing at each pixel or photosite, and therefore theoretically, attaining greater image uniformity.