A geographical cluster is a localized anomaly, usually an excess of something given the distribution or variation of something else. Often it is considered as an incidence rate that is unusual in that there is more of some variable than might be expected. Examples would include: a local excess disease rate, a crime hot spot, areas of high unemployment, accident blackspots, unusually high positive residuals from a model, high concentrations of flora or fauna, physical features or events like earthquake epicenters etc... Identifying these extreme regions may be useful in that there could be implicit geographical associations with other variables that can be identified and would be of interest. Pattern detection via the identification of such geographical clusters is a very simple and generic form of geographical analysis that has many applications in many different contexts. The emphasis is on localized clustering or patterning because this may well contain the most useful information. A geographical cluster is different from a high concentration as it is generally second order, involving the factoring in of the distribution of something else. == Geographical cluster detection == Identifying geographical clusters can be an important stage in a geographical analysis. Mapping the locations of unusual concentrations may help identify causes of these. Some techniques include the Geographical Analysis Machine and Besag and Newell's cluster detection method.
Tesla Dojo
Tesla Dojo is a series of supercomputers designed and built by Tesla for computer vision video processing and recognition. It was used for training Tesla's machine learning models to improve its Full Self-Driving (FSD) advanced driver-assistance system. It went into production in July 2023. Dojo's goal was to efficiently process millions of terabytes of video data captured from real-life driving situations from Tesla's 4+ million cars. This goal led to a considerably different architecture than conventional supercomputer designs. In August 2025, Bloomberg News reported that the Dojo project had been disbanded, though it was restarted in January 2026. == History == Tesla operates several massively parallel computing clusters for developing its Autopilot advanced driver assistance system. Its primary unnamed cluster using 5,760 Nvidia A100 graphics processing units (GPUs) was touted by Andrej Karpathy in 2021 at the fourth International Joint Conference on Computer Vision and Pattern Recognition (CCVPR 2021) to be "roughly the number five supercomputer in the world" at approximately 81.6 petaflops, based on scaling the performance of the Nvidia Selene supercomputer, which uses similar components. However, the performance of the primary Tesla GPU cluster has been disputed, as it was not clear if this was measured using single-precision or double-precision floating point numbers (FP32 or FP64). Tesla also operates a second 4,032 GPU cluster for training and a third 1,752 GPU cluster for automatic labeling of objects. The primary unnamed Tesla GPU cluster has been used for processing one million video clips, each ten seconds long, taken from Tesla Autopilot cameras operating in Tesla cars in the real world, running at 36 frames per second. Collectively, these video clips contained six billion object labels, with depth and velocity data; the total size of the data set was 1.5 petabytes. This data set was used for training a neural network intended to help Autopilot computers in Tesla cars understand roads. By August 2022, Tesla had upgraded the primary GPU cluster to 7,360 GPUs. Dojo was first mentioned by Elon Musk in April 2019 during Tesla's "Autonomy Investor Day". In August 2020, Musk stated it was "about a year away" due to power and thermal issues. Dojo was officially announced at Tesla's Artificial Intelligence (AI) Day on August 19, 2021. Tesla revealed details of the D1 chip and its plans for "Project Dojo", a datacenter that would house 3,000 D1 chips; the first "Training Tile" had been completed and delivered the week before. In October 2021, Tesla released a "Dojo Technology" whitepaper describing the Configurable Float8 (CFloat8) and Configurable Float16 (CFloat16) floating point formats and arithmetic operations as an extension of Institute of Electrical and Electronics Engineers (IEEE) standard 754. At the follow-up AI Day in September 2022, Tesla announced it had built several System Trays and one Cabinet. During a test, the company stated that Project Dojo drew 2.3 megawatts (MW) of power before tripping a local San Jose, California power substation. At the time, Tesla was assembling one Training Tile per day. In August 2023, Tesla powered on Dojo for production use as well as a new training cluster configured with 10,000 Nvidia H100 GPUs. In January 2024, Musk described Dojo as "a long shot worth taking because the payoff is potentially very high. But it's not something that is a high probability." In June 2024, Musk explained that ongoing construction work at Gigafactory Texas is for a computing cluster claiming that it is planned to comprise an even mix of "Tesla AI" and Nvidia/other hardware with a total thermal design power of at first 130 MW and eventually exceeding 500 MW. In August 2025, Bloomberg News reported that the Dojo project was disbanded, though Musk announced it would be restarted in January 2026 with a new chip iteration. == Technical architecture == The fundamental unit of the Dojo supercomputer is the D1 chip, designed by a team at Tesla led by ex-AMD CPU designer Ganesh Venkataramanan, including Emil Talpes, Debjit Das Sarma, Douglas