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76-396: Dither is an intentionally applied form of noise used to randomize quantization error , preventing large-scale patterns such as color banding in images. Dither is routinely used in processing of both digital audio and video data, and is often one of the last stages of mastering audio to a CD . A common use of dither is converting a grayscale image to black and white , so that

152-452: A binomial distribution . In areas where the probability is low, this distribution will be close to the classic Poisson distribution of shot noise. A simple Gaussian distribution is often used as an adequately accurate model. Film grain is usually regarded as a nearly isotropic (non-oriented) noise source. Its effect is made worse by the distribution of silver halide grains in the film also being random. Some noise sources show up with

228-509: A compact disc contains only 16 bits per sample, but throughout the production process, a greater number of bits are typically used to represent the sample, this must be reduced to 16 bits to make the CD. There are multiple ways to do this. One can, for example, simply discard the excess bits – called truncation. One can also round the excess bits to the nearest value. Each of these methods, however, results in predictable and determinable errors in

304-401: A compression artifact . High levels of noise are almost always undesirable, but there are cases when a certain amount of noise is useful, for example to prevent discretization artifacts (color banding or posterization ). Some noise also increases acutance (apparent sharpness). Noise purposely added for such purposes is called dither ; it improves the image perceptually, though it degrades

380-468: A normal distribution . The relationship of probabilities of results follows a bell-shaped, or Gaussian curve , typical of dither generated by analog sources such as microphone preamplifiers. If the bit depth of a recording is sufficiently great, that preamplifier noise will be sufficient to dither the recording. Noise shaping is a filtering process that shapes the spectral energy of quantization error, typically to either de-emphasize frequencies to which

456-535: A standard deviation proportional to the square root of the image intensity, and the noise at different pixels are independent of one another. In addition to photon shot noise, there can be additional shot noise from the dark leakage current in the image sensor; this noise is sometimes known as "dark shot noise" or "dark-current shot noise". Dark current is greatest at "hot pixels" within the image sensor. The variable dark charge of normal and hot pixels can be subtracted off (using "dark frame subtraction"), leaving only

532-511: A better representation of the original ( Figure 3 ). Dithering helps to reduce color banding and flatness. One of the problems associated with using a fixed color palette is that many of the needed colors may not be available in the palette, and many of the available colors may not be needed; a fixed palette containing mostly shades of green would not be well-suited for an image of a desert , for instance. The use of an optimized color palette can be of benefit in such cases. An optimized color palette

608-477: A breakdown of image quality at higher sensitivities in two ways: noise levels increase and fine detail is smoothed out by the more aggressive noise reduction. In cases of extreme noise, such as astronomical images of very distant objects, it is not so much a matter of noise reduction as of extracting a little information buried in a lot of noise; techniques are different, seeking small regularities in massively random data. In video and television , noise refers to

684-527: A computer, involve some form of noise reduction . There are many procedures for this, but all attempt to determine whether the actual differences in pixel values constitute noise or real photographic detail, and average out the former while attempting to preserve the latter. However, no algorithm can make this judgment perfectly (for all cases), so there is often a tradeoff made between noise removal and preservation of fine, low-contrast detail that may have characteristics similar to noise. A simplified example of

760-442: A digital photograph taken in good light, to optical and radioastronomical images that are almost entirely noise, from which a small amount of information can be derived by sophisticated processing. Such a noise level would be unacceptable in a photograph since it would be impossible even to determine the subject. Principal sources of Gaussian noise in digital images arise during acquisition. The sensor has inherent noise due to

836-439: A higher level of added noise for full elimination of audible distortion than noise with rectangular or triangular distribution . Triangular distributed noise also minimizes noise modulation  – audible changes in the volume level of residual noise behind quiet music that draw attention to the noise. Dither can be useful to break up periodic limit cycles , which are a common problem in digital filters. Random noise

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912-415: A lack of need for ISO gain (higher ISO above the base setting of the camera). This equates to a sufficient signal level (from the image sensor) which is passed through the remaining signal processing electronics, resulting in a high signal-to-noise ratio, or low noise, or optimal exposure. Conversely, in darker conditions, faster shutter speeds, closed apertures, or some combination of all three, there can be

988-456: A lack of sufficient photons hitting the image sensor to generate a suitable voltage from the image sensor to overcome the noise floor of the signal chain, resulting in a low signal-to-noise ratio, or high noise (predominately read noise). In these conditions, increasing ISO gain (higher ISO setting) will increase the image quality of the output image, as the ISO gain will amplify the low voltage from

