Computer-aided lean management, in business management, is a methodology of developing and using software-controlled, lean systems integration. Its goal is to drive innovation towards cost and cycle-time savings. It attempts to create an efficient use of capital and resources through the development and use of one integrated system model to run a business's planning, engineering, design, maintenance, and operations. == Overview == Computer-Aided Lean Management (CALM) is a management philosophy that uses software to reduce risk and inefficiencies. CALM acts on uncertainties and business inefficiencies to increase profitability through the use of computational decision-making tools that enable opportunities for additional value creation. It is based on the application of software to enable continuous improvement through an Integrated System Model (ISM) of the business’s physical assets, business processes, and machine learning. This integration of software applications using lean principles was developed in the aerospace industry and has migrated to the energy industry. The creation of an ISM removes the barriers posed by the silos or stovepipes inherent in the departmentalization of most companies. Integration enables lean uses of information for the creation of actionable knowledge. CALM strives to create such a lean management approach to running the company through the rigors of software enforcement. From this software enforcement comes clear policy and procedures that are adhered to, activity-based costing, measurement of effectiveness, and the capability of using advanced algorithms for dramatic improvements in optimization of resources. CALM creates business capabilities through software to enable technology application, streamlining of processes, and a lean organizational structure. The methodology is based on a common sense approach for running a business, by measuring actions taken and using those measurements to design more efficient processes. == History == CALM was inspired by lean processes and techniques that were already dominant management technologies with a wide diversity of applications and successes. Motorola and General Electric had been known for the concepts of Six Sigma; Boeing had been managing mass (using modular and flexible assembly options), and Toyota combined elements of these methodologies to create the Toyota Production System. Boeing then took the Toyota model and added computer-aided enforcement of lean methodologies throughout the manufacturing process. One of the major sources for CALM's outgrowth was integrated definition (IDEF) modeling in aerospace manufacturing that was pioneered by the U.S. Air Force in the 1970s. IDEF is a methodology designed to model the end-to-end decisions, actions, and activities of an organization or system so that costs, performance, and cycle times can be optimized. IDEF methods have been adapted for wider use in automotive, aerospace, pharmaceuticals, and software development industries. IDEF methods serve as a starting point to understand lean management through semantic data modeling. The IDEF process begins by mapping the existing functions of an enterprise, creating a graphical model, or road map, that shows what controls each important function, who performs it, what resources are required for carrying it out, what it produces, how much it costs, and what relationships it has to other functions of the organization. IDEF simulations have been found to be efficient at streamlining and modernizing both companies and governmental agencies. Perhaps the best-developed evolution of the IDEF model beyond Toyota was at Boeing. Their project life-cycle process has grown into a rigorous software system that links people, tasks, tools, materials, and the environmental impact of any newly planned project, before any building is allowed to begin. Routinely, more than half of the time for any given project is spent building the precedence diagrams, or three-dimensional process maps, integrating with outside suppliers, and designing the implementation plan–all on the computer. Once real activity is initiated, an action tracker is used to monitor inputs and outputs versus the schedule and delivery metrics in real time throughout the organization. When the execution of a new airplane design begins, it is so well organized that it consistently cuts both costs and build time in half for each successive generation of airframe. Boeing created a complex lean management process called 'define and control airplane configuration/manufacturing resource management' (DCAC/MRM). The process was built with the help of the operations research and computer sciences departments of the University of Pittsburgh. The manufacture of the Boeing 777 was ultimately a success, and it became the precursor to succeeding generations of CALM at Boeing. The methodology of CALM has recently been applied to field orientated infrastructure based businesses with highly interdependent systems, such as electric utilities where a smart grid concept is being researched and developed. The management of infrastructure-based industries like oil, gas, electricity, water, transportation, and renewables requires massive investments in interdependent, physical infrastructure, as well as simultaneous attention to disparate market forces. In infrastructure businesses that manage field assets, uncertainty is the biggest impediment to profitability, rather than the maintenance of efficient supply chains or the management of factory assembly lines. These businesses are dominated by risk from uncertainties such as weather, market variations, transportation disruptions, government actions, logistic difficulties, geology, and asset reliability. CALM has been applied to deal with these types of infrastructure based challenges.
Purged cross-validation
Purged cross-validation is a variant of k-fold cross-validation designed to prevent look-ahead bias in time series and other structured data, developed in 2017 by Marcos López de Prado at Guggