Abstract: Method and apparatus for performing halftoning of an image, using two 2-dimensional look up tables (LUTS). The first LUT receives coordinates of an image value and outputs a screen reference value which then serves, together with the image value as address for the second LUT. The output of the second LUT is the halftone value.

Abstract: Disclosed is a method for printing a colour image composed of at least one photographic image and at least one additional element, such as text, a logo or a colour background, using different colours, wherein a maximum of six different colours are used and these colours consist of a first group composed of the three primary colours, Cyan, Magenta and Yellow supplemented with Black and a second group composed of two special colours Orange and either Blue or Green, wherein the photographic image is printed using only colours from the first group and wherein the additional element of the colour image is printed substantially using colours from the second group.

Abstract: The present invention relates to the manipulation of differential gloss as may be inherent in halftoned images by utilization of tags. By selectively applying halftones with anisotropic structure characteristics, which are significantly different in orientation while remaining identical in density, as directed by tag settings, a gloss image may be superimposed within an image without the need for special toners or paper. Conventional copier systems will not typically be able to copy such a superimposed gloss image.

Abstract: To reduce low-frequency moiré in secondary colors and tertiary colors in four color screens, between at least two halftone screens, screen vectors wa2, wb2 are arranged to match each other, while other screen vectors are arranged not to match each other. A halftone screen is an orthogonal screen in which screen vector wa2 is perpendicular to basis vector ra1. A halftone screen is a non-orthogonal screen in which screen vector wb2 is perpendicular to basis vector rb1. When screen vector wa2 matches screen vector wb2, spatial frequency spectra corresponding to screen vectors wa2 and wab2, match each other. With such a relationship, because a pair of spatial frequency spectra can match each other between two colors, wider intervals can be provided for the spatial frequency spectra of the remaining colors of four colors, which would suppress low-frequency moiré.

Abstract: An image data processing apparatus determines whether an input element provided by a computer is either a command for processing continuous tone data or continuous tone data. When the input element provided by the computer is a continuous tone data processing command, a parameter (period, angle, form of a macroscopic dot) received by a parameter input unit is replaced by an approximate value realized by a multiple-valued recorder, a continuous tone screen threshold-valued matrix is selected on the basis of the parameter replaced by the parameter replacement unit, and continuous tone data is converted to multiple-valued data in accordance with the selected threshold-valued matrix for outputting halftone data to the multiple-valued recorder.

Abstract: One method for halftone image watermarking assigns halftone watermark dot values to pseudorandom locations in an image and diffuses the error of the watermark to neighboring pixel locations of these dots. This method may be used in conjunction with a robust watermark spread throughout image before embedding the halftone watermark. The robust watermark carries a key used to decode the halftone watermark. Another method for halftone image watermarking computes a watermark image at the resolution of a halftone image. The method modulates the halftone image with the watermark image.

Abstract: Apparatus defines a dither mask (DM) and printmask (PM) with corresponding dimensions. In one invention form the DM dimension is not an integral factor or multiple of the PM dimension. The two dimensions may be lengths or widths; preferably the apparatus manages both; the corresponding dimensions differ by at least three pixels, and by a multiple of two pixels—more preferably eight or a multiple of eight. Preferably one dimension is an integral multiple of 256 pixels differing by eight pixels from the other. Another invention form has a scanning printhead making multiple passes across a print medium to form swaths of marks, a mechanism to define an offset smaller than at least one of the two dimensions, and a unit to index one mask by that offset between forming of successive swaths. This is valuable if DM and PM are established by preprogrammed circuits (e.g.

Abstract: When a halftone dot image structure reproduction mode is selected in a proof image data generating apparatus, color image data are generated using threshold matrixes having respective screen angles which are essentially equal to the screen angles of printing plates for a color print and screen ruling ratios between the threshold matrixes which are essentially equal to the screen ruling ratios between the printing plates for the color print, and the processed color image data are supplied to a color printer. The color printer outputs a color proof having a rosette pattern similar to the rosette pattern in the color print based on the supplied color image data.

Abstract: A circuit for generating a threshold bias signal for processing n color separations representing a color image includes a threshold bias register which holds and outputs the current threshold bias signal.