1064-508: A significant orientation in images. For example, image sensors are sometimes subject to row noise or column noise. A common source of periodic noise in an image is from electrical interference during the image capturing process. An image affected by periodic noise will look like a repeating pattern has been added on top of the original image. In the frequency domain this type of noise can be seen as discrete spikes. Significant reduction of this noise can be achieved by applying notch filters in

1140-433: A similar effect. By alternating each pixel's color value rapidly between two approximate colors in the panel's color space, a display panel that natively supports only 18-bit color (6 bits per channel) can represent a 24-bit color image (8 bits per channel). Dithering such as this, in which the computer's display hardware is the primary limitation on color depth , is commonly employed in software such as web browsers . Since

1216-439: A similar, but non-random, display. The dominant noise in the brighter parts of an image from an image sensor is typically that caused by statistical quantum fluctuations, that is, variation in the number of photons sensed at a given exposure level. This noise is known as photon shot noise . Shot noise follows a Poisson distribution , which can be approximated by a Gaussian distribution for large image intensity. Shot noise has

1292-401: A true feature of the image. But a definitive answer is not available. This decision can be assisted by knowing the characteristics of the source image and of human vision. Most noise reduction algorithms perform much more aggressive chroma noise reduction, since there is little important fine chroma detail that one risks losing. Furthermore, many people find luminance noise less objectionable to

1368-438: A web browser may be retrieving graphical elements from an external source, it may be necessary for the browser to perform dithering on images with too many colors for the available display. It was due to problems with dithering that a color palette known as the web-safe color palette was identified, for use in choosing colors that would not be dithered on systems capable of displaying only 256 colors simultaneously. But even when

1444-434: Is correlated to the signal, the result is potentially cyclical or predictable. In some fields, especially where the receptor is sensitive to such artifacts, cyclical errors yield undesirable artifacts. In these fields introducing dither converts the error to random noise. The field of audio is a primary example of this. The human ear functions much like a Fourier transform , wherein it hears individual frequencies. The ear

1520-403: Is a nonlinear optical effect that limits the launched optical power in fiber optic systems. This power limit can be increased by dithering the transmit optical center frequency, typically implemented by modulating the laser's bias input. See also polarization scrambling . Phase dithering can be used to improve the quality of the output in direct digital synthesis . Another common application

1596-400: Is a discrete step... if a signal is quantized without using dither, there will be quantization distortion related to the original input signal... In order to prevent this, the signal is "dithered", a process that mathematically removes the harmonics or other highly undesirable distortions entirely, and that replaces it with a constant, fixed noise level. The final version of audio that goes onto

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1672-517: Is a major part of the "read noise" of an image sensor, that is, of the constant noise level in dark areas of the image. In color cameras where more amplification is used in the blue color channel than in the green or red channel, there can be more noise in the blue channel. At higher exposures, however, image sensor noise is dominated by shot noise, which is not Gaussian and not independent of signal intensity. Also, there are many Gaussian denoising algorithms. Fat-tail distributed or "impulsive" noise

1748-455: Is a photograph, it is likely to have thousands or even millions of distinct colors. The process of constraining the available colors to a specific color palette effectively throws away a certain amount of color information. A number of factors can affect the resulting quality of a color-reduced image. Perhaps most significant is the color palette that will be used in the reduced image. For example, an original image ( Figure 1 ) may be reduced to

1824-399: Is analogous to the halftone technique used in printing . For this reason, the term dithering is sometimes used interchangeably with the term halftoning , particularly in association with digital printing . The ability of inkjet printers to print isolated dots has increased the use of dithering in printing. A typical desktop inkjet printer can print, at most, just 16 colors as this is

1900-448: Is application specific. For example, if the fine details on the castle are not considered important, low pass filtering could be an appropriate option. If the fine details of the castle are considered important, a viable solution may be to crop off the border of the image entirely. In low light, correct exposure requires the use of slow shutter speed (i.e. long exposure time) or an opened aperture (lower f-number ), or both, to increase

1976-411: Is appropriate. This can effectively lower the audible noise level, by putting most of that noise in a frequency range where it is less critical. Dithering is used in computer graphics to create the illusion of color depth in images on systems with a limited color palette . In a dithered image, colors that are not available in the palette are approximated by a diffusion of colored pixels from within

