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Chroma key

Chroma key compositing, or chroma keying, is a visual-effects and post-production technique for compositing (layering) two or more images or video streams together based on colour hues (chroma range). The technique has been used in many fields to remove a background from the subject of a photo or video – particularly the newscasting, motion picture, and video game industries. A colour range in the foreground footage is made transparent, allowing separately filmed background footage or a static image to be inserted into the scene. The chroma keying technique is commonly used in video production and post-production. This technique is also referred to as colour keying, colour-separation overlay (CSO; primarily by the BBC ), or by various terms for specific colour-related variants such as green screen or blue screen; chroma keying can be done with backgrounds of any colour that are uniform and distinct, but green and blue backgrounds are more commonly used because they differ most distinctly in hue from any human skin colour. No part of the subject being filmed or photographed may duplicate the colour used as the backing, or the part may be erroneously identified as part of the backing.

It is commonly used for live weather forecast broadcasts in which a news presenter is seen standing in front of a large CGI map which is really a large blue or green background. Using a blue screen, different weather maps are added on the parts of the image in which the colour is blue. If the news presenter wears blue clothes, their clothes will also be replaced with the background video. Chroma keying is also common in the entertainment industry for visual effects in movies and video games. Rotoscopy may instead be carried out on subjects that are not in front of a green (or blue) screen. Motion tracking can also be used in conjunction with chroma keying, such as to move the background as the subject moves.

Predecessors
Prior to the introduction of travelling mattes and optical printing, double exposure was used to introduce elements into a scene which were not present in the initial exposure. This was done using black draping where a green screen would be used today. George Albert Smith first used this approach in 1898. In 1903, The Great Train Robbery by Edwin S. Porter used double exposure to add background scenes to windows which were black when filmed on set, using a garbage matte to expose only the window areas.

In order to have figures in one exposure actually move in front of a substituted background in the other, a travelling matte was needed, to occlude the correct portion of the background in each frame. In 1918 Frank Williams patented a travelling matte technique, again based on using a black background. This was used in many films, such as The Invisible Man.

In the 1920s, Walt Disney used a white backdrop to include human actors with cartoon characters and backgrounds in his Alice Comedies.

From bluescreen to greenscreen
The blue screen method was developed in the 1930s at RKO Radio Pictures. At RKO, Linwood Dunn used an early version of the travelling matte to create "wipes" – where there were transitions like a windshield wiper in films such as Flying Down to Rio (1933). Credited to Larry Butler, a scene featuring a genie escaping from a bottle was the first use of a proper bluescreen process to create a travelling matte for The Thief of Bagdad (1940), which won the Academy Award for Best Special Effects that year. In 1950, Warner Brothers employee and ex-Kodak researcher Arthur Widmer began working on an ultraviolet travelling matte process. He also began developing bluescreen techniques: one of the first films to use them was the 1958 adaptation of the Ernest Hemingway novella, The Old Man and the Sea, starring Spencer Tracy.

The name "Chroma-Key" was RCA's trade name for the process, as used on its NBC television broadcasts, incorporating patents granted to RCA's Albert N. Goldsmith. A very early broadcast use was NBC's George Gobel Show in fall 1957.

Petro Vlahos was awarded an Academy Award for his refinement of these techniques in 1964. His technique exploits the fact that most objects in real-world scenes have a colour whose blue-colour component is similar in intensity to their green-colour component. Zbigniew Rybczyński also contributed to bluescreen technology. An optical printer with two projectors, a film camera and a "beam splitter", was used to combine the actor in front of a blue screen together with the background footage, one frame at a time. In the early 1970s, American and British television networks began using green backdrops instead of blue for their newscasts. During the 1980s, minicomputers were used to control the optical printer. For the film The Empire Strikes Back, Richard Edlund created a "quad optical printer" that accelerated the process considerably and saved money. He received a special Academy Award for his innovation.

For decades, travelling matte shots had to be done "locked-down", so that neither the matted subject nor the background could shift their camera perspective at all. Later, computer-timed, motion-control cameras alleviated this problem, as both the foreground and background could be filmed with the same camera moves.

Meteorologists on television often use a field monitor, to the side of the screen, to see where they are putting their hands against the background images. A newer technique is to project a faint image onto the screen.

Some films make heavy use of chroma key to add backgrounds that are constructed entirely using computer-generated imagery (CGI). Performances from different takes can be composited together, which allows actors to be filmed separately and then placed together in the same scene. Chroma key allows performers to appear to be in any location without leaving the studio.

Advances in computer technology have simplified the incorporation of motion into composited shots, even when using handheld cameras. Reference points such as a painted grid, X's marked with tape, or equally spaced tennis balls attached to the wall, can be placed onto the coloured background to serve as markers. In post-production, a computer can use these markers to compute the camera's position and thus render an image that matches the perspective and movement of the foreground perfectly. Modern advances in software and computational power have eliminated the need to accurately place the markers — the software figures out their position in space; a potential disadvantage of this is that it requires camera movement, possibly contributing to modern cinematographic techniques whereby the camera is always in motion.

Process

The principal subject is filmed or photographed against a background consisting of a single colour or a relatively narrow range of colours, usually blue or green because these colours are considered to be the furthest away from skin tone. The portions of the video which match the pre-selected colour are replaced by the alternate background video. This process is commonly known as "keying", "keying out" or simply a "key".

Processing a green backdrop
Green is used as a backdrop for TV and electronic cinematography more than any other colour because television weather presenters tended to wear blue suits. When chroma keying first came into use in television production, the blue screen that was then the norm in the movie industry was used out of habit, until other practical considerations caused the television industry to move from blue to green screens. Broadcast-quality colour television cameras use separate red, green and blue image sensors, and early analog TV chroma keyers required RGB component video to work reliably. From a technological perspective it was equally possible to use the blue or green channel, but because blue clothing was an ongoing challenge, the green screen came into common use. Newscasters sometimes forget the chroma key dress code, and when the key is applied to clothing of the same colour as the background, the person would seem to disappear into the key. Because green clothing is less common than blue, it soon became apparent that it was easier to use a green matte screen than it was to constantly police the clothing choices of on-air talent. Also, because the human eye is more sensitive to green wavelengths, which lie in the middle of the visible light spectrum, the green analog video channel typically carried more signal strength, giving a better signal to noise ratio compared to the other component video channels, so green screen keys could produce the cleanest key. In the digital television and cinema age, much of the tweaking that was required to make a good quality key has been automated. However, the one constant that remains is some level of colour coordination to keep foreground subjects from being keyed out.

Processing a blue backdrop
Before electronic chroma keying, compositing was done on (chemical) film. The camera colour negative was printed onto high-contrast black and white negative, using either a filter or the high contrast film's colour sensitivity to expose only blue (and higher) frequencies. Blue light only shines through the colour negative where there is not blue in the scene, so this left the film clear where the blue screen was, and opaque elsewhere, except it also produced clear for any white objects (since they also contained blue). Removing these spots could be done by a suitable double-exposure with the colour positive (thus turning any area containing red or green opaque), and many other techniques. The result was film that was clear where the blue screen was, and opaque everywhere else. This is called a female matte, similar to an alpha matte in digital keying. Copying this film onto another high-contrast negative produced the opposite male matte. The background negative was then packed with the female matte and exposed onto a final strip of film, then the camera negative was packed with the male matte and was double-printed onto this same film. These two images combined creates the final effect.

Major factors
The most important factor for a key is the colour separation of the foreground (the subject) and background (the screen) – a blue screen will be used if the subject is predominantly green (for example plants), despite the camera being more sensitive to green light.

In analog television, colour is represented by the phase of the chroma subcarrier relative to a reference oscillator. Chroma key is achieved by comparing the phase of the video to the phase corresponding to the pre-selected colour. In-phase portions of the video are replaced by the alternate background video.

In digital colour TV, colour is represented by three numbers (red, green, blue intensity levels). Chroma key is achieved by a simple numerical comparison between the video and the pre-selected colour. If the colour at a particular point on the screen matches (either exactly, or in a range), then the video at that point is replaced by the alternate background.

Lighting
In order to create an illusion that characters and objects filmed are present in the intended background scene, the lighting in the two scenes must be a reasonable match. For outdoor scenes, overcast days create a diffuse, evenly coloured light which can be easier to match in the studio, whereas direct sunlight needs to be matched in both direction and overall colour based on time of day.

A studio shot taken in front of a green screen will naturally have ambient light the same colour as the screen, due to its light scattering. This effect is known as spill. This can look unnatural or cause portions of the characters to disappear, so must be compensated for, or avoided by using a larger screen placed far from the actors.

Camera
The depth of field used to record the scene in front of the coloured screen should match that of the background. This can mean recording the actors with a larger depth of field than normal.