Abstract: Using a resolution supplied from an image output apparatus and ruling information supplied from a ruling information storage unit, a screen ruling of threshold data stored in a threshold data storage unit is determined, and threshold data which provides a screen ruling closest to a desired screen ruling supplied from a screen ruling input unit is selected and supplied to a binarization processor which is supplied with multivalued image data from an image processing apparatus. The binarization processor compares the selected threshold data and the multivalued image data to generate binary image data.

Abstract: The present invention is a method and apparatus for reducing two-color moiréoften found during the rendering of full color images using halftoning techniques, by providing shared screen angles between distinct color separations.

Abstract: An encoding system includes data in an underlying image by controlling or modifying halftone settings, which are used in the associated printing color process to produce a hard-copy document or an on-screen image. The system encodes the data into the image by selectively varying, in accordance with the data, the order of various color channels, and/or the screen angles and/or spatial frequencies, or scales, of associated halftone screens. The system encodes an N-bit payload in the image by modifying the halftone settings of certain or all of the color channels in accordance with the data. The system thus uses the color channels also as “data channels.” The system prints the encoded image by incorporating the modified halftone settings into the respective halftone screens, and applying the inks in a conventional manner.

Abstract: When clustered-dot dithering is employed in laser printers a banding effect sometimes results from the interaction of the dither matrix with non-uniform line spacing in the printer. We have found that we can lessen the effect of this interaction if we change the dither matrix as it moves over the image. We do this by modulating the dither matrix (halftone cell) as a function of the spatial position of the sub-area in the image. Halftone cells can be formed in a variety of patterns (e.g. vertical, horizontal, etc.) but generally their threshold values grow from a minimum value to a maximum value. Our process is to modulate the halftone cell according to a function: f (s, h) where s is the spatial position of the sub-area of the image and h is the halftone cell. We modulate the cell by altering the relative positions of the threshold values in the cell as we move the cell over the image.

Abstract: An image data generation part 400 generates image data, attaches a tag to the image data, and then outputs the resultant data. A screen processing part 420 carries out a screen process on the image data in accordance with the characteristic indicated by the tag, and outputs the tag to a parameter generation part 428. The parameter generation part 428 adjusts a parameter of a correction process in an image processing part 424 so that a detected misregistration does not interfere with the screen characteristic. The image processing part 424 applies such a correction process as to cancel a detected misregistration in an output image to input image data in accordance with the parameter of the correction process as input. A print processing part 440 controls an apparatus main body 2 to cause it to print corrected image data.

Abstract: There is disclosed a method wherein an origin is set on the dither pattern and the dither pattern is rotated relative to the origin by a required screen angle. By rotating the dither pattern, real-number coordinates of an origin of adjacent dither patterns are obtained. Coordinates of the origin of the adjacent dither pattern are corrected by rounding fractions of the real-coordinate so that the real-number coordinates are changed to integer coordinates. An angle which a segment connecting an origin of the dither pattern to be based on and that of the adjacent dither pattern obtained after the correction forms with a horizontal line is selected as a screen angle. By this, the shape of the dither pattern obtained after being rotated becomes uniform, preventing the occurrence of moire.

Abstract: In a gradation display method, an image is divided into pixels having fine areas, this pixel is furthermore divided into very fine pixels (Si) having very fine areas, and then gradation is displayed based upon a ratio of a colored very fine pixel (Si) with respect to all of very fine pixels (Si) within a pixel. Also, the above-described colored very fine pixel (Si) is formed by both a first growth core which is formed by increasing the number of colored very fine pixels of a single cluster, and a second growth core which is formed by increasing the number of colored very fine pixels of another single cluster.

Abstract: The screened printing data are subjected to a filtering method, the raster information being maintained. Intermediate tonal values are produced by the filtering method, using the binary tonal values, the intermediate tonal values being configured in such a way that, by means of a colour space transformation, transformed tonal values and/or intermediate tonal values can be formed which represent a true-to-colour proof.

Abstract: A user-generated image is processed, using amplitude-modulated screening, into high-resolution, raster-fomat halftones. The halftones are subdivided into a plurality of segments whose size is determined by the original processed resolution, the resolution of the output device, the original image size, and the size of the media on the output device. These segments are processed into continuous-tone matrices which are combined and color-converted as required by the particular output device. When printed on the output device, the resulting image is a faithful reproduction of the user-generated image as it would appear after being printed on a press.