Williams, Bill Chang, and Rajiv Kurian. The D1 chip is manufactured by the Taiwan Semiconductor Manufacturing Company (TSMC) using 7 nanometer (nm) semiconductor nodes, has 50 billion transistors and a large die size of 645 mm2 (1.0 square inch). Updating at Artificial Intelligence (AI) Day in 2022, Tesla announced that Dojo would scale by deploying multiple ExaPODs, in which there would be: 10 Cabinets per ExaPOD (1,062,000 cores, 3,000 D1 chips) 2 System Trays per Cabinet (106,200 cores, 300 D1 chips) 6 Training Tiles per System Tray (53,100 cores, along with host interface hardware) 25 D1 chips per Training Tile (8,850 cores) 354 computing cores per D1 chip According to Venkataramanan, Tesla's senior director of Autopilot hardware, Dojo will have more than an exaflop (a million teraflops) of computing power. For comparison, according to Nvidia, in August 2021, the (pre-Dojo) Tesla AI-training center used 720 nodes, each with eight Nvidia A100 Tensor Core GPUs for 5,760 GPUs in total, providing up to 1.8 exaflops of performance. === D1 chip === Each node (computing core) of the D1 processing chip is a general purpose 64-bit CPU with a superscalar core. It supports internal instruction-level parallelism, and includes simultaneous multithreading (SMT). It doesn't support virtual memory and uses limited memory protection mechanisms. Dojo software/applications manage chip resources. The D1 instruction set supports both 64-bit scalar and 64-byte single instruction, multiple data (SIMD) vector instructions. The integer unit mixes reduced instruction set computer (RISC-V) and custom instructions, supporting 8, 16, 32, or 64 bit integers. The custom vector math unit is optimized for machine learning kernels and supports multiple data formats, with a mix of precisions and numerical ranges, many of which are compiler composable. Up to 16 vector formats can be used simultaneously. ==== Node ==== Each D1 node uses a 32-byte fetch window holding up to eight instructions. These instructions are fed to an eight-wide decoder which supports two threads per cycle, followed by a four-wide, four-way SMT scalar scheduler that has two integer units, two address units, and one register file per thread. Vector instructions are passed further down the pipeline to a dedicated vector scheduler with two-way SMT, which feeds either a 64-byte SIMD unit or four 8×8×4 matrix multiplication units. The network on-chip (NOC) router links cores into a two-dimensional mesh network. It can send one packet in and one packet out in all four directions to/from each neighbor node, along with one 64-byte read and one 64-byte write to local SRAM per clock cycle. Hardware native operations transfer data, semaphores and barrier constraints across memories and CPUs. System-wide double data rate 4 (DDR4) synchronous dynamic random-access memory (SDRAM) memory works like bulk storage. ==== Memory ==== Each core has a 1.25 megabytes (MB) of SRAM main memory. Load and store speeds reach 400 gigabytes (GB) per second and 270 GB/sec, respectively. The chip has explicit core-to-core data transfer instructions. Each SRAM has a unique list parser that feeds a pair of decoders and a gather engine that feeds the vector register file, which together can directly transfer information across nodes. ==== Die ==== Twelve nodes (cores) are grouped into a local block. Nodes are arranged in an 18×20 array on a single die, of which 354 cores are available for applications. The die runs at 2 gigahertz (GHz) and totals 440 MB of SRAM (360 cores × 1.25 MB/core). It reaches 376 teraflops using 16-bit brain floating point (BF16) numbers or using configurable 8-bit floating point (CFloat8) numbers, which is a Tesla proposal, and 22 teraflops at FP32. Each die comprises 576 bi-directional serializer/deserializer (SerDes) channels along the perimeter to link to other dies, and moves 8 TB/sec across all four die edges. Each D1 chip has a thermal design power of approximately 400 watts. === Training Tile === The water-cooled Training Tile packages 25 D1 chips into a 5×5 array. Each tile supports 36 TB/sec of aggregate bandwidth via 40 input/output (I/O) chips - half the bandwidth of the chip mesh network. Each tile supports 10 TB/sec of on-tile bandwidth. Each tile has 11 GB of SRAM memory (25 D1 chips × 360 cores/D1 × 1.25 MB/core). Each tile achieves 9 petaflops at BF16/CFloat8 precision (25 D1 chips × 376 TFLOP/D1). Each tile consumes 15 kilowatts; 288 amperes at 52 volts. === System Tray === Six tiles are aggregated into a System Tray, which is integrated with a host interface. Each host interface includes 512 x86 cores, providing a Linux-based user environment. Previously, the Dojo System Tray was known as the Training Matrix, which includes six Training Tiles, 20 Dojo Interface Processor cards across four host servers, and Ethernet-l
Data communication