Clothing
A chroma key subject must avoid wearing clothes which are similar in colour to the chroma key colour(s) (unless intentional e.g., wearing a green top to make it appear that the subject has no body), because the clothing may be replaced with the background image/video. An example of intentional use of this is when an actor wears a blue covering over a part of his body to make it invisible in the final shot. This technique can be used to achieve an effect similar to that used in the Harry Potter films to create the effect of an invisibility cloak. The actor can also be filmed against a chroma-key background and inserted into the background shot with a distortion effect, in order to create a cloak that is marginally detectable.

Difficulties emerge with blue screen when a costume in an effects shot must be blue, such as Superman's traditional blue outfit. In the 2002 film Spider-Man, in scenes where both Spider-Man and the Green Goblin are in the air, Spider-Man had to be shot in front of a green screen and the Green Goblin had to be shot in front of a blue screen. The colour difference is because Spider-Man wears a costume which is red and blue in colour and the Green Goblin wears a costume which is entirely green in colour. If both were shot in front of the same screen, parts of one character would be erased from the shot.

For a clean division of foreground from background, it is also important that clothing and hair in the foreground shot have a fairly simple silhouette, as fine details such as frizzy hair may not resolve properly. Similarly, partially transparent elements of the costume cause problems.

Background colour

Blue was originally used for the film industry as making the separations required a film that would only respond to the screen colour, and film that responded only to blue and higher frequencies (ultraviolet, etc.) was far easier to manufacture and make reliable than film that somehow excluded both frequencies higher and lower than the screen colour.

In television and digital film making, however, it is equally easy to extract any colour, and green quickly became the favoured colour. Bright green is less likely to be in the foreground objects, colour film emulsions usually had much finer grain in the green, and lossy compression used for analog video signals and digital images and movies retain more detail in the green channel. Green can also be used outdoors where the light colour temperature is significantly blue. Red is avoided as it is in human skin, and any other colour is a mix of primaries and thus produces a less clean extraction.

A so-called "yellow screen" is accomplished with a white backdrop. Ordinary stage lighting is used in combination with a bright yellow sodium lamp. The sodium light falls almost entirely in a narrow frequency band, which can then be separated from the other light using a prism, and projected onto a separate but synchronized film carrier within the camera. This second film is high-contrast black and white, and is processed to produce the matte.

A newer technique is to use a retroreflective curtain in the background, along with a ring of bright LEDs around the camera lens. This requires no light to shine on the background other than the LEDs, which use an extremely small amount of power and space unlike big stage lights, and require no rigging. This advance was made possible by the invention in the 1990s of practical blue LEDs, which also allow for emerald green LEDs.

There is also a form of colour keying that uses light spectrum invisible to human eye. Called Thermo-Key, it uses infrared as the key colour, which would not be replaced by background image during postprocessing.

For Star Trek: The Next Generation, an ultraviolet light matting process was proposed by Don Lee of CIS Hollywood and developed by Gary Hutzel and the staff of Image G. This involved a fluorescent orange backdrop which made it easier to generate a holdout matte, thus allowing the effects team to produce effects in a quarter of the time needed for other methods.

In principle, any type of still background can be used as a chroma key instead of a solid colour. First the background is captured without actors or other foreground elements; then the scene is recorded. The image of the background is used to cancel the background in the actual footage; for example in a digital image, each pixel will have a different chroma key. This is sometimes referred to as a difference matte. However, this makes it easy for objects to be accidentally removed if they happen to be similar to the background, or for the background to remain due to camera noise or if it happens to change slightly from the reference footage. A background with a repeating pattern alleviates many of these issues, and can be less sensitive to wardrobe colour than solid-colour backdrops.

There is some use of the specific full-intensity magenta colour in digital colour images to encode (1-bit) transparency; this is sometimes referred to as "magic pink". This is not a photographic technique and the extraction of the foreground from the background is trivial.

Even lighting

The biggest challenge when setting up a blue screen or green screen is even lighting and the avoidance of shadow because it is best to have as narrow a colour range as possible being replaced. A shadow would present itself as a darker colour to the camera and might not register for replacement. This can sometimes be seen in low-budget or live broadcasts where the errors cannot be manually repaired or scenes reshot. The material being used affects the quality and ease of having it evenly lit. Materials which are shiny will be far less successful than those that are not. A shiny surface will have areas that reflect the lights making them appear pale, while other areas may be darkened. A matte surface will diffuse the reflected light and have a more even colour range. In order to get the cleanest key from shooting green screen, it is necessary to create a value difference between the subject and the green screen. In order to differentiate the subject from the screen, a two-stop difference can be used, either by making the green screen two stops higher than the subject, or vice versa.

Sometimes a shadow can be used to create a visual effect. Areas of the blue screen or green screen with a shadow on them can be replaced with a darker version of the desired background video image, making it look like the person is casting a shadow on them. Any spill of the chroma key colour will make the result look unnatural. A difference in the focal length of the lenses used can affect the success of chroma key.

Exposure
Another challenge for blue screen or green screen is proper camera exposure. Underexposing or overexposing a coloured backdrop can lead to poor saturation levels. In the case of video cameras, underexposed images can contain high amounts of noise, as well. The background must be bright enough to allow the camera to create a bright and saturated image.

Programming
There are several different quality- and speed-optimised techniques for implementing colour keying in software.

In most versions, a function f(r, g, b) → α is applied to every pixel in the image. α (alpha) has a meaning similar to that in alpha compositing techniques. α ≤ 0 means the pixel is fully in the green screen, α ≥ 1 means the pixel is fully in the foreground object, and intermediate values indicate the pixel is partially covered by the foreground object (or it is transparent). A further function g(r, g, b) → (r, g, b) is needed to remove green spill on the foreground objects.

A very simple f function for green screen is A(r+b) − Bg where A and B are user adjustable constants with a default value of 1.0. A very simple g is (r, min(g,b), b). This is fairly close to the capabilities of analog and film-based screen pulling.

Modern examples of these functions are best described by two closed nested surfaces in 3D RGB space, often quite complex. Colours inside the inner surface are considered green screen. Colours outside the outer surface are opaque foreground. Colours between the surfaces are partially covered, they are more opaque the closer they are to the outer surface. Sometimes more closed surfaces are used to determine how to remove green spill. It is also very common for f to depend on more than just the current pixel's colour, it may also use the (x, y) position, the values of nearby pixels, the value from reference images or a statistical colour model of the scene, and values from user-drawn masks. These produce closed surfaces in space with more than three dimensions.

A different class of algorithm tries to figure out a 2D path that separates the foreground from the background. This path can be the output, or the image can be drawn by filling the path with α = 1 as a final step. An example of such an algorithm is the use of active contour. Most research in recent years has been into these algorithms.

title: Chroma key


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Lock

Lock(s) may refer to:

Common meanings

 * Lock and key, a mechanical device used to secure items of importance
 * Lock (water navigation), a device for boats to transit between different levels of water, as in a canal

Arts and entertainment

 * Lock (film), a 2016 Punjabi- language film
 * Lock (Saga of the Skolian Empire), a sentient machine in the novels by Catherine Asaro
 * Lock (waltz), a dance figure
 * Locked (miniseries), Indian web miniseries
 * The Lock (Constable), an 1825 painting by John Constable
 * The Lock (Fragonard) or The Bolts , a 1777 painting by Jean-Honoré Fragrance
 * Locks (album), by Garnet Crow, 2009
 * Locked (miniseries), an crime thriller miniserieses

Fictional characters

 * Lock, from The Nightmare Before Christmas
 * Lock, from Go! Princess PreCure

People

 * Lock (surname)
 * Ormer Locklear (1891–1920), American stunt pilot and film actor nicknamed "Lock"
 * George Locks (1889–1965), English cricketer
 * Lock Martin (1916–1959), stage name of American actor Joseph Lockard Martin, Jr.

Places

 * Lock, Ohio , an unincorporated community in the United States
 * Lock, South Australia, a small town in the center of the Eyre Peninsula
 * Lock Island, an island in the River Thames in England
 * Lock Island (Nunavut), an island Peel Sound in Nunavut, Canada

Sports

 * Lock (rugby league), a player position in rugby league, known as loose forward in the United Kingdom
 * Lock (rugby union), a player position in rugby union
 * Lock, any of several grappling holds in wrestling, judo and other martial arts

Computing

 * Lock (computer science), a bookkeeping object used to serialize concurrent access
 * Lock (database), a feature used when multiple users access a database concurrently
 * File locking, describes a mechanism that restricts access to a computer file
 * SIM lock, a restriction on mobile phones to work only in certain countries or with certain providers

Other technologies

 * Lock and key, a mechanical device used to secure items of importance
 * Lock (firearm), the ignition mechanism of small arms
 * Lock (water navigation), a device for boats to transit between different levels of water, as in a canal
 * Lock (weapons guidance), missile navigation system's target acquisition fix
 * Fermentation lock, a device in beer and wine making that allows carbon dioxide to escape while not allowing air to enter
 * Rope lock, a device used in theater fly systems
 * Airlock, a compartment for transfer between environments with different atmospheres

Other uses

 * Lock of hair, a piece of hair
 * Dreadlocks, or locks, rope-like strands of hair formed by locking or braiding

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Lock


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Identity map pattern

In the design of DBMS, the identity map pattern is a database access design pattern used to improve performance by providing a context-specific, in-memory cache to prevent duplicate retrieval of the same object data from the database.