Abstract: A method for performing a digital multistage screening of a half-tone image with a screen having any desired screen resolution and any desired screen angle, in which the screening is carried out by reading out threshold values and comparing the threshold values read out with the color values of the half-tone image. Threshold value matrices are used in which the threshold values represent one or more screen dots of a given screen, with which the desired screen resolution and the desired angle are approximated. While the threshold values are being read out, an error between the coordinates of the desired screen and of the given screen is determined, and the error is compensated for by correcting the read address for the threshold value matrix, as soon as the error exceeds a predefined limiting value. Instead of the threshold value matrices, printing-value matrices can also be used.

Abstract: A computer implemented method to include microscopic perforations (perforations) in an printing plate is revealed. The particles improve the properties of the plate towards printability of an image on different kinds of offset presses. The perforations are formed by perforations which are added in a fully digital way. Aspects of the invention include of three alternative embodiments for include the repelling particles, and these alternative embodiments may be uses alone or in combination depending on the user's preferred workflow. The third alternative embodiment adds the perforations through an additional layer in the page description, this layer comprising a pattern which erases small particles in the original design elements. The first alternative embodiment adds the perforations through a modified screening method. The second alternative embodiment includes perforations into existing bitmaps.

Abstract: There is disclosed an image processing apparatus in which a pattern table stores a plurality of screen patterns which include a predetermined number of pattern data and have different data patterns. An in-pattern position calculator generates an in-pattern position signal indicating a position of an input image signal in the screen pattern from main and sub scanning synchronizing signals. A pattern selecting signal combining section generates a pattern selecting signal for selecting a specified pattern in the pattern table from the input image signal, combines the pattern selecting signal and the in-pattern position signal supplied from the in-pattern position calculator, and supplies an address in the pattern table. A controller reads pattern data corresponding to the address in the pattern table from the pattern table and supplies image data.

Abstract: A frequency-modulation halftone screen and method for making same, utilizing local randomization of a deterministic screen. The deterministic screen optimizes uniformity of the halftone dot distribution, while the local randomization suppresses artifacts due to subject moiré.

Abstract: Dots defining the number of screen lines, of at least one color component of a plurality of color components, which number is different from that defined for each of other color components are generated on the basis of the screen method in which dot shape after binarization defines a halftone dot. A printing method and apparatus for generating binary data so that the size of such dots arranged concentrated to determine the number of screen lines differs among image constituting color components in the image after the binarization.

Abstract: A method of compensating for dot gain in printing with stochastic screens comprises obtaining continuous tone CMYK files and screening the files at a resolution that is lower than the resolution of an output device that will be used to print the files. The lower resolution stochasticly screened files are then expanded to the resolution of the output device, thereby effectively increasing the size of the dots by creating a number of subdots for each dot in the lower resolution stochasticly screened files. Subdots within the expanded stochasticly screened files can then be selectively removed to compensate for dot gain. In addition, overlapping dots in the screened CMYK files are removed and additional stochasticly screened files are created that print a dot of a color of the previously overlapping dots and at the location of the previously overlapping dots to prevent colors from running together when printing on certain media.

Abstract: The result of integrating a halftone dot-shape can be clustered. When the edge of the halftone dot-shape extends across a “vertical” edge of a window, the window is altered until the edge of the halftone dot-shape no longer crosses either vertical edge of the altered window. The image density of the portion of the halftone dot-shape contained within the altered window is determined. The block of image density of the portion of the halftone dot shape contained within the altered window is aligned with the right edge, the left edge, split between the left and right edges, or clustered in the “center” of the altered window. An amount of the determined block that extends into the original sample window is determined. This amount extending into the original window determines the amount of image density to be generated in the final output image based on that sample location of the window.

Abstract: A halftone screening method creates screens of a plurality of colors, where each of the screens is divided into a plurality of cells, and intentionally changes a dot position of certain colors within cells of the screens of the certain colors relative to a dot position of a reference color within a cell of the screen of the reference color, so as to suppress a color tone change caused by positional errors of the screens.

Abstract: A high addressable multibit screening device and method for use in a PDL interpreter environment achieve improved printing resolution and quality. A PDL interpreter receives a PDL document from a host source, which identifies one or more objects that can be fully toned (black) or partially toned (line art or images). Each of these objects can be processed differently. Fully toned objects are processed within the interpreter and directly output in a predetermined output. Partially toned objects are sent to a high addressable screening module within the interpreter for processing prior to outputting in a desired output format. The high addressable screening module screens the partially toned objects to obtain multibit screened data for output.