Data communication is the transfer of data over a point-to-point or point-to-multipoint communication channel. Data communication comprises data transmission and data reception and can be classified as analog transmission and digital communications. Analog data communication conveys voice, data, image, signal or video information using a continuous signal, which varies in amplitude, phase, or some other property. In baseband analog transmission, messages are represented by a sequence of pulses by means of a line code; in passband analog transmission, they are communicated by a limited set of continuously varying waveforms, using a digital modulation method. Passband modulation and demodulation are carried out by modem equipment. Digital transmission and digital reception are the transfer of either a digitized analog signal or a born-digital bitstream. Baseband digital transmission is regarded as comprising part of a digital signal, whereas passband transmission of digital data may also or alternatively be considered a form of digital-to-analog conversion. Data communication channels include copper wires, optical fibers, wireless communication using radio spectrum, storage media and computer buses. The data are represented as an electromagnetic signal, such as an electrical voltage, radiowave, microwave, or infrared signal. == Distinction between related subjects == Digital transmission or data transmission traditionally belongs to telecommunications and electrical engineering. Basic principles of data transmission may also be covered within the computer science or computer engineering topic of data communications, which also includes computer networking applications and communication protocols, for example, routing, switching and inter-process communication. Although the Transmission Control Protocol (TCP) involves transmission, TCP and other transport layer protocols are covered in computer networking but not discussed in a textbook or course about data transmission. In most textbooks, the term analog transmission only refers to the transmission of an analog message signal (without digitization) by means of an analog signal, either as a non-modulated baseband signal or as a passband signal using an analog modulation method such as AM or FM. It may also include analog-over-analog pulse modulated baseband signals such as pulse-width modulation. In a few books within the computer networking tradition, analog transmission also refers to passband transmission of bit-streams using digital modulation methods such as FSK, PSK and ASK. The theoretical aspects of data transmission are covered by information theory and coding theory. == Protocol layers and sub-topics == Courses and textbooks in the field of data transmission typically deal with the following OSI model protocol layers and topics: Layer 1, the physical layer: Channel coding including Digital modulation schemes Line coding schemes Forward error correction (FEC) codes Bit synchronization Multiplexing Equalization Channel models Layer 2, the data link layer: Channel access schemes, media access control (MAC) Packet mode communication and Frame synchronization Error detection and automatic repeat request (ARQ) Flow control Layer 6, the presentation layer: Source coding (digitization and data compression), and information theory. Cryptography (may occur at any layer) It is also common to deal with the cross-layer design of those three layers. == Applications and history == Data (mainly but not exclusively informational) has been sent via non-electronic (e.g. optical, acoustic, mechanical) means since the advent of communication. Analog signal data has been sent electronically since the advent of the telephone. However, the first data electromagnetic transmission applications in modern time were electrical telegraphy (1809) and teletypewriters (1906), which are both digital signals. The fundamental theoretical work in data transmission and information theory by Harry Nyquist, Ralph Hartley, Claude Shannon and others during the early 20th century, was done with these applications in mind. In the early 1960s, Paul Baran invented distributed adaptive message block switching for digital communication of voice messages using switches that were low-cost electronics. Donald Davies invented and implemented modern data communication during 1965–7, including packet switching, high-speed routers, communication protocols, hierarchical computer networks and the essence of the end-to-end principle. Baran's work did not include routers with software switches and communication protocols, nor the idea that users, rather than the network itself, would provide the reliability. Both were seminal contributions that influenced the development of computer networks. Data transmission is utilized in computers in computer buses and for communication with peripheral equipment via parallel ports and serial ports such as RS-232 (1969), FireWire (1995) and USB (1996). The principles of data transmission are also utilized in storage media for error detection and correction since 1951. The first practical method to overcome the problem of receiving data accurately by the receiver using digital code was the Barker code invented by Ronald Hugh Barker in 1952 and published in 1953. Data transmission is utilized in computer networking equipment such as modems (1940), local area network (LAN) adapters (1964), repeaters, repeater hubs, microwave links, wireless network access points (1997), etc. In telephone networks, digital communication is utilized for transferring many phone calls over the same copper cable or fiber cable by means of pulse-code modulation (PCM) in combination with time-division multiplexing (TDM) (1962). Telephone exchanges have become digital and software controlled, facilitating many value-added services. For example, the first AXE telephone exchange was presented in 1976. Digital communication to the end user using Integrated Services Digital Network (ISDN) services became available in the late 1980s. Since the end of the 1990s, broadband access techniques such as ADSL, Cable modems, fiber-to-the-building (FTTB) and fiber-to-the-home (FTTH) have become widespread to small offices and homes. The current tendency is to replace traditional telecommunication services with packet mode communication such as IP telephony and