If the requested data has already been loaded from the database, the identity map returns the same instance of the already instantiated object, but if it has not been loaded yet, it loads it and stores the new object in the map. In this way, it follows a similar principle to lazy loading.

There are 4 types of identity maps
 * 1) Explicit
 * 2) Generic
 * 3) Session
 * 4) Class

title: Identity map pattern


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Cepstrum

In Fourier analysis, the cepstrum (plural cepstra, adjective cepstral) is the result of computing the inverse Fourier transform (IFT) of the logarithm of the estimated signal spectrum. The method is a tool for investigating periodic structures in frequency spectra. The power cepstrum has applications in the analysis of human speech.

The term cepstrum was derived by reversing the first four letters of spectrum. Operations on cepstra are labelled quefrency analysis (or quefrency alanysis ), liftering, or cepstral analysis. It may be pronounced in the two ways given, the second having the advantage of avoiding confusion with kepstrum.

Origin
The concept of the cepstrum was introduced in 1963 by B. P. Bogert, M. J. Healy, and J. W. Tukey. It serves as a tool to investigate periodic structures in frequency spectra. Such effects are related to noticeable echos or reflections in the signal, or to the occurrence of harmonic frequencies (partials, overtones). Mathematically it deals with the problem of deconvolution of signals in the frequency space.

References to the Bogert paper, in a bibliography, are often edited incorrectly. The terms "quefrency", "alanysis", "cepstrum" and "saphe" were invented by the authors by rearranging the letters in frequency, analysis, spectrum, and phase. The invented terms are defined in analogy to the older terms.

General definition
The cepstrum is the result of following sequence of mathematical operations:
 * transformation of a signal from the time domain to the frequency domain
 * computation of the logarithm of the spectral amplitude
 * transformation to frequency domain, where the final independent variable, the quefrency, has a time scale.

Types
The cepstrum is used in many variants. Most important are:
 * power cepstrum: The logarithm is taken from the "power spectrum"
 * complex cepstrum: The logarithm is taken from the spectrum, which is calculated via Fourier analysis

The following abbreviations are used in the formulas to explain the cepstrum:

Power cepstrum
The "cepstrum" was originally defined as power cepstrum by the following relationship:

 * $$C_{p}=\left|\mathcal{F}^{-1}\left\{\log\left(\left|\mathcal{F}\{f(t)\}\right|^2\right)\right\}\right|^2$$

The power cepstrum has main applications in analysis of sound and vibration signals. It is a complementary tool to spectral analysis.

Sometimes it is also defined as:

 * $$C_{p}=\left|\mathcal{F}\left\{\log\left(\left|\mathcal{F}\{f(t)\}\right|^2\right)\right\}\right|^2$$

Due to this formula, the cepstrum is also sometimes called the spectrum of a spectrum. It can be shown that both formulas are consistent with each other as the frequency spectral distribution remains the same, the only difference being a scaling factor which can be applied afterwards. Some articles prefer the second formula.

Other notations are possible due to the fact that the log of the power spectrum is equal to the log of the spectrum if a scaling factor 2 is applied:
 * $$\log |\mathcal{F}|^2 = 2 \log |\mathcal{F}| $$

and therefore:
 * $$C_{p}=\left|\mathcal{F}^{-1}\left\{2\log |\mathcal{F}|\right\}\right|^2, \text{ or} $$
 * $$C_{p}=4\cdot\left|\mathcal{F}^{-1}\left\{\log |\mathcal{F}| \right\}\right|^2,$$

which provides a relationship to the real cepstrum (see below).

Further, it shall be noted, that the final squaring operation in the formula for the power spectrum $$C_{p}$$ is sometimes called unnecessary and therefore sometimes omitted.

The real cepstrum is directly related to the power cepstrum:

 * $$C_{p}=4\cdot C_{r}^2$$

It is derived from the complex cepstrum (defined below) by discarding the phase information (contained in the imaginary part of the complex logarithm). It has a focus on periodic effects in the amplitudes of the spectrum:

 * $$C_{r}=\mathcal{F}^{-1}\left\{\log(\mathcal{|\mathcal{F}\{f(t) \}|})\right\}$$

Complex cepstrum
The complex cepstrum was defined by Oppenheim in his development of homomorphic system theory. The formula is provided also in other literature.

 * $$C_{c}=\mathcal{F}^{-1}\left\{\log( \mathcal{F}\{f(t) \})\right\}$$

As $$\mathcal{F}$$ is complex the log-term can be also written with $$\mathcal{F}$$ as a product of magnitude and phase, and subsequently as a sum. Further simplification is obvious, if log is a natural logarithm with base e:

 * $$\log(\mathcal{F}) = \log(\mathcal{|F| \cdot e^{i\varphi}})$$
 * $$\log_e(\mathcal{F}) = \log_e(\mathcal{|F|}) + \log_e(e^{i\varphi}) = \log_e(\mathcal{|F|}) + i\varphi$$

Therefore: The complex cepstrum can be also written as:

 * $$C_{c}=\mathcal{F}^{-1}\left\{\log_e(\mathcal{|F|}) + i\varphi\right\}$$

The complex cepstrum retains the information about the phase. Thus it is always possible to return from the quefrency domain to the time domain by the inverse operation:

 * $$f(t)=\mathcal{F}^{-1}\left\{b^\left(\mathcal{F}\{C_c\}\right)\right\},$$

where b is the base of the used logarithm.

Main application is the modification of the signal in the quefrency domain (liftering) as an analog operation to filtering in the spectral frequency domain. An example is the suppression of echo effects by suppression of certain quefrencies.

The phase cepstrum (after phase spectrum) is related to the complex cepstrum as
 * phase spectrum = (complex cepstrum − time reversal of complex cepstrum)2.

Related concepts
The independent variable of a cepstral graph is called the quefrency. The quefrency is a measure of time, though not in the sense of a signal in the time domain. For example, if the sampling rate of an audio signal is 44100 Hz and there is a large peak in the cepstrum whose quefrency is 100 samples, the peak indicates the presence of a fundamental frequency that is 44100/100 = 441 Hz. This peak occurs in the cepstrum because the harmonics in the spectrum are periodic and the period corresponds to the fundamental frequency, since harmonics are integer multiples of the fundamental frequency.

The kepstrum, which stands for "Kolmogorov-equation power-series time response", is similar to the cepstrum and has the same relation to it as expected value has to statistical average, i.e. cepstrum is the empirically measured quantity, while kepstrum is the theoretical quantity. It was in use before the cepstrum.

The autocepstrum is defined as the cepstrum of the autocorrelation. The autocepstrum is more accurate than the cepstrum in the analysis of data with echoes.

Playing further on the anagram theme, a filter that operates on a cepstrum might be called a lifter. A low-pass lifter is similar to a low-pass filter in the frequency domain. It can be implemented by multiplying by a window in the quefrency domain and then converting back to the frequency domain, resulting in a modified signal, i.e. with signal echo being reduced.

Interpretation
The cepstrum can be seen as information about the rate of change in the different spectrum bands. It was originally invented for characterizing the seismic echoes resulting from earthquakes and bomb explosions. It has also been used to determine the fundamental frequency of human speech and to analyze radar signal returns. Cepstrum pitch determination is particularly effective because the effects of the vocal excitation (pitch) and vocal tract (formants) are additive in the logarithm of the power spectrum and thus clearly separate.

The cepstrum is a representation used in homomorphic signal processing, to convert signals combined by convolution (such as a source and filter) into sums of their cepstra, for linear separation. In particular, the power cepstrum is often used as a feature vector for representing the human voice and musical signals. For these applications, the spectrum is usually first transformed using the mel scale. The result is called the mel-frequency cepstrum or MFC (its coefficients are called mel-frequency cepstral coefficients, or MFCCs). It is used for voice identification, pitch detection and much more. The cepstrum is useful in these applications because the low-frequency periodic excitation from the vocal cords and the formant filtering of the vocal tract, which convolve in the time domain and multiply in the frequency domain, are additive and in different regions in the quefrency domain.

Note that a pure sine wave can not be used to test the cepstrum for its pitch determination from quefrency as a pure sine wave does not contain any harmonics and does not lead to quefrency peaks. Rather, a test signal containing harmonics should be used (such as the sum of at least two sines where the second sine is some harmonic (multiple) of the first sine, or better, a signal with a square or triangle waveform, as such signals provide many overtones in the spectrum.).