Abstract: A maximum color identifying portion 41 identifies a maximum color from coloring material colors used to reproduce a color of a line segment after color conversion into coloring material colors by a character/line color converting portion 31 is applied to the rasterized image signal. A structure deciding portion 42 outputs a screen parameter flag that controls a screen parameter in compliance with the identified maximum color and a drawing direction of the line segment such that the screen process in the maximum color is executed at a screen angle, that is different from the drawing direction of the line segment, in a character/line screen processing portion 35. The character/line screen processing portion 35 applies the screen process to the image in accordance with the screen parameter flag by using the screen parameter at the screen angle that is different from the drawing direction of the line segment. Accordingly, disappearance of the line segment due to the screen process is avoided.

Abstract: A method for calibrating a printer includes printing a set of color samples with the printer, the set of samples or calibration target generated dynamically in response to selected printer variables, and reflecting at least a portion of the printer gamut. Each printed color sample in the set of samples is measured calorimetrically, to determine the printer's response thereto, so that a calibration table can be generated, taking into account printer variables selected by a user.

Abstract: Image processing apparatus and image processing method for formation of high quality image by high-speed error diffusion processing by execution of more complicated threshold condition processing in a simple manner. When error diffusion processing is performed on multivalued image data having plural density components and the result of processing is outputted, upon execution of error diffusion processing on a first density component among the plural density components, a threshold value used in the error diffusion processing is determined based on a density value of a second density component, then the error diffusion processing is performed on the first density component based on the determined threshold value, and the result of execution of the error diffusion processing is outputted.

Abstract: In order to reproduce a gradation image of a plurality of colors with dither method, a plurality of patterns including first and second patterns are provided which makes dot in the reproduced image grow as lines and as lumps as gradation level increases with increase in gradation level. One of the patterns for a color of the received image data is selected, and received multi-level image data are screened with the selected pattern to generate bi-level image data for reproducing the image. In a different way, a plurality of patterns including first and second patterns are provided which make dots to be reproduced grow discretely along lines at low gradation levels as the gradation level increases. Screen angles of the first and second patterns are different by 90° from each other. One of the patterns is selected based on a color of received image data, and the received image data are screened with the selected patterns to generate bi-level image data.

Abstract: An image generating system that warps both the image data and halftone screens of a halftone screen system to minimize moirè patterns. Merely warping image data to minimize moirè patterns results in offsets within the image data which should have a corresponding adjustment or warp in halftone screens used in the image generating system to render the color image separation layers. Therefore, the image generating system provides moirè pattern minimization by warping screens of the halftone screen system to correspond to the warping of the image data. The image generating system uses line screens for halftoning the chromatic image separation layers of color images and a hexagonal dot screen for halftoning the luminescent image separation layer. The halftone screen system uses the relatively large average screen displacement angles offered by line screening while providing a dynamic tone range performance similar to that of the performance of dot screening.

Abstract: A method for reducing edge effect (white gapping) between objects formed on a photoconductive member of an imaging device includes, during processing of a given color plane, under exposing (partially exposing) the photoconductive member for image data that specifies a color to be developed on at least one color plane but specifies no color to be developed on the given color plane. Under exposing occurs relative to a development threshold for the image processing of the given color plane. As such, the under exposing does not enable development of that image data during image processing of the given color plane. The under exposing occurs relative to a high frequency halftone screen for minimizing contamination (unwanted development) during the partial exposure.

Abstract: An image forming apparatus includes an image reader for reading images, a memory for storing images read by the image reader, a compression circuit for compressing an arbitrary portion of an image placed on a page memory, a compressed image memory for storing images compressed by the compression circuit, a decompression circuit for decompressing images placed on the compressed image memory, a page memory for developing images decompressed by the decompression circuit, and a printer for outputting images on the page memory. When a plurality of images stored in the memory are to be screened, combined on the page memory and to be output, the images are developed such that screen patterns of respective images to be combined are superposed on the page memory. As a result, an image forming apparatus which is capable of screening, combining and printing a plurality of stored images without increasing memory capacity is provided.