IPTV. Transmitting analog signals digitally allows for greater signal processing capability. The ability to process a communications signal means that errors caused by random processes can be detected and corrected. Digital signals can also be sampled instead of continuously monitored. The multiplexing of multiple digital signals is much simpler compared to the multiplexing of analog signals. Because of all these advantages, because of the vast demand to transmit computer data and the ability of digital communications to do so and because recent advances in wideband communication channels and solid-state electronics have allowed engineers to realize these advantages fully, digital communications have grown quickly. The digital revolution has also resulted in many digital telecommunication applications where the principles of data transmission are applied. Examples include second-generation (1991) and later cellular telephony, video conferencing, digital TV (1998), digital radio (1999), and telemetry. Data transmission, digital transmission or digital communications is the transfer of data over a point-to-point or point-to-multipoint communication channel. Examples of such channels include copper wires, optical fibers, wireless communication channels, storage media and computer buses. The data are represented as an electromagnetic signal, such as an electrical voltage, radio wave, microwave, or infrared light. While analog transmission is the transfer of a continuously varying analog signal over an analog channel, digital communication is the transfer of discrete messages over a digital or an analog channel. The messages are either represented by a sequence of pulses by means of a line code (baseband transmission) or by a limited set of continuously varying waveforms (passband transmission), using a digital modulation method. The passband modulation and corresponding demodulation (also known as detection) are carried out by modem equipment. According to the most common definition of a digital signal, both baseband and passband signals representing bit-streams are considered as digital transmission, while an alternative definition only considers the baseband signal as digital, and passband transmission of digital data as a form of digital-to-analog conversion. Data transmitted may be digital messages originating from a data source, for example, a computer or a keyboard. It may also be an analog signal, such as a phone call or a video signal, digitized into a bit-stream, for example,e using pulse-code modulation (PCM) or more advanced source coding (analog-to-digital conversion and
Downloadable content
Downloadable content (DLC) is additional content created for an already released video game, distributed through the Internet by the game's publisher. It can be added for no extra cost or as a form of video game monetization, enabling the publisher to gain additional revenue from a title after it has been purchased, often using a microtransaction system. DLC can range from cosmetic content, such as skins, to new in-game content, like characters, levels, modes, and larger expansions that may contain a mix of such content as a continuation of the base game. In some games, multiple DLCs (including future DLC not yet released) may be bundled as part of a "season pass"—typically at a discount rather than purchasing each DLC individually. While the Dreamcast was the first home console to support DLC (albeit in a limited form due to hardware and internet connection limitations), Microsoft's Xbox helped popularize the concept. Since the seventh generation of video game consoles, DLC has been a prevalent feature of major video game platforms with internet connectivity. == Etymology == Since the popularization of microtransactions in online distribution platforms such as Steam, the term DLC has become a synonymous for any form of paid content in video games, regardless of whether they constitute the download of new content. Furthermore, this led to the creation of the oxymoronic term "on-disc DLC" for content included on the game's original files but locked behind a paywall. == History == === Precursors to DLC === The earliest form of downloadable content were offerings of full games, such as on the Atari 2600's GameLine service, which allowed users to download games using a telephone line. A similar service, Sega Channel, allowed for the downloading of games to the Sega Genesis over a cable line. While the GameLine and Sega Channel services allowed for the distribution of entire titles, they did not provide downloadable content for existing titles. Expansion packs were sold at retail for some PC games, which featured content such as additional levels, characters, or maps for a base game. They often required an installation of the original game in order to function, but some games (such as Half-Life) had "standalone" expansions, which were essentially spin-off games that reused engine code and assets from the original game. === On consoles === The Dreamcast was the first console to feature online support as a standard; DLC was available, though limited in size due to the narrowband connection and the 200 block limit of the Visual Memory Unit memory card. These online features were still considered a breakthrough in video games. With the release of the Xbox, Microsoft was the second company to implement downloadable content. Many Xbox titles, including Splinter Cell, Halo 2, and Ninja Gaiden, offered varying amounts of extra content, available for download through the Xbox Live service. Most of this content was available free. With the