An important property of the cepstral domain is that the convolution of two signals can be expressed as the addition of their complex cepstra:
 * $$x_1 * x_2 \mapsto x'_1 + x'_2.$$

Applications
The concept of the cepstrum has led to numerous applications:
 * dealing with reflection inference (radar, sonar applications, earth seismology)
 * estimation of speaker fundamental frequency (pitch)
 * speech analysis and recognition
 * medical applications in analysis of electroencephalogram (EEG) and brain waves
 * machine vibration analysis based on harmonic patterns (gearbox faults, turbine blade failures, ...)

Recently, cepstrum-based deconvolution was used on surface electromyography signals, to remove the effect of the stochastic impulse train, which originates an sEMG signal, from the power spectrum of the sEMG signal itself. In this way, only information about the motor unit action potential (MUAP) shape and amplitude was maintained, which was then used to estimate the parameters of a time-domain model of the MUAP itself.

A short-time cepstrum analysis was proposed by Schroeder and Noll in the 1960s for application to pitch determination of human speech.

title: Cepstrum


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Lifter

Lifter may refer to:
 * Ion-propelled aircraft, a device that can generate thrust using ionised air with no moving parts
 * Lifter (band), an American grunge band
 * Lifter Puller, an American indie rock band
 * Lifter (album), a 2001 album by American band Edgewater
 * Lifter (comics), a Marvel Comics character
 * Liquid fluoride thorium reactor, shortened to "LFTR" and pronounced "lifter"
 * Tappet, part of an internal combustion engine
 * A filter that operates on a cepstrum, in signal processing
 * "Lifter", a song by Deftones from the album Adrenaline

title: Lifter


text:
Koch snowflake

The Koch snowflake (also known as the Koch curve, Koch star, or Koch island ) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" by the Swedish mathematician Helge von Koch.

The Koch snowflake can be built up iteratively, in a sequence of stages. The first stage is an equilateral triangle, and each successive stage is formed by adding outward bends to each side of the previous stage, making smaller equilateral triangles. The areas enclosed by the successive stages in the construction of the snowflake converge to $$\tfrac{8}{5}$$ times the area of the original triangle, while the perimeters of the successive stages increase without bound. Consequently, the snowflake encloses a finite area, but has an infinite perimeter.

The Koch snowflake has been constructed as an example of a continuous curve where drawing a tangent line to any point is impossible. Unlike the earlier Weierstrass function where the proof was purely analytical, the Koch snowflake was created to be possible to geometrically represent at the time, so that this property could also be seen through "naive intuition".

Construction
The Koch snowflake can be constructed by starting with an equilateral triangle, then recursively altering each line segment as follows:
 * 1) divide the line segment into three segments of equal length.
 * 2) draw an equilateral triangle that has the middle segment from step 1 as its base and points outward.
 * 3) remove the line segment that is the base of the triangle from step 2.

The first iteration of this process produces the outline of a hexagram.

The Koch snowflake is the limit approached as the above steps are followed indefinitely. The Koch curve originally described by Helge von Koch is constructed using only one of the three sides of the original triangle. In other words, three Koch curves make a Koch snowflake.

A Koch curve–based representation of a nominally flat surface can similarly be created by repeatedly segmenting each line in a sawtooth pattern of segments with a given angle.

Perimeter of the Koch snowflake
Each iteration multiplies the number of sides in the Koch snowflake by four, so the number of sides after $$n$$ iterations is given by:

$$N_{n} = 3 \cdot 4^{n}\, .$$

If the original equilateral triangle has sides of length $$s$$, the length of each side of the snowflake after $$n$$ iterations is:

$$S_{n} = \frac{S_{n-1}}{3} = \frac{s}{3^{n}}\, ,$$

an inverse power of three multiple of the original length. The perimeter of the snowflake after $$n$$ iterations is:

$$ P_{n} = N_{n} \cdot S_{n} = 3 \cdot s \cdot {\left(\frac{4}{3}\right)}^n\, .$$

The Koch curve has an infinite length, because the total length of the curve increases by a factor of $$\tfrac{4}{3}$$ with each iteration. Each iteration creates four times as many line segments as in the previous iteration, with the length of each one being $$\tfrac{1}{3}$$ the length of the segments in the previous stage. Hence, the length of the curve after $$n$$ iterations will be $$(\tfrac{4}{3})^{n}$$ times the original triangle perimeter and is unbounded, as $$n$$ tends to infinity.

Limit of perimeter
As the number of iterations tends to infinity, the limit of the perimeter is:

$$\lim_{n \rightarrow \infty} P_n = \lim_{n \rightarrow \infty} 3 \cdot s \cdot \left(\frac{4}{3} \right)^n = \infty\, ,$$

since $$\tfrac{4}{3} > 1$$.

An $$\tfrac{\ln 4}{\ln 3}$$-dimensional measure exists, but has not been calculated so far. Only upper and lower bounds have been invented.

Area of the Koch snowflake
In each iteration a new triangle is added on each side of the previous iteration, so the number of new triangles added in iteration $$n$$ is:

$$T_{n} = N_{n-1} = 3 \cdot 4^{n-1} = \frac{3}{4} \cdot 4^{n}\,$$

The area of each new triangle added in an iteration is $$\tfrac{1}{9}$$ of the area of each triangle added in the previous iteration, so the area of each triangle added in iteration $$n$$ is:

$$a_{n} = \frac{a_{n-1}}{9} = \frac{a_{0}}{9^n}\, .$$

where $$a_{0}$$ is the area of the original triangle. The total new area added in iteration $$n$$ is therefore:

$$b_{n} = T_{n} \cdot a_{n} = \frac{3}{4} \cdot {\left(\frac{4}{9}\right)}^{n} \cdot a_{0}$$

The total area of the snowflake after $$n$$ iterations is:

$$A_{n} = a_0 + \sum_{k=1}^{n} b_k = a_0\left(1 + \frac{3}{4} \sum_{k=1}^{n} \left(\frac{4}{9}\right)^{k} \right)= a_0\left(1 + \frac{1}{3} \sum_{k=0}^{n-1} \left(\frac{4}{9}\right)^{k} \right)\, .$$

Collapsing the geometric sum gives:

$$A_{n} = a_0 \left( 1 + \frac{3}{5} \left( 1 - \left(\frac{4}{9}\right)^{n} \right) \right) = \frac{a_0}{5} \left( 8 - 3 \left(\frac{4}{9}\right)^{n} \right)\, .$$

Limits of area
The limit of the area is:

$$\lim_{n \rightarrow \infty} A_n = \lim_{n \rightarrow \infty} \frac{a_{0}}{5} \cdot \left(8 - 3 \left(\frac{4}{9} \right)^n \right) = \frac{8}{5} \cdot a_{0}\, ,$$

since $$\tfrac{4}{9} < 1$$.

Thus, the area of the Koch snowflake is $$\tfrac{8}{5}$$ of the area of the original triangle. Expressed in terms of the side length $$s$$ of the original triangle, this is: $$\frac{2s^2\sqrt{3}}{5}.$$

Solid of revolution
The volume of the solid of revolution of the Koch snowflake about an axis of symmetry of the initiating equilateral triangle of unit side is $$\frac{11\sqrt{3}}{135} \pi.$$

Other properties
The Koch snowflake is self-replicating with six smaller copies surrounding one larger copy at the center. Hence, it is an irrep-7 irrep-tile (see Rep-tile for discussion).

The fractal dimension of the Koch curve is $$\tfrac{\ln 4}{\ln 3} \approx 1.26186$$. This is greater than that of a line ($$=1$$) but less than that of Peano's space-filling curve ($$=2$$).

It is impossible to draw a tangent line to any point of the curve.

Representation as a de Rham curve
The Koch curve arises as a special case of a de Rham curve. The de Rham curves are mappings of Cantor space into the plane, usually arranged so as to form a continuous curve. Every point on a continuous de Rham curve corresponds to a real number in the unit interval. For the Koch curve, the tips of the snowflake correspond to the dyadic rationals: each tip can be uniquely labeled with a distinct dyadic rational.

Tessellation of the plane
It is possible to tessellate the plane by copies of Koch snowflakes in two different sizes. However, such a tessellation is not possible using only snowflakes of one size. Since each Koch snowflake in the tessellation can be subdivided into seven smaller snowflakes of two different sizes, it is also possible to find tessellations that use more than two sizes at once. Koch snowflakes and Koch antisnowflakes of the same size may be used to tile the plane.

Thue–Morse sequence and turtle graphics
A turtle graphic is the curve that is generated if an automaton is programmed with a sequence. If the Thue–Morse sequence members are used in order to select program states:

 * If $$t(n) = 0$$, move ahead by one unit,
 * If $$t(n) = 1$$, rotate counterclockwise by an angle of $$\tfrac{\pi}{3}$$,

the resulting curve converges to the Koch snowflake.

Representation as Lindenmayer system
The Koch curve can be expressed by the following rewrite system (Lindenmayer system):

 * Alphabet :  F
 * Constants :  +, −
 * Axiom :  F
 * Production rules:
 * F → F+F--F+F

Here, F means "draw forward", - means "turn right 60°", and + means "turn left 60°".