2052-402: Is explicitly applied. The grain of photographic film is a signal-dependent noise, with similar statistical distribution to shot noise . If film grains are uniformly distributed (equal number per area), and if each grain has an equal and independent probability of developing to a dark silver grain after absorbing photons , then the number of such dark grains in an area will be random with

2128-436: Is for situations in which the graphics file format is the limiting factor. In particular, the commonly used GIF format is restricted to the use of 256 or fewer colors. Images such as these have a defined color palette containing a limited number of colors that the image may use. For such situations, graphical editing software may be responsible for dithering images prior to saving them in such restrictive formats. Dithering

2204-409: Is indicative of light density in the focal plane (e.g., photons per square micron). With constant f-numbers, as focal length increases, the lens aperture diameter increases, and the lens collects more light from the subject. As the focal length required to capture a scene at a specific angle of view is roughly proportional to the width of the sensor, given an f-number the amount of light collected

2280-637: Is one in which the available colors are chosen based on how frequently they are used in the original source image. If the image is reduced based on an optimized palette the result is often much closer to the original ( Figure 4 ). The number of colors available in the palette is also a contributing factor. If, for example, the palette is limited to only 16 colors then the resulting image could suffer from additional loss of detail, resulting in even more pronounced problems with flatness and color banding ( Figure 5 ). Once again, dithering can help to minimize such artifacts ( Figure 6 ). One common application of dithering

2356-427: Is one such application. If the signal being dithered is to undergo further processing, then it should be processed with a triangular-type dither that has an amplitude of two quantization steps so that the dither values computed range from, for example, −1 to +1, or 0 to 2. This is the lowest power ideal dither, in that it does not introduce noise modulation (which would manifest as a constant noise floor), and eliminates

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2432-411: Is possible to round up or down in a random pattern. If a series of random numbers between 0.0 and 0.9 (ex: 0.6, 0.1, 0.3, 0.6, 0.9, etc.) is generated and added to the 4.8, two times out of ten the result will truncate back to 4 (if 0.0 or 0.1 are added to 4.8) and eight times out of ten it will truncate to 5. Each given situation has a random 20% chance of rounding to 4 or 80% chance of rounding to 5. Over

2508-403: Is roughly proportional to the area of the sensor, resulting in a better signal-to-noise ratio for larger sensors. With constant aperture diameters, the amount of light collected and the signal-to-noise ratio for shot noise are both independent of sensor size. In the case of images bright enough to be in the shot noise limited regime, when the image is scaled to the same size on screen, or printed at

2584-498: Is sometimes called salt-and-pepper noise or spike noise. An image containing salt-and-pepper noise will have dark pixels in bright regions and bright pixels in dark regions. This type of noise can be caused by analog-to-digital converter errors, bit errors in transmission, etc. It can be mostly eliminated by using dark frame subtraction , median filtering , combined median and mean filtering and interpolating around dark/bright pixels. Dead pixels in an LCD monitor produce

2660-402: Is the least unsightly and distracting. The error diffusion techniques were some of the first methods to generate blue-noise dithering patterns. However, other techniques such as ordered dithering can also generate blue-noise dithering without the tendency to degenerate into areas with artifacts. Reducing the color depth of an image can have significant visual side effects. If the original image

2736-463: Is the same. For example, the noise level produced by a Four Thirds sensor at ISO 800 is roughly equivalent to that produced by a full frame sensor (with roughly four times the area) at ISO 3200, and that produced by a 1/2.5" compact camera sensor (with roughly 1/16 the area) at ISO 100. All cameras will have roughly the same ISO setting for a given scene at the same shutter speed and the same f-number – resulting in substantially less noise with

2812-429: Is therefore very sensitive to distortion , or additional frequency content, but far less sensitive to additional random noise at all frequencies such as found in a dithered signal. In an analog system, the signal is continuous , but in a PCM digital system, the amplitude of the signal out of the digital system is limited to one of a set of fixed values or numbers. This process is called quantization . Each coded value

2888-464: Is to get through EMC tests by using spread spectrum clock dithering of frequency to smear out single frequency peaks. Another type of temporal dithering has recently been introduced in financial markets , in order to reduce the incentive to engage in high-frequency trading . ParFX, a London foreign exchange market that began trading in 2013, imposes brief random delays on all incoming orders; other currency exchanges are reportedly experimenting with