advent of the GameCube, Nintendo was the third company to implement downloadable content. Many GameCube titles offered varying amounts of extra content from Game Boy Advance titles with the GameCube – Game Boy Advance link cable. All of this content was available free. The Xbox 360 (2005) included more robust support for digital distribution, including DLC downloads and purchases, via its Xbox Live Marketplace service. Microsoft believed that publishers would benefit by offering small pieces of content at a small cost ($1 to $5), rather than full expansion packs (~$20), as this would allow players to pick and chose what content they desired, providing revenue to the publishers. Microsoft also utilized a digital currency known as "Microsoft Points" for transactions, which could also be purchased through physical gift cards to avoid the banking fees associated with the small price points. The PlayStation 3 (2006) adopted the same approach with their downloadable hub, the PlayStation Store. Sony planned on having the bulk of its content be purchased separately via many separate online microtransactions for PlayStation Network titles, including Gran Turismo HD Concept and Gran Turismo 5 Prologue. The Wii (2006) featured a sparser amount of downloadable content on their Wii Shop Channel, the bulk of which is accounted for by digital distribution of emulated Nintendo titles from previous generations. Music video games, such as titles from the Guitar Hero and Rock Band franchises, took significant advantage of downloadable content as a means of offering new songs to be played in-game. Harmonix claimed that Guitar Hero II would feature "more online content than anyone has ever seen in a game to this date." Rock Band features the largest number of downloadable items of any console video game, with a steady number of new songs that were added weekly between 2007 and 2013. Acquiring all the downloadable content for Rock Band would, as of July 12, 2012, cost $5,880.10. === On personal computers === As the popularity and speed of internet connections rose, so did the popularity of using the internet for digital distribution of media. User-created game mods and maps were distributed exclusively online, as they were mainly created by people without the infrastructure capable of distributing the content through physical media. In 1997, Cavedog offered a new unit every month as free downloadable content for their real-time strategy computer game Total Annihilation. Later PC digital distribution platforms, such as Games for Windows Marketplace and Steam, would add support for DLC in a similar manner to consoles. === On handhelds === Nokia phones of the late 1990s and early 2000s shipped with side-scrolling shooter Space Impact, available on various models. With the introduction of WAP in 2000, additional downloadable content for the game, with extra levels, became available. The Nintendo Wi-Fi Connection service on the Nintendo DS could be used to obtain a form of DLC for certain games, such as Picross DS—where players could download puzzle "packs" of classic puzzles from previous Picross series games (such as Mario's Picross). as well as downloadable user generated content. Due to the Nintendo DS's use of cartridges and lack of dedicated storage, most "DLC" for DS games was limited in scope, or in some cases (such as Professor Layton and the Curious Village and Moero! Nekketsu Rhythm Damashii Osu! Tatakae! Ouendan 2), was already part of the game's data on the cartridge, and merely unlocked. Its successor, the Nintendo 3DS, natively supported the purchase of DLC for supported titles via Nintendo eShop. Starting with iPhone OS 3, downloadable content became available for the platform via applications bought from the App Store. While this ability was initially only available to developers for paid applications, Apple eventually allowed for developers to offer this in free applications as well in October 2009. == On-disc DLC == In some cases, a purchased DLC may not actually download new content to the device, but merely consists of data used to enable associated content that is already present within the game's data. DLC of this nature revealed via data mining is typically referred to as "on-disc DLC" or PULC (premium unlockable content). This practice has sometimes been considered controversial, with publishers being accused of using what is effectively a microtransaction to lock access to content that was already contained within the game as sold at retail. Data relating to future DLC may be included on-disc or downloaded during updates for technical reasons as well, either to ensure online multiplayer compatibility for existing content between players who have not yet purchased the new DLC, or as dormant support code for planned content that is still in development at the time of the release. == Monetization == Downloadable content is often offered for a price. Since Facebook games popularized the business model of microtransactions, some have criticized downloadable content as being overpriced and an incentive for developers to leave items out of the initial release, with The Elder Scrolls IV: Oblivion's horse armor DLC having faced a mixed reception upon its release for that reason. However, by 2009, the Horse Armor DLC was one of the top ten content packs that Bethesda had sold, which justified the DLC model for future games. Where a normal software disc may allow its license sold or traded, DLC is generally locked to a specific user's account and does not come with the ability to transfer that license to another user. In addition to individual content downloads, video game publishers sometimes offer a "season pass", which allows users to pre-order a selection of upcoming content over a specific time period, and ensuring the customer's ability to immediately obtain the content upon release. As users do not have the ability to fully preview the content before their purchase, there is a chance that the content of a season