To create the Koch snowflake, one would use F--F--F (an equilateral triangle) as the axiom.

Variants of the Koch curve
Following von Koch's concept, several variants of the Koch curve were designed, considering right angles (quadratic), other angles (Cesàro), circles and polyhedra and their extensions to higher dimensions (Sphereflake and Kochcube, respectively)

Squares can be used to generate similar fractal curves. Starting with a unit square and adding to each side at each iteration a square with dimension one third of the squares in the previous iteration, it can be shown that both the length of the perimeter and the total area are determined by geometric progressions. The progression for the area converges to $$2$$ while the progression for the perimeter diverges to infinity, so as in the case of the Koch snowflake, we have a finite area bounded by an infinite fractal curve. The resulting area fills a square with the same center as the original, but twice the area, and rotated by $$\tfrac{\pi}{4}$$ radians, the perimeter touching but never overlapping itself.

The total area covered at the $$n$$th iteration is: $$A_{n} = \frac{1}{5} + \frac{4}{5} \sum_{k=0}^n \left(\frac{5}{9}\right)^k \quad  \mbox{giving}  \quad  \lim_{n \rightarrow \infty} A_n = 2\, ,$$

while the total length of the perimeter is: $$P_{n} = 4  \left(\frac{5}{3}\right)^na\, ,$$ which approaches infinity as $$n$$ increases.

Functionalisation
In addition to the curve, the paper by Helge von Koch that has established the Koch curve shows a variation of the curve as an example of a continuous everywhere yet nowhere differentiable function that was possible to represent geometrically at the time. From the base straight line, represented as AB, the graph can be drawn by recursively applying the following on each line segment: Each point of AB can be shown to converge to a single height. If $$y = \phi(x)$$ is defined as the distance of that point to the initial base, then $$\phi(x)$$ as a function is continuous everywhere and differentiable nowhere.
 * Divide the line segment (XY) into three parts of equal length, divided by dots C and E.
 * Draw a line DM, where M is the middle point of CE, and DM is perpendicular to the initial base of AB, having the length of $$\frac{CE\sqrt{3}}{2}$$.
 * Draw the lines CD and DE and erase the lines CE and DM.

title: Koch snowflake


text:
Thomas Crapper

Thomas Crapper (baptised 28 September 1836; died 27 January 1910) was an English plumber and businessman. He founded Thomas Crapper & Co in London, a plumbing equipment company. His notability with regard to toilets has often been overstated, mostly due to the publication in 1969 of a fictional biography by New Zealand satirist Wallace Reyburn.

Crapper held nine patents, three of them for water closet improvements such as the floating ballcock. He improved the S-bend plumbing trap in 1880 by inventing the U-bend. The firm's lavatorial equipment was manufactured at premises in nearby Marlborough Road (now Draycott Avenue). The company owned the world's first bath, toilet and sink showroom in King's Road. Crapper was noted for the quality of his products and received several royal warrants.

Manhole covers with Crapper's company's name on them in Westminster Abbey have become one of London's minor tourist attractions.

Life
Thomas Crapper was born in Thorne, West Riding of Yorkshire, in 1836; the exact date is unknown, but he was baptised on 28 September 1836. His father, Charles, was a sailor. In 1853, he was apprenticed to his brother George, a master plumber in Chelsea, and thereafter spent three years as a journeyman plumber.

Thomas Crapper Water Closet Products Advertisement

In 1861 Crapper set himself up as a sanitary engineer with his own brass foundry and workshops in nearby Marlborough Road.

In the 1880s Prince Albert (later Edward VII) purchased his country seat of Sandringham House in Norfolk and asked Thomas Crapper & Co. to supply the plumbing, including thirty lavatories with cedarwood seats and enclosures, thus giving Crapper his first Royal Warrant. The firm received further warrants from Edward as king and from George V, both as Prince of Wales and as king.

In 1904 Crapper retired, passing the firm to his nephew George and his business partner Robert Marr Wharam. Crapper lived at 12 Thornsett Road, Anerley, for the last six years of his life and died on 27 January 1910. He was buried in the nearby Elmers End Cemetery.

Posthumous fate of the Crapper company
In 1966 the Crapper company was sold by then-owner Robert G. Wharam (son of Robert Marr Wharam) upon his retirement to its rival John Bolding & Sons. Bolding went into liquidation in 1969. The company fell out of use until it was acquired by Simon Kirby, a historian and collector of antique bathroom fittings, who relaunched the company in Stratford-upon-Avon, producing authentic reproductions of Crapper's original Victorian bathroom fittings.

Achievements
As the first man to set up public showrooms for displaying sanitary ware, Crapper became known as an advocate of sanitary plumbing, popularising the notion of installation inside people's homes. He also helped refine and develop improvements to existing plumbing and sanitary fittings. As a part of his business he maintained a foundry and metal shop, which enabled him to try out new designs and develop more efficient plumbing solutions.

Crapper improved the S-bend trap in 1880. The new U-bend plumbing trap was a significant improvement on the "S" as it could not jam, and unlike the S-bend, it did not have a tendency to dry out and did not need an overflow. The BBC nominated the S-bend as one of the 50 Things That (have) Made the Modern Economy.

Crapper held nine patents, three of them for water closet improvements such as the floating ballcock, but none for the flush toilet itself.

Crapper's advertisements implied the siphonic flush was his invention. One such advertisement read, "Crapper's Valveless Water Waste Preventer (Patent #4,990) One movable part only", even though patent 4,990 (for a minor improvement to the water waste preventer) was not his, but that of Albert Giblin in 1898. However, Crapper's nephew, George, did improve the siphon mechanism by which the water flow starts. A patent for this development was awarded in 1897.

Origin of the word "crap"
It has often been claimed in popular culture that the profane slang term for human bodily waste, crap, originated with Thomas Crapper because of his association with lavatories. A common version of this story is that American servicemen stationed in England during World War I saw his name on cisterns and used it as Army slang, i.e., "I'm going to the crapper".

The word crap is actually of Middle English origin and predates its application to bodily waste. Its most likely etymological origin is a combination of two older words: the Dutch krappen (to pluck off, cut off, or separate) and the Old French crappe (siftings, waste or rejected matter, from the medieval Latin crappa). In English, it was used to refer to chaff and also to weeds or other rubbish. Its first recorded application to bodily waste, according to the Oxford English Dictionary, appeared in 1846, 10 years after Crapper was born, under a reference to a crapping ken, or a privy, where ken means a house.

title: Thomas Crapper


text:
Cunt

Cunt is a vulgar word for the vulva. It is used in a variety of ways, including as a term of disparagement. "Cunt" is often used as a disparaging and obscene term for a woman in the United States, an unpleasant or objectionable person (regardless of gender) in the United Kingdom and Ireland, or a contemptible man in Australia and New Zealand. In Australia and New Zealand, it can also be a neutral or positive term when used with a positive qualifier (e.g., "He's a good cunt"). The term has various derivative senses, including adjective and verb uses.

History
The earliest known use of the word, according to the Oxford English Dictionary, was as part of a placename: an Oxford street called Gropecunt Lane, c. 1230, now by the name of Grove Passage or Magpie Lane. Use of the word as a term of abuse is relatively recent, dating from the late nineteenth century. The word was not considered vulgar in the Middle Ages, but became so during the seventeenth century, and it was omitted from dictionaries from the late eighteenth century until the 1960s.

Etymology
The etymology of cunt is a matter of debate, but most sources consider the word to have derived from a Germanic word (Proto-Germanic *kuntō, stem *kuntōn-), which appeared as kunta in Old Norse. Scholars are uncertain of the origin of the Proto-Germanic form itself. There are cognates in most Germanic languages, most of which also have the same meaning as the English cunt, such as the Swedish, Faroese and Nynorsk kunta; West Frisian and Middle Low German kunte; another Middle Low German kutte; Middle High German kotze (meaning "prostitute"); modern German kott; Middle Dutch conte; modern Dutch words kut (same meaning) and kont ("butt", "arse"); and perhaps Old English cot.

The etymology of the Proto-Germanic term is disputed. It may have arisen by Grimm's law operating on the Proto-Indo-European root ' "create, become" seen in gonads, genital, gamete, genetics, gene, or the Proto-Indo-European root ' "woman" (gunê, seen in gynaecology). Relationships to similar-sounding words such as the Latin cunnus ("vulva"), and its derivatives French con, Spanish coño, and Portuguese cona, or in Persian kos (کُس), have not been conclusively demonstrated. Other Latin words related to cunnus are cuneus ("wedge") and its derivative cunēre ("to fasten with a wedge", (figurative) "to squeeze in"), leading to English words such as cuneiform ("wedge-shaped"). In Middle English, cunt appeared with many spellings, such as coynte, cunte and queynte, which did not always reflect the actual pronunciation of the word.