2964-424: Is to more accurately display graphics containing a greater range of colors than the display hardware is capable of showing. For example, dithering might be used in order to display a photographic image containing millions of colors on video hardware that is only capable of showing 256 colors at a time. The 256 available colors would be used to generate a dithered approximation of the original image. Without dithering,

3040-516: Is typically less objectionable than the harmonic tones produced by limit cycles. Rectangular probability density function (RPDF) dither noise has a uniform distribution ; any value in the specified range has the same probability of occurring. Triangular probability density function (TPDF) dither noise has a triangular distribution ; values in the center of the range have a higher probability of occurring. Triangular distribution can be achieved by adding two independent RPDF sources. Gaussian PDF has

3116-415: The signal-to-noise ratio . An image sensor in a digital camera contains a fixed amount of pixels (which define the advertised megapixels of the camera). These pixels have what is called a well depth. The pixel well can be thought of as a bucket. The ISO setting on a digital camera is the first (and sometimes only) user adjustable ( analog ) gain setting in the signal processing chain . It determines

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3192-523: The 216-color web-safe palette . If the original pixel colors are simply translated into the closest available color from the palette, no dithering will occur ( Figure 2 ). However, typically this approach will result in flat areas (contours) and a loss of detail and may produce patches of color that are significantly different from the original. Shaded or gradient areas may produce color banding which may be distracting. The application of dithering can help to minimize such visual artifacts and usually results in

3268-504: The amount of gain applied to the voltage output from the image sensor and has a direct effect on read noise . All signal processing units within a digital camera system have a noise floor . The difference between the signal level and the noise floor is called the signal-to-noise ratio . A higher signal-to-noise ratio equates to a better quality image. In bright sunny conditions, a slow shutter speed, wide open aperture, or some combination of all three, there can be sufficient photons hitting

3344-418: The amount of light (photons) captured which in turn reduces the impact of shot noise. If the limits of shutter (motion) and aperture (depth of field) have been reached and the resulting image is still not bright enough, then higher gain ( ISO sensitivity ) should be used to reduce read noise. On most cameras, slower shutter speeds lead to increased salt-and-pepper noise due to photodiode leakage currents . At

3420-456: The available palette. The human eye perceives the diffusion as a mixture of the colors within it (see color vision ). Dithered images, particularly those using palettes with relatively few colors, can often be distinguished by a characteristic graininess or speckled appearance. Dithering introduces noise or a pattern into an image, and often the patterning is visible. In these circumstances, it has been shown that dither generated from blue noise

3496-449: The colors in the original image would be quantized to the closest available color, resulting in a displayed image that is a poor representation of the original. The very earliest uses were to reduce images to 1-bit black and white. This may have been done for printing even earlier than for bit-mapped video graphics. It was common for making images to display on 1-bit video displays for X and Apollo and similar Unix workstations. The dithering

3572-476: The combination of dot or no dot from cyan, magenta, yellow and black print heads. To reproduce a large range of colors, dithering is used. In densely printed areas, where the color is dark the dithering is not always visible because the dots of ink merge producing a more uniform print. However, a close inspection of the light areas of a print where dots are further apart reveals dithering patterns. There are several algorithms designed to perform dithering. One of

3648-430: The cost of a doubling of read noise variance (41% increase in read noise standard deviation), this salt-and-pepper noise can be mostly eliminated by dark frame subtraction . Banding noise, similar to shadow noise , can be introduced through brightening shadows or through color-balance processing. In digital photography, incoming photons are converted to a charge in the form of electrons. This voltage then passes through

3724-432: The density of black dots in the new image approximates the average gray level in the original. The term dither was published in books on analog computation and hydraulically controlled guns shortly after World War II . Though he did not use the term dither , the concept of dithering to reduce quantization patterns was first applied by Lawrence G. Roberts in his 1961 MIT master's thesis and 1962 article. By 1964 dither

3800-448: The ear is most sensitive or separate the signal and noise bands completely. If dither is used, its final spectrum depends on whether it is added inside or outside the feedback loop of the noise shaper. If inside, the dither is treated as part of the error signal and shaped along with actual quantization error. If outside, the dither is treated as part of the original signal and linearises quantization without being shaped itself. In this case,

3876-494: The earliest, and still one of the most popular, is the Floyd–Steinberg dithering algorithm, which was developed in 1975. One of the strengths of this algorithm is that it minimizes visual artifacts through an error-diffusion process; error-diffusion algorithms typically produce images that more closely represent the original than simpler dithering algorithms. Dithering methods include: Stimulated Brillouin scattering (SBS)