Horus Music
Horus Music Limited is a global digital distribution and label services company. Established in 2006, Horus Music allows artists, labels and right-holders to send their music to over 200 download, streaming, and interactive platforms including iTunes, Google Play, Amazon, VEVO, 7digital, Spotify, Beatport, Deezer, Tidal, as well as offering digital marketing and playlisting opportunities. == History == The company were named Best Business Partner of 2014 by Huawei Technology of China, and were also a finalist in the International Trade category as part of the Leicester Mercury Business Awards during that same year. Their client base consists of unsigned and independent musicians and record labels, as well as well known recording artists. In November 2015, Horus Music sponsored the UK’s first Independent Label Week, in order to highlight the music that is released by the UK’s indie labels. In 2016, Horus Music celebrated their 10th anniversary Horus Music's sister companies Help for Bands and Help For Writers, provide advice and opportunities for musicians and E-book distribution for writers, respectively. Anara Publishing opened in 2017 which allows the company to work closely with a handpicked roster of musicians to provide royalty administration and sync licensing services. On 21 April 2017, Her Majesty Queen Elizabeth II’s 91st birthday, Horus Music was awarded with the Queen’s Award for Enterprise in International Trade. In 2021, Horus Music, UnitedMasters, and Symphonic Distribution partnered with pioneering music fintech company, beatBread, to offer clients access to more capital. beatBread's chordCashAI technology provides an automated advance experience for independent musicians while enable clients to choose their own terms and retain ownership of their music. == Clients == Horus Music has partnered with a number of charities including Save the Children, for the recording "Look into Your Heart", featuring Beverley Knight with Rolling Stones' Mick Jagger and Ronnie Wood, 100% of proceeds from the single were donated to the charity. The Pixel Project, who produced songs about violence against women and the blood cancer charity Bloodwise. The company have spoken openly about the state of the music industry and artists' rights and were one of the first distributors to remove their catalogue from Rdio after the streaming service was acquired by Pandora. Their relationships with artists and labels, as well as leading industry contacts, means they have the ability to work with musicians in a myriad of ways, including offering performance opportunities and even local auditions for TV shows such as The Voice UK. == Horus Music India == Horus Music India opened in 2016 and is based in Mumbai. By opening Horus Music India, the company are able to expand on their local connections as well as to provide a much more personalised service to musicians based in this area. The appointment of two Business Development Managers in India cemented their move.
Color normalization
Color normalization is a topic in computer vision concerned with artificial color vision and object recognition. In general, the distribution of color values in an image depends on the illumination, which may vary depending on lighting conditions, cameras, and other factors. Color normalization allows for object recognition techniques based on color to compensate for these variations. == Main concepts == === Color constancy === Color constancy is a feature of the human internal model of perception, which provides humans with the ability to assign a relatively constant color to objects even under different illumination conditions. This is helpful for object recognition as well as identification of light sources in an environment. For example, humans see an object approximately as the same color when the sun is bright or when the sun is dim. === Applications === Color normalization has been used for object recognition on color images in the field of robotics, bioinformatics and general artificial intelligence, when it is important to remove all intensity values from the image while preserving color values. One example is in case of a scene shot by a surveillance camera over the day, where it is important to remove shadows or lighting changes on same color pixels and recognize the people that passed. Another example is automated screening tools used for the detection of diabetic retinopathy as well as molecular diagnosis of cancer states, where it is important to include color information during classification. == Known issues == The main issue about certain applications of color normalization is that the result looks unnatural or too distant from the original colors. In cases where there is a subtle variation between important aspects, this can be problematic. More specifically, the side effect can be that pixels become divergent and not reflect the actual color value of the image. A way of combating this issue is to use color normalization in combination with thresholding to correctly and consistently segment a colored image. == Transformations and algorithms == There is a vast array of different transformations and algorithms for achieving color normalization