The word, in its modern meaning, is attested in Middle English. Proverbs of Hendyng, a manuscript from some time before 1325, includes the advice: "Ȝeue þi cunte to cunnig and craue affetir wedding. (Give your cunt wisely and make [your] demands after the wedding.)"

Generally
The word cunt is generally regarded in English-speaking countries as profanity and unsuitable for normal public discourse. It has been described as "the most heavily tabooed word of all English words", although John Ayto, editor of the Oxford Dictionary of Slang, says "nigger" is more taboo.

Feminist perspectives
Some American feminists of the 1970s sought to eliminate disparaging terms for women, including "bitch" and "cunt". In the context of pornography, Catharine MacKinnon argued that use of the word acts to reinforce a dehumanisation of women by reducing them to mere body parts; and in 1979 Andrea Dworkin described the word as reducing women to "the one essential – 'cunt: our essence ... our offence'".

Despite criticisms, there is a movement among feminists that seeks to reclaim cunt not only as acceptable, but as an honorific, in much the same way that queer has been reappropriated by LGBT people and nigger has been by some African-Americans. Proponents include artist Tee Corinne in The Cunt Coloring Book (1975); Eve Ensler in "Reclaiming Cunt" from The Vagina Monologues (1996); and Inga Muscio in her book, Cunt: A Declaration of Independence (1998).

Germaine Greer, the feminist writer and professor of English who once published a magazine article entitled "Lady, Love Your Cunt" (anthologised in 1986), discussed the origins, usage and power of the word in the BBC series Balderdash and Piffle, explaining how her views had developed over time. In the 1970s she had "championed" the use of the word for the female genitalia, thinking it "shouldn't be abusive"; she rejected the "proper" word vagina, a Latin name meaning "sword-sheath" originally applied by male anatomists to all muscle coverings (see synovial sheath) – not just because it refers only to the internal canal but also because of the implication that the female body is "simply a receptacle for a weapon". But in 2006, referring to its use as a term of abuse, she said that, though used in some quarters as a term of affection, it had become "the most offensive insult one man could throw at another" and suggested that the word was "sacred", and "a word of immense power, to be used sparingly". Greer said in 2006 that cunt' is one of the few remaining words in the English language with a genuine power to shock."

Usage: pre-twentieth century
Cunt has been attested in its anatomical meaning since at least the 13th century. While Francis Grose's 1785 A Classical Dictionary of The Vulgar Tongue listed the word as "C**T: a nasty name for a nasty thing", it did not appear in any major English dictionary from 1795 to 1961, when it was included in Webster's Third New International Dictionary with the comment "usu. considered obscene". Its first appearance in the Oxford English Dictionary was in 1972, which cites the word as having been in use from 1230 in what was supposedly a London street name of "Gropecunte Lane". It was, however, also used before 1230, having been brought over by the Anglo-Saxons, originally not an obscenity but rather an ordinary name for the vulva or vagina. Gropecunt Lane was originally a street of prostitution, a red light district. It was normal in the Middle Ages for streets to be named after the goods available for sale therein, hence the prevalence in cities having a medieval history of names such as "Silver Street" and "Fish Street". In some locations, the former name has been bowdlerised, as in the City of York, to the more acceptable "Grape Lane".

The somewhat similar word 'queynte' appears several times in Chaucer's Canterbury Tales (c. 1390), in bawdy contexts, but since it is used openly, does not appear to have been considered obscene at that time. A notable use is from the "Miller's Tale": "Pryvely he caught her by the queynte." The Wife of Bath also uses this term, "For certeyn, olde dotard, by your leave/You shall have queynte right enough at eve .... What aileth you to grouche thus and groan?/Is it for ye would have my queynte alone?" In modernised versions of these passages the word "queynte" is usually translated simply as "cunt". However, in Chaucer's usage there seems to be an overlap between the words "cunt" and "quaint" (possibly derived from the Latin for "known"). "Quaint" was probably pronounced in Middle English in much the same way as "cunt". It is sometimes unclear whether the two words were thought of as distinct from one another. Elsewhere in Chaucer's work the word queynte seems to be used with meaning comparable to the modern "quaint" (curious or old-fashioned, but nevertheless appealing). This ambiguity was still being exploited by the 17th century; Andrew Marvell's ... then worms shall try / That long preserved virginity, / And your quaint honour turn to dust, / And into ashes all my lust in To His Coy Mistress depends on a pun on these two senses of "quaint".

By Shakespeare's day, the word seems to have become obscene. Although Shakespeare does not use the word explicitly (or with derogatory meaning) in his plays, he still uses wordplay to sneak it in obliquely. In Act III, Scene 2, of Hamlet, as the castle's residents are settling in to watch the play-within-the-play, Hamlet asks his girlfriend Ophelia, "Lady, shall I lie in your lap?" Ophelia replies, "No, my lord." Hamlet, feigning shock, says, "Do you think I meant country matters?" Then, to drive home the point that the accent is definitely on the first syllable of country, Shakespeare has Hamlet say, "That's a fair thought, to lie between maids' legs." In Twelfth Night (Act II, Scene V) the puritanical Malvolio believes he recognises his employer's handwriting in an anonymous letter, commenting "There be her very Cs, her Us, and her Ts: and thus makes she her great Ps", unwittingly punning on "cunt" and "piss", and while it has also been argued that the slang term "cut" is intended, Pauline Kiernan writes that Shakespeare ridicules "prissy puritanical party-poopers" by having "a Puritan spell out the word 'cunt' on a public stage". A related scene occurs in Henry V: when Katherine is learning English, she is appalled at the gros, et impudique words "foot" and "gown", which her teacher has mispronounced as coun. It is usually argued that Shakespeare intends to suggest that she has misheard "foot" as foutre (French, "fuck") and "coun" as con (French "cunt", also used to mean "idiot").

Similarly, John Donne alludes to the obscene meaning of the word without being explicit in his poem The Good-Morrow, referring to sucking on "country pleasures". The 1675 Restoration comedy The Country Wife also features such word play, even in its title.

By the 17th century, a softer form of the word, "cunny", came into use. A well-known use of this derivation can be found in the 25 October 1668 entry of the diary of Samuel Pepys. He was discovered having an affair with Deborah Willet: he wrote that his wife "coming up suddenly, did find me embracing the girl con [with] my hand sub [under] su [her] coats; and endeed I was with my main [hand] in her cunny. I was at a wonderful loss upon it and the girl also ...."

Cunny was probably derived from a pun on coney, meaning "rabbit", rather as pussy is connected to the same term for a cat. (Philip Massinger (1583–1640): "A pox upon your Christian cockatrices! They cry, like poulterers' wives, 'No money, no coney.'") Because of this slang use as a synonym for a taboo term, the word "coney", when it was used in its original sense to refer to rabbits, came to be pronounced as (rhymes with "phoney"), instead of the original  (rhymes with "honey"). Eventually, the taboo association led to the word "coney" becoming deprecated entirely and replaced by the word "rabbit".

Robert Burns (1759–1796) used the word in his Merry Muses of Caledonia, a collection of bawdy verses which he kept to himself and were not publicly available until the mid-1960s. In "Yon, Yon, Yon, Lassie", this couplet appears: "For ilka birss upon her cunt, Was worth a ryal ransom" ("For every hair upon her cunt was worth a royal ransom" ).

As a term of abuse

Merriam-Webster states it is a "usually disparaging and obscene" term for a woman, and that it is an "offensive way to refer to a woman" in the United States. In American slang, the term can also be used to refer to "a fellow male homosexual one dislikes". Australian scholar Emma Alice Jane describes how the term as used on modern social media is an example of what she calls "gendered vitriol", and an example of misogynistic e-bile. As a broader derogatory term, it is comparable to prick and means "a fool, a dolt, an unpleasant person – of either sex". This sense is common in New Zealand, British, and Australian English, where it is usually applied to men or as referring specifically to "a despicable, contemptible or foolish" man.

During the 1971 Oz trial for obscenity, prosecuting counsel asked writer George Melly, "Would you call your 10-year-old daughter a cunt?" Melly replied, "No, because I don't think she is."

In the 1975 film One Flew Over the Cuckoo's Nest, the central character McMurphy, when pressed to explain exactly why he does not like the tyrannical Nurse Ratched, says, "Well, I don't want to break up the meeting or nothing, but she's something of a cunt, ain't she, Doc?"

Other usage
In informal British, Irish, New Zealand, and Australian English, and occasionally but to a lesser extent in Canadian English, it can be used with no negative connotations to refer to a (usually male) person. In this sense, it may be modified by a positive qualifier (funny, clever, etc.). For example, "This is my mate Brian. He's a good cunt."

It can also be used to refer to something very difficult or unpleasant (as in "a cunt of a job").

In the Survey of English Dialects the word was recorded in some areas as meaning "the vulva of a cow". This was pronounced as [kʌnt] in Devon, and [kʊnt] in the Isle of Man, Gloucestershire and Northumberland. Possibly related was the word cunny [kʌni], with the same meaning, in Wiltshire.