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3952-423: The eye, since its textured appearance mimics the appearance of film grain . The high sensitivity image quality of a given camera (or RAW development workflow) may depend greatly on the quality of the algorithm used for noise reduction. Since noise levels increase as ISO sensitivity is increased, most camera manufacturers increase the noise reduction aggressiveness automatically at higher sensitivities. This leads to

4028-416: The fill factor is close to 100%. Temperature can also have an effect on the amount of noise produced by an image sensor due to leakage. With this in mind, it is known that DSLRs will produce more noise during summer than in winter. An image is a picture, photograph or any other form of 2D representation of any scene. Most algorithms for converting image sensor data to an image, whether in-camera or on

4104-411: The final noise floor is the sum of the flat dither spectrum and the shaped quantization noise. While real-world noise shaping usually includes in-loop dithering, it is also possible to use it without adding dither at all, in which case quantization error is evident at low signal levels. Colored dither is sometimes mentioned as dither that has been filtered to be different from white noise . Noise shaping

4180-411: The first four times out of five it is rounded up to 5, and the fifth time it is rounded to 4. This would average out to exactly 4.8 over the long term. Unfortunately, however, it still results in repeatable and determinable errors, and those errors still manifest themselves as distortion to the ear. This leads to the dither solution. Rather than predictably rounding up or down in a repeating pattern, it

4256-410: The frequency domain. The following images illustrate an image affected by periodic noise, and the result of reducing the noise using frequency domain filtering. Note that the filtered image still has some noise on the borders. Further filtering could reduce this border noise, however it may also reduce some of the fine details in the image. The trade-off between noise reduction and preserving fine details

4332-540: The full frame camera. Conversely, if all cameras were using lenses with the same aperture diameter, the ISO settings would be different across the cameras, but the noise levels would be roughly equivalent. The image sensor has individual photosites to collect light from a given area. Not all areas of the sensor are used to collect light, due to other circuitry. A higher fill factor of a sensor causes more light to be collected, allowing for better ISO performance based on sensor size. With backside-illuminated CMOS sensors,

4408-416: The harmonic distortion from quantization. If a colored dither is used instead at these intermediate processing stages, then frequency content may bleed into other frequency ranges that are more noticeable and become distractingly audible. If the signal being dithered is to undergo no further processing – if it is being dithered to its final result for distribution – then a colored dither or noise shaping

4484-411: The image sensor and generate a higher signal-to-noise ratio through the remaining signal processing electronics. It can be seen that a higher ISO setting (applied correctly) does not, in and of itself, generate a higher noise level, and conversely, a higher ISO setting reduces read noise. The increase in noise often found when using a higher ISO setting is a result of the amplification of shot noise and

4560-434: The image sensor to completely fill, or otherwise reach near capacity of the pixel wells. If the capacity of the pixel wells is exceeded, this equates to over exposure . When the pixel wells are at near capacity, the photons themselves that have been exposed to the image sensor, generate enough energy to excite the emission of electrons in the image sensor and generate sufficient voltage at the image sensor output, equating to

4636-426: The impossibility of unambiguous noise reduction: an area of uniform red in an image might have a very small black part. If this is a single pixel, it is likely (but not certain) to be spurious and noise; if it covers a few pixels in an absolutely regular shape, it may be a defect in a group of pixels in the image-taking sensor (spurious and unwanted, but not strictly noise); if it is irregular, it may be more likely to be

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4712-438: The level of illumination and its own temperature, and the electronic circuits connected to the sensor inject their own share of electronic circuit noise . A typical model of image noise is Gaussian, additive, independent at each pixel , and independent of the signal intensity, caused primarily by Johnson–Nyquist noise (thermal noise), including that which comes from the reset noise of capacitors ("kTC noise"). Amplifier noise

4788-481: The long haul, these results will average to 4.8 and their quantization error will be random noise. This noise is less offensive to the ear than the determinable distortion that other solutions would produce. Dither is added before any quantization or re-quantization process, in order to de-correlate the quantization noise from the input signal and to prevent non-linear behavior (distortion). Quantization with lesser bit depth requires higher amounts of dither. The result of