Abstract: An image forming apparatus having first and second basic cells each containing a predetermined number of cells in a main scanning direction and a sub-scanning direction and disposed adjacent to each other in the sub-scanning direction, a gradation processing portion arranged to perform a gradation expressing process for each basic cell in accordance with a density of a supplied image and a dot forming portion capable of forming dots on a recording medium to correspond to each pixel subjected to the gradation expressing process by the gradation processing portion. The gradation processing portion performs the gradation expressing process in such a manner that enlargement of dots in the first and second basic cells adjacent to each other in the sub-scanning direction is inhibited in the sub-scanning direction until the dots are enlarged and connected to each other in the main scanning direction.

Abstract: In a hi-fi color printing system, an inverted halftone screen is provided having the same angle and frequency as a halftone screen for an opposing color. The dots of the inverse halftone screen are configured to be located midway between the centers of the dots of the half-tone screen. The halftone screen and inverted halftone screen are used in the printing process to extend the gamut of colors within a printing system, render improved neutral colors, and provide an improved transition through neutral regions of color space. The present invention allows for additional printing of multiple colors without the need for increasing the number of screens used in the image processing system.

Abstract: A method and system of designing a digital halftoning screen for forming images on output sheets according to a set of image signals. The method generates a halftone line screen having multiple levels, each level having multiple line segments, each line segment having an equal pre-determined number of elements. The method stochastically assigns threshold values to pixels corresponding to a first element within the multiple line segments of a first level and assigns a same threshold value to a pixel corresponding to a single level to create a first element stochastic fill sequence. The method then assigns threshold values to pixels corresponding to a first element within the multiple line segments of the remaining levels of the halftone line screen according to the first element stochastic fill sequence.

Abstract: An image processing apparatus, which performs color conversion for input tone data in an RGB color space to obtain tone data for a CMY color space, and which performs halftone processing to convert the tone data in the CMY color space to image reproduction data, is characterized in that a gamma characteristic A for an output density for a tone in the RGB color space is identical to a gamma characteristic B for an output density for a tone in the CMY color space in the halftone processing. In accordance with the invention, for the color conversion, even when the tone data for the RGB color space between the grid points of a color conversion table is obtained by interpolating the tone data for the CMY color space, the halftone process is performed for the RGB tone data in accordance with the same gamma characteristic B. Thus, image reproduction data can be obtained that provide the same output density as the output density allocated for the tone data of the RGB color space.

Abstract: A method for providing color correction to a color marking engine for halftone and contone images includes the step of first generating a test pattern. This test pattern has a plurality of discrete images disposed thereon with the discrete images having characteristics that are correlated with parameters of the print job. In one mode, they relate to halftone images that have differing densities of dots, each less than 100% density. The images are correlated to different bit values for the same densities such that the maximum density value for the pixel is offset for different images. A user then views the different images and determine which one is closest to a true gray and then selects the offset bit value for that image as the marking engine offset. This can then be applied to that particular marking engine. This can be utilized for a plurality of marking engines (651) with a single RIP operation (649 and 651).

Abstract: This is a halftone circuit which, in addition to the usual counting and addressing mechanisms, has control over the phase, angle and direction of the addressing circuitry of the array in memory so that regular dots, mirror images of dots and out-of-phase dots can be created from a single array, thus saving memory hardware. The mirror images can be made by counting rows in either direction, the angle can be varied by varying the number of pixels shifted between scans, and the phase can be varied by setting the starting point to any row and column. In this way, a single array can be used to create a number of dots.

Abstract: A system provides a halftone image having reduced moire patterns by applying a screen function of the type having a first function exhibiting symmetry about a point and a second function exhibiting symmetry about a line. In a progression of tone levels, such a screen function creates first dots, then lines, then dots. For example, a screen function may include the sum of a first function of the type (1−cos(pi*(x+y))*cos(pi*(y−x))) and a second function being a piecewise linear function of x, where {x,y} is a coordinate location in a unit cell mapped to a halftone cell mapped to the image pixel grid. In other embodiments, a unit cell is defined on the grid by a vector. The vector has a component along an axis of the grid. The component has a noninteger length. Unit cells of the type so defined implement rational tangent angles not possible with conventional halftone cells.

Abstract: An analog color image signal sent from a D/A converter is compared with a triangular-wave signal generated by a triangular-wave generator, to produce a pulse-width modulation signal serving as a dot signal. The phase of a clock signal supplied to the triangular-wave generator is shifted on a line-by-line basis to produce a screen angle of each color so that the initial phases become different from one another for the respective colors.