The word "cunty" is also known, although used rarely: a line from Hanif Kureishi's My Beautiful Laundrette is the definition of England by a Pakistani immigrant as "eating hot buttered toast with cunty fingers", suggestive of hypocrisy and a hidden sordidness or immorality behind the country's quaint façade. This term is attributed to British novelist Henry Green. In the United States, "cunty" is sometimes used in cross-dressing drag ball culture for a drag queen that "projects feminine beauty" and was the title of a hit song by Aviance. A visitor to a New York drag show tells of the emcee praising a queen with "cunty, cunty, cunty" as she walks past.

Rapper Azealia Banks is known for her frequent usage of the word, and her fans are known as the Kunt Brigade. She's said in one interview:

"'To be cunty is to be feminine and to be, like, aware of yourself. Nobody's fucking with that inner strength and delicateness. The cunts, the gay men, adore that. My friends would say, 'Oh you need to cunt it up! You're being too banjee.'"

Frequency of use
Frequency of use varies widely. According to research in 2013 and 2014 by Aston University and the University of South Carolina, based on a corpus of nearly 9 billion words in geotagged tweets, the word was most frequently used in the United States in New England and was least frequently used in the south-eastern states. In Maine, it was the most frequently used "cuss word" after "asshole".

Literature
James Joyce was one of the first major 20th-century novelists to put the word "cunt" into print. In the context of one of the central characters in Ulysses (1922), Leopold Bloom, Joyce refers to the Dead Sea and to "... the oldest people. Wandered far away over all the earth, captivity to captivity, multiplying, dying, being born everywhere. It lay there now. Now it could bear no more. Dead: an old woman's: the grey sunken cunt of the world." Joyce uses the word figuratively rather than literally; but while Joyce used the word only once in Ulysses, with four other wordplays ('cunty') on it, D. H. Lawrence later used the word ten times in Lady Chatterley's Lover (1928), in a more direct sense. Mellors, the gamekeeper and eponymous lover, tries delicately to explain the definition of the word to Lady Constance Chatterley: "If your sister there comes ter me for a bit o' cunt an' tenderness, she knows what she's after." The novel was the subject of an unsuccessful UK prosecution in 1961 against its publishers, Penguin Books, on grounds of obscenity.

Samuel Beckett was an associate of Joyce, and in his Malone Dies (1956), he writes: "His young wife had abandoned all hope of bringing him to heel, by means of her cunt, that trump card of young wives." In 1998, Inga Muscio published Cunt: A Declaration of Independence. In Ian McEwan's novel Atonement (2001), set in 1935, the word is used in the draft of a love letter mistakenly sent instead of a revised version and, although not spoken, is an important plot pivot.

Irvine Welsh uses the word widely in his novels, such as Trainspotting, generally as a generic placeholder for a man, and not always negatively, e.g. "Ah wis the cunt wi the fuckin pool cue in ma hand, n the plukey cunt could huv the fat end ay it in his pus if he wanted, like."

Art
The word is occasionally used in the titles of works of art, such as Peter Renosa's portrait of the pop singer Madonna, I am the Cunt of Western Civilization, from a 1990 quote by the singer. One of the first works of Gilbert & George was a self-portrait in 1969 entitled "Gilbert the Shit and George the Cunt". The London performance art group the Neo Naturists had a song and an act called "Cunt Power", a name which potter Grayson Perry borrowed for one of his early works: "An unglazed piece of modest dimensions, made from terracotta like clay – labia carefully formed with once wet material, about its midriff". Australian artist Greg Taylor's display of scores of white porcelain vulvas, "CUNTS and other conversations" (2009), was deemed controversial for both its title and content, with Australia Post warning the artist that the publicity postcards were illegal.

Theatre
Theatre censorship was effectively abolished in the UK in 1968; prior to that, all theatrical productions had to be vetted by Lord Chamberlain's Office. English stand-up comedian Roy "Chubby" Brown claims that he was the first person to say the word on stage in the United Kingdom.

United Kingdom
Broadcast media is regulated for content, and media providers such as the BBC have guidelines which specify how "cunt" and similar words should be treated. In a survey of 2000 commissioned by the British Broadcasting Standards Commission, Independent Television Commission, BBC and Advertising Standards Authority, "cunt" was regarded as the most offensive word which could be heard, above "motherfucker" and "fuck". Nevertheless, there have been occasions when, particularly in a live broadcast, the word has been aired outside editorial control:
 * The Frost Programme, broadcast 7 November 1970, was the first time the word was known to have been used on British television, in an aside by Felix Dennis. This incident has since been reshown many times.
 * Bernard Manning first said on television the line "They say you are what you eat. I'm a cunt."
 * This Morning broadcast the word in 2000, used by model Caprice Bourret while being interviewed live about her role in The Vagina Monologues.

The first scripted uses of the word on British television occurred in 1979, in the ITV drama No Mama No. In Jerry Springer – The Opera (BBC, 2005), the suggestion that the Christ character might be gay was found more controversial than the chant describing the Devil as "cunting, cunting, cunting, cunting cunt".

In July 2007 BBC Three broadcast an hour-long documentary, entitled The 'C' Word, about the origins, use and evolution of the word from the early 1900s to the present day. Presented by British comedian Will Smith, viewers were taken to a street in Oxford once called Gropecunt Lane and presented with examples of the acceptability of "cunt" as a word. (Note that "the C-word" is also a long-standing euphemism for cancer; Lisa Lynch's book led to a BBC1 drama, both with that title. )

The Attitudes to potentially offensive language and gestures on TV and radio report by Ofcom, based on research conducted by Ipsos MORI, categorised the usage of the word 'cunt' as a highly unacceptable pre-watershed, but generally acceptable post-watershed, along with 'fuck' and 'motherfucker'. Discriminatory words were generally considered as more offensive than the most offensive non-discriminatory words such as 'cunt' by the UK public, with discriminatory words being more regulated as a result.

United States
The first scripted use on US television was on the Larry Sanders Show in 1992, and a notable use occurred in Sex and the City. In the US, an episode of the NBC TV show 30 Rock, titled "The C Word", centered around a subordinate calling protagonist Liz Lemon (Tina Fey) a "cunt" and her subsequent efforts to regain her staff's favour. Characters in the popular TV series The Sopranos often used the term. Jane Fonda uttered the word on a live airing of the Today Show, a network broadcast-TV news program, in 2008 when being interviewed by co-host Meredith Vieira about The Vagina Monologues. Coincidentally, nearly two years later in 2010, also on the Today Show, Vieira interviewed a thirteen-year-old girl said the word twice to describe the contents of text messages she was privy to that were central to a well publicised and violent assault. Meredith gently cautioned the girl to choose her words more carefully. As this was a live broadcast on the East Coast, the slurs already were already broadcast, but the producers removed the audio for the Central, Mountain, and Pacific feeds as well as online. Like the Fonda incident, Vieira issued an apology later in the show. Media Critic Thomas Francis commented on what he perceived to be hypocrisy in the media industry:

"Isn't it interesting how the national media licks its chops over this story, delighting in every gory detail, only to caution a 13-year-old girl to be 'careful about our language'? Why should she be careful, Meredith? Because there are 13-year-old girls in the audience? There's so much violence and vulgarity in modern American culture, words like cunt are like so many deck chairs on the Titanic."

In 2018, Canadian comedian Samantha Bee had to apologise after calling Ivanka Trump, a White House official and the daughter of US President Donald Trump, a "feckless cunt".

Radio
On 6 December 2010 on the BBC Radio 4 Today programme, presenter James Naughtie referred to the British Culture Secretary Jeremy Hunt as "Jeremy Cunt"; he later apologised for what the BBC called the inadvertent use of "an offensive four-letter word". In the programme following, about an hour later, Andrew Marr referred to the incident during Start the Week where it was said that "we won't repeat the mistake" whereupon Marr slipped up in the same way as Naughtie had.

Film
In the United States, the word's first appearance was in graffiti on a wall in the 1969 film Bronco Bullfrog. The first spoken use of the word in mainstream cinema occurs in Carnal Knowledge (1971), in which Jonathan (Jack Nicholson) asks, "Is this an ultimatum? Answer me, you ball-busting, castrating, son of a cunt bitch! Is this an ultimatum or not?" In the same year, the word was used in the film Women in Revolt, in which Holly Woodlawn shouts "I love cunt" whilst avoiding a violent boyfriend. Nicholson later used it again, in One Flew Over the Cuckoo's Nest (1975). Two early films by Martin Scorsese, Mean Streets (1973) and Taxi Driver (1976), use the word in the context of the virgin-whore dichotomy, with characters using it after they were rejected (in Mean Streets) or after they have slept with the woman (in Taxi Driver).