4864-424: The long-term average 4.5 instead of 4, so that over the long-term the value is closer to its actual value. This, on the other hand, still results in determinable (though more complicated) error. Every other time the value 4.8 comes up the result is an error of 0.2, and the other times it is −0.8. This still results in a repeating, quantifiable error. Another plausible solution would be to take 4.8 and round it so that

4940-518: The process still yields distortion, but the distortion is of a random nature so the resulting noise is, effectively, de-correlated from the intended signal. In a seminal paper published in the AES Journal , Lipshitz and Vanderkooy pointed out that different noise types, with different probability density functions (PDFs) behave differently when used as dither signals, and suggested optimal levels of dither signal for audio. Gaussian noise requires

5016-457: The random dot pattern that is superimposed on the picture as a result of electronic noise, the "snow" that is seen with poor (analog) television reception or on VHS tapes. Interference and static are other forms of noise, in the sense that they are unwanted, though not random, which can affect radio and television signals. Digital noise is sometimes present on videos encoded in MPEG-2 format as

5092-422: The result. Using dither replaces these errors with a constant, fixed noise level. Take, for example, a waveform that consists of the following values: If the waveform is reduced by 20%, then the following are the new values: If these values are truncated it results in the following data: If these values are rounded instead it results in the following data: For any original waveform, the process of reducing

5168-405: The same size, the pixel count makes little difference to perceptible noise levels – the noise depends primarily on the total light over the whole sensor area, not how this area is divided into pixels. For images at lower signal levels (higher ISO settings) where read noise (noise floor) is significant, more pixels within a given sensor area will make the image noisier if the per pixel read noise

5244-605: The shot noise, or random component, of the leakage. If dark-frame subtraction is not done, or if the exposure time is long enough that the hot pixel charge exceeds the linear charge capacity, the noise will be more than just shot noise, and hot pixels appear as salt-and-pepper noise. The noise caused by quantizing the pixels of a sensed image to a number of discrete levels is known as quantization noise. It has an approximately uniform distribution . Though it can be signal dependent, it will be signal independent if other noise sources are big enough to cause dithering , or if dithering

5320-491: The signal processing chain of the digital camera and is digitized by an analog-to-digital converter . Any voltage fluctuations in the signal processing chain that contribute to deviation from the ideal value, proportional to the photon count, are called read noise. The amount of light collected over the whole sensor during the exposure is the largest determinant of signal levels that determine signal-to-noise ratio for shot noise and hence apparent noise levels. The f-number

5396-427: The sine wave's cycle. It is precisely this error that manifests itself as distortion . What the ear hears as distortion is the additional content at discrete frequencies created by the regular and repeated quantization error. A plausible solution would be to take the 2 digit number (say, 4.8) and round it one direction or the other. For example, it could be rounded to 5 one time and then 4 the next time. This would make

5472-479: The technique. The use of such temporal buffering or dithering has been advocated more broadly in financial trading of equities, commodities, and derivatives. Image noise The original meaning of "noise" was "unwanted signal"; unwanted electrical fluctuations in signals received by AM radios caused audible acoustic noise ("static"). By analogy, unwanted electrical fluctuations are also called "noise". Image noise can range from almost imperceptible specks on

5548-436: The total number of available colors in the display hardware is high enough to properly render full-color digital photographs, banding may still be evident to the eye, especially in large areas of smooth shade transitions. Modest dithering can resolve this without making the image appear grainy . High-end still image processing software commonly uses these techniques for improved display. Another useful application of dithering

5624-452: The waveform amplitude by 20% results in regular errors. Take for example a sine wave that, for some portion, matches the values above. Every time the sine wave's value hit 3.2, the truncated result would be off by 0.2, as in the sample data above. Every time the sine wave's value hit 4.0, there would be no error since the truncated result would be off by 0.0, also shown above. The magnitude of this error changes regularly and repeatedly throughout

5700-472: Was being used in the modern sense described in this article. The technique was in use at least as early as 1915, though not under the name dither . Dither is utilized in many different fields where digital processing and analysis are used. These uses include systems using digital signal processing , such as digital audio , digital video , digital photography , seismology , radar and weather forecasting systems. Quantization yields error. If that error

5776-423: Was usually pre-computed and only the dithered image was stored; computation and memory were far too limited to compute it live . An example home computer users may have seen was emulation of lower resolution CGA 4 color graphics on higher resolution monochrome Hercules graphics cards , with the colors being translated to ordered dither patterns. Some liquid-crystal displays use temporal dithering to achieve

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