and a limited list is presented here. The performance of an algorithm is dependent on the task and one algorithm which performs better than another in one task might perform worse in another (no free lunch theorem). Additionally, the choice of the algorithm depends on the preferences of the user for the end-result, e.g. they may want a more natural-looking color image. === Grey world === The grey world normalization makes the assumption that changes in the lighting spectrum can be modelled by three constant factors applied to the red, green and blue channels of color. More specifically, a change in illuminated color can be modelled as a scaling α, β and γ in the R, G and B color channels and as such the grey world algorithm is invariant to illumination color variations. Therefore, a constancy solution can be achieved by dividing each color channel by its average value as shown in the following formula: ( α R , β G , γ B ) → ( α R α n ∑ i R , β G β n ∑ i G , γ B γ n ∑ i B ) {\displaystyle \left(\alpha R,\beta G,\gamma B\right)\rightarrow \left({\frac {\alpha R}{{\frac {\alpha }{n}}\sum _{i}R}},{\frac {\beta G}{{\frac {\beta }{n}}\sum _{i}G}},{\frac {\gamma B}{{\frac {\gamma }{n}}\sum _{i}B}}\right)} As mentioned above, grey world color normalization is invariant to illuminated color variations α, β and γ, however it has one important problem: it does not account for all variations of illumination intensity and it is not dynamic; when new objects appear in the scene it fails. To solve this problem there are several variants of the grey world algorithm. Additionally there is an iterative variation of the grey world normalization, however it was not found to perform significantly better. === Histogram equalization === Histogram equalization is a non-linear transform which maintains pixel rank and is capable of normalizing for any monotonically increasing color transform function. It is considered to be a more powerful normalization transformation than the grey world method. The results of histogram equalization tend to have an exaggerated blue channel and look unnatural, due to the fact that in most images the distribution of the pixel values is usually more similar to a Gaussian distribution, rather than uniform. === Histogram specification === Histogram specification transforms the red, green and blue histograms to match the shapes of three specific histograms, rather than simply equalizing them. It refers to a class of image transforms which aims to obtain images of which the histograms have a desired shape. As specified, firstly it is necessary to convert the image so that it has a particular histogram. Assume an image x. The following formula is the equalization transform of this image: y = f ( x ) = ∫ 0 x p x ( u ) d u {\displaystyle y=f(x)=\int \limits _{0}^{x}p_{x}(u)du} Then assume wanted image z. The equalization transform of this image is: y ′ = g ( z ) = ∫ 0 z p z ( u ) d u {\displaystyle y'=g(z)=\int \limits _{0}^{z}p_{z}(u)du} Of course p z ( u ) {\displaystyle p_{z}(u)} is the histogram of the output image. The formula to find the inverse of the above transform is: z = g − 1 ( y ′ ) {\displaystyle z=g^{-1}(y')} Therefore, since images y and y' have the same equalized histogram they are actually the same image, meaning y = y' and the transform from the given image x to the wanted image z is: z = g − 1 ( y ′ ) = g − 1 ( y ) = g − 1 ( f ( x ) ) {\displaystyle z=g^{-1}(y')=g^{-1}(y)=g^{-1}(f(x))} Histogram specification has the advantage of producing more realistic looking images, as it does not exaggerate the blue channel like histogram equalization. === Comprehensive Color Normalization === The comprehensive color normalization is shown to increase localization and object classification results in combination with color indexing. It is an iterative algorithm which works in two stages. The first stage is to use the red, green and blue color space with the intensity normalized, to normalize each pixel. The second stage is to normalize each color channel separately, so that the sum of the color components is equal to one third of the number of pixels. The iterations continue until convergence, meaning no additional changes. Formally: Normalize the color image f ( t ) = [ f i j ( t ) ] i = 1... N , j = 1... M {\displaystyle f^{(t)}=[f_{ij}^{(t)}]_{i=1...N,j=1...M}} which consists of color vectors f i j ( t ) = ( r i j ( t ) , g i j ( t ) , b i j ( t ) ) T . {\displaystyle f_{ij}^{(t)}=(r_{ij}^{(t)},g_{ij}^{(t)},b_{ij}^{(t)})^{T}.} For the first step explained above, compute: S i j := r i j ( t ) + g i j ( t ) + b i j ( t ) {\displaystyle S_{ij}:=r_{ij}^{(t)}+g_{ij}^{(t)}+b_{ij}^{(t)}} which leads to r i j ( t + 1 ) = r i j ( t ) S i j , g i j ( t + 1 ) = g i j ( t ) S i j {\displaystyle r_{ij}^{(t+1)}={\frac {r_{ij}^{(t)}}{S_{ij}}},g_{ij}^{(t+1)}={\frac {g_{ij}^{(t)}}{S_{ij}}}} and b i j ( t + 1 ) = b i j ( t ) S i j . {\displaystyle b_{ij}^{(t+1)}={\frac {b_{ij}^{(t)}}{S_{ij}}}.} For the second step explained above, compute: r ′ = 3 N M ∑ i = 1 N ∑ j = 1 M r i j ( t + 1 ) {\displaystyle r'={\frac {3}{NM}}\sum _{i=1}^{N}\sum _{j=1}^{M}r_{ij}^{(t+1)}} and normalize r i j ( t + 2 ) = r i j ( t + 1 ) r ′ . {\displaystyle r_{ij}^{(t+2)}={\frac {r_{ij}^{(t+1)}}{r'}}.} Of course the same process is done for b' and g'. Then these two steps are repeated until the changes between iteration t and t+2 are less than some set threshold. Comprehensive color normalization, just like the histogram equalization method previously mentioned, produces results that may look less natural due to the reduction in the number of color values.