In notable instances, the word has been edited out. Saturday Night Fever (1977) was released in two versions, "R" (Restricted) and "PG" (Parental Guidance), the latter omitting or replacing dialogue such as Tony Manero (John Travolta)'s comment to Annette (Donna Pescow), "It's a decision a girl's gotta make early in life, if she's gonna be a nice girl or a cunt". This differential persists, and in The Silence of the Lambs (1991), Agent Starling (Jodie Foster) meets Dr. Hannibal Lecter (Anthony Hopkins) for the first time and passes the cell of "Multiple Miggs", who says to Starling: "I can smell your cunt." In versions of the film edited for television the word is dubbed with the word scent. The 2010 film Kick-Ass caused a controversy when the word was used by Hit-Girl because the actress playing the part, Chloë Grace Moretz, was 11 years old at the time of filming.

In Britain, use of the word "cunt" may result in an "18" rating from the British Board of Film Classification (BBFC), and this happened to Ken Loach's film Sweet Sixteen, because of an estimated twenty uses of "cunt". Still, the BBFC's guidelines at "15" state that "very strong language may be permitted, depending on the manner in which it is used, who is using the language, its frequency within the work as a whole and any special contextual justification". Also directed by Loach, My Name is Joe was given a 15 certificate despite more than one instance of the word. The 2010 Ian Dury biopic Sex & Drugs & Rock & Roll was given a "15" rating despite containing seven uses of the word. The BBFC have also allowed it at the "12" level, in the case of well known works such as Hamlet.

Comedy
In their Derek and Clive dialogues, Peter Cook and Dudley Moore, particularly Cook, used the word in the 1976 sketch "This Bloke Came Up To Me", with "cunt" used 35 times. The word is also used extensively by British comedian Roy 'Chubby' Brown, which ensures that his stand-up act has never been fully shown on UK television.

Australian stand-up comedian Rodney Rude frequently refers to his audiences as "cunts" and makes frequent use of the word in his acts, which got him arrested in Queensland and Western Australia for breaching obscenity laws of those states in the mid-1980s. Australian comedic singer Kevin Bloody Wilson makes extensive use of the word, most notably in the songs Caring Understanding Nineties Type and You Can't Say "Cunt" in Canada.

The word appears in American comic George Carlin's 1972 standup routine on the list of the seven dirty words that could not, at that time, be said on American broadcast television, a routine that led to a U.S. Supreme Court decision. While some of the original seven are now heard on US broadcast television from time to time, "cunt" remains generally taboo except on premium paid subscription cable channels like HBO or Showtime. Comedian Louis C.K. uses the term frequently in his stage act as well as on his television show Louie on FX network, which bleeps it out.

In 2018, Canadian comedian Samantha Bee had to apologise after calling Ivanka Trump a cunt on American late night TV show Full Frontal with Samantha Bee.

Music
The 1977 Ian Dury and The Blockheads album, New Boots and Panties, used the word in the opening line of the track "Plaistow Patricia", thus: "Arseholes, bastards, fucking cunts and pricks", particularly notable as there is no musical lead-in to the lyrics.

In 1979, during a concert at New York's Bottom Line, Carlene Carter introduced a song about mate-swapping called "Swap-Meat Rag" by stating, "If this song doesn't put the cunt back in country, nothing will." However use of the word in lyrics is not recorded before the Sid Vicious's 1978 version of "My Way", which marked the first known use of the word in a UK top 10 hit, as a line was changed to "You cunt/I'm not a queer". The following year, "cunt" was used more explicitly in the song "Why D'Ya Do It?" from Marianne Faithfull's album Broken English: "Why'd ya do it, she screamed, after all we've said,

Every time I see your dick I see her cunt in my bed."

The Happy Mondays song, "Kuff Dam" (i.e. "Mad fuck" in reverse), from their 1987 debut album, Squirrel and G-Man Twenty Four Hour Party People Plastic Face Carnt Smile (White Out), includes the lyrics "You see that Jesus is a cunt / And never helped you with a thing that you do, or you don't". Biblical scholar James Crossley, writing in the academic journal, Biblical Interpretation, analyses the Happy Mondays' reference to "Jesus is a cunt" as a description of the "useless assistance" of a now "inadequate Jesus". A phrase from the same lyric, "Jesus is a cunt" was included on the notorious Cradle of Filth T-shirt which depicted a masturbating nun on the front and the slogan "Jesus is a cunt" in large letters on the back. The T-shirt was banned in New Zealand, in 2008.

Liz Phair in "Dance of Seven Veils" on her 1993 album Exile in Guyville, uses the word in the line "I only ask because I'm a real cunt in spring".

The word has been used by numerous non-mainstream bands, such as the Australian band TISM, who released an extended play in 1993 Australia the Lucky Cunt (a reference to Australia's label the "lucky country"). They also released a single in 1998 entitled "I Might Be a Cunt, but I'm Not a Fucking Cunt", which was banned. The American grindcore band Anal Cunt, on being signed to a bigger label, shortened their name to AxCx.

"Cunt" is uncommon for rap, but there are some examples of its appearance:
 * In Busta Rhymes's song "Light Your Ass on Fire" from the Neptunes album Clones, the word appears in a verse "I see your little gap between your cunt and yo ass."
 * The word appears once in Nicki Minaj's 2010 song "Roman's Revenge". The song includes the lyric "I'm a bad bitch, I'm a cunt." She uses this word again in the song "Ganja Burn" from 2018 album Queen, in a verse: "Watch them cunts learn".
 * The word appears 9 times in Azealia Banks' song "212", where in two verses she sings "Imma ruin you, cunt." She is also known to refer to her fans as "kunts". Banks has said she is "tired" of defending her profanity-laden lyrics from critics, saying they reflect her everyday speech and experiences.
 * It also appears in Flo Milli song "Not Friendly", where she sings a verse "Stay in your place, you little bitty cunt."

Computer and video games
The 2004 video game Grand Theft Auto: San Andreas was the first major video game to use the word, along with being the first in the series to use the words nigga, motherfucker, and cocksucker. It was used just once, by the British character Kent Paul (voiced by Danny Dyer), who refers to Maccer as a "soppy cunt" in the mission Don Peyote.

The 2004 title The Getaway: Black Monday by SCEE used the word several times during the game.

In the 2008 title Grand Theft Auto IV (developed by Rockstar North and distributed by Take Two Interactive), the word, amongst many other expletives, was used by James Pegorino who, after finding out that his personal bodyguard had turned states, exclaimed "The world is a cunt!" while aiming a shotgun at the player.

Linguistic variants and derivatives
Various euphemisms, minced forms and in-jokes are used to imply the word without actually saying it, thereby escaping obvious censure and censorship.

Spoonerisms
Deriving from a dirty joke: "What's the difference between a circus and a strip club?"- "The circus has a bunch of cunning stunts...". The phrase cunning stunt has been used in popular music. Its first documented appearance was by the English band Caravan, who released the album Cunning Stunts in July 1975; the title was later used by Metallica for a CD/Video compilation, and in 1992 the Cows released an album with the same title. In his 1980s BBC television programme, Kenny Everett played a vapid starlet, Cupid Stunt.

Acronyms
There are numerous informal acronyms, including various apocryphal stories concerning academic establishments, such as the Cambridge University National Trust Society.

Puns
The name "Mike Hunt" is a frequent pun on my cunt; it has been used in a scene from the movie Porky's, and for a character in the BBC radio comedy Radio Active in the 1980s. "Has Anyone Seen Mike Hunt?" were the words written on a "pink neon sculpture" representing the letter C, in a 2004 exhibition of the alphabet at the British Library in collaboration with the International Society of Typographic Designers.

As well as obvious references, there are also allusions. On I'm Sorry I Haven't a Clue, Stephen Fry once defined countryside as the act of "murdering Piers Morgan".

Derived meanings
The word "cunt" forms part of some technical terms used in seafaring and other industries.
 * In nautical usage, a cunt splice is a type of rope splice used to join two lines in the rigging of ships. Its name has been bowdlerised since at least 1861, and in more recent times it is commonly referred to as a "cut splice".
 * The Dictionary of Sea Terms, found within Dana's 1841 maritime compendium The Seaman's Friend, defines the word cuntline as "the space between the bilges of two casks, stowed side by side. Where one cask is set upon the cuntline between two others, they are stowed bilge and cuntline." The "bilge" of a barrel or cask is the widest point, so when stored together the two casks would produce a curved V-shaped gap. The glossary of The Ashley Book of Knots by Clifford Ashley, first published in 1944, defines cuntlines as "the surface seams between the strands of a rope." Though referring to a different object from Dana's definition, it similarly describes the crease formed by two abutting cylinders.
 * In US military usage personnel refer privately to a common uniform item, a flat, soft cover (hat) with a fold along the top resembling an invagination, as a cunt cap. The proper name for the item is garrison cap or overseas cap, depending on the organisation in which it is worn.

 * Cunt hair (sometimes as red cunt hair) has been used since the late 1950s to signify a very small distance.
 * Cunt-eyed has been used to refer to a person with narrow, squinting eyes.

title: Cunt