Abstract: A multi-color image forming apparatus and method to form a color image by overlapping multiple gradation pattern images formed for each of the recording colors based on the input color image information, wherein the screen angles of the unit gradation patterns of the multiple gradation pattern images are set such that they are separated from one another by 20 degrees or more, and in which the first unit gradation pattern is formed using a line pattern in which the colored dot patterns are made to extend in the direction corresponding to a first screen angle and the second unit gradation pattern is formed using a line pattern in which the colored dot patterns are made to extend in the direction corresponding to a second screen angle which is different from the first screen angle by 90 degrees.

Abstract: A method and apparatus for halftoning where at most one halftoned gray, or multi-level, pixel will occur in those halftone cells having a constant area of ink. The method and apparatus includes placing a threshold array and the pixel tonal values within the same range if the threshold array and pixel tonal values are in different ranges. The elements in the threshold array are then compared to the pixel tonal values in order to determine a resulting output value.The preferred apparatus for halftoning includes a memory for storing the threshold array; a multiplier for multiplying one 8-bit value representing the number of pixels in a halftone cell by a second 8-bit value which is a pixel tonal value; a comparator for comparing the results of the multiplier with an element from the threshold array; and a multiplexer for selecting a resulting output value based upon the output generated by the comparator.

Abstract: A method and apparatus are disclosed which permit a seamless halftoning of an image by halftoning regions of the image independently and/or in parallel. Each region of the image being arbitrarily determined, and being halftoned on the basis of halftoned pixel results of pixels within a predetermined neighborhood of the region. The arrangement providing a greater flexibility in the independent halftoning of the regions, while providing substantially seamless joins between abutting halftoned regions of the image. Further, the arrangement also provides a mechanism for parallel processing (halftoning) of abutting regions of an image with substantially seamless results.

Abstract: Dither patterns are generated for use in converting a gray-scale image to a bi-level image. The dither patterns simulate halftone screen patterns with arbitrary screen angles. The dither patterns are made up of unit patterns, and have sizes calculated so that the unit patterns match up at the edges of the dither pattern.

Abstract: An image processing system and method is presented which is capable of maintaining a high line count while preventing the generation of low-frequency periodic structures, using the supertiling method for image output devices such as printers. Threshold value matrix patterns are used for each supertile, and the input image data is compared with the threshold value. A dot pattern (binary image data) is generated based on the result of the comparison. Each supertile is divided up into a plurality (3.times.3) of halftone cells, and a dot pattern is generated for each halftone cell. A plurality of threshold value matrix patterns P1-P10 having identical shapes is used, and the pattern to be applied is selected randomly. This results in unevenness in the "centers of gravity" of the dots in the halftone cells. Thus, no periodic structures appear.

Abstract: The dot patterns can be used to reduce dot gain and moire effects in halftone images involve printing areas that have inwardly curved edges and variable elongation. Colored images having screens that use these patterns can be printed with the screens at 45.degree. relative angular separations. Alternatively the dot patterns can be regarded as reversed variable oval patterns with varying elongation of the generally oval shaped non-printing areas.

Abstract: The output mode of an output device for rendering electronic images on an output medium may be characterized by different user-selectable settings such as: paper type, ink type, etc. Apart from the screen characteristics such as screen ruling, frequency and angle, a calibration curve can be communicated via the page description language (e.g. PostScript Level 2) for each color component. Sets of calibration curves can be prepared for specific types of rendering, and be referenced by name. By this name indirection and by naming conventions based upon the output mode or screening parameters, calibration changes can be introduced quickly and consistently.

Abstract: An improved display of a color image is achieved by an optimum placement of color dots using an efficient stochastic screening process in which display elements are formed according to a priority ranking of color and according to a spatial-priority matrix. Various combinations of basic colors are ranked in priority according to visibility such that elements in a stochastic screen are first formed for the most visible colors. The number of elements in the screen that are used to represent more than one basic color is minimized. In preferred embodiments, a spatial-priority matrix is used to control the placement of colors in a stochastic screen such that an optimally uniform distribution of colors is achieved. A process for generating a spatial priority matrix for display devices that do not have a one-to-one display aspect ratio is described.