The Holocaust and social media
The representation of the Holocaust on social media has been a subject of scholarly inquiry and media attention. == Selfies at Holocaust memorial sites == Some visitors take selfies at Holocaust memorials, which has been the subject of controversy. In 2018, Rhian Sugden, a British model, received criticism after posting a selfie at the Memorial to the Murdered Jews of Europe in Berlin with the caption "ET phone home". She later removed the caption, but defended taking the photograph. Other celebrities have also been criticised for photographs at the Berlin memorial, including Indian actress Priyanka Chopra and US politician Pete Buttigieg, whose husband posted a photograph of him at the memorial on a personal social media account. The Israeli artist and satirist Shahak Shapira set up the website yolocaust.de in 2017 to expose people who take inappropriate selfies at the Holocaust memorial in Berlin. Shapira went through thousands of selfies posted to social media sites such as Facebook, Instagram, Tinder, and Grindr, choosing the twelve that he found most offensive. When the images were moused over, the website replaces the memorial backdrop with black and white images of Nazi victims. "Yolocaust" is a portmanteau of "Holocaust" and YOLO, an acronym for "you only live once". The website went viral, receiving 1.2 million views in the first 24 hours after its launch. Shapira honored requests to take down all of the photographs, which he had used without permission, and the website remains with only a textual documentation of the project. In an analysis of comments by Internet users on the project, Christoph Bareither estimated that 75% were positive. However, the memorial's architect, Peter Eisenman, criticized the website. In his 2018 book Postcards from Auschwitz, Grinnell professor Daniel P. Reynolds defends the practice of selfie-taking at Holocaust sites. In 2019, the Auschwitz-Birkenau State Museum requested that visitors not take inappropriate selfies, although the museum's staff acknowledged that other visitors take selfies in a thoughtful and respectful manner, which they did not criticize. In an academic paper, Gemma Commane and Rebekah Potton analyze the use of Instagram to share tourist photographs at Holocaust sites and conclude that "Instagram encourages conversation and empathy, keeping the Holocaust visible in youth discourses". According to their analysis, most images are tagged with respectful hashtags such as #tragic, #remembrance, and #sadness. The Auschwitz museum has an official Instagram account, auschwitzmemorial, which it uses to share selected appropriate Instagram posts. However, the image feed for the hashtag "Auschwitz" includes potentially offensive images such as an image of "Nazi Vs. Jews #beerpong". This image, according to the authors, expresses "mockery and contempt" for Holocaust victims. They also document offensive memes using images of Holocaust atrocities and shared on Instagram. Some social media users post in order to criticize what they see as inappropriate behavior at Holocaust sites, with one commenting, "Taking photos posing next to razor wire, selfies with victim's hair in the background, and even group shots in front of the crematoria had to be seen to be believed." == Assessment of tourism == Social media posts have been used by researchers to analyze the phenomenon of Holocaust-related tourism. == Social media groups == People have created groups on Facebook to discuss issues related to the Holocaust. One paper analyses two such groups, "The Holocaust and My Family" and "The Descendants of the Victims and Survivors of the Holocaust" in which people engage in collective trauma processing. == Eva.stories == In 2019, Israeli high-tech entrepreneur Mati Kochavi created a fictitious Instagram account for Eva Heyman, a Hungarian-Jewish girl who was murdered in Auschwitz concentration camp. The project met with mixed reception. Israeli prime minister Benjamin Netanyahu praised the project, saying that it "exposes the immense tragedy of our people through the story of one girl". == Holocaust denial == The issue of Holocaust denial on social media has also attracted attention. In October 2020, Facebook reversed its policy and banned Holocaust denial from the platform. Founder Mark Zuckerberg had previously argued that such content should not be banned on freedom of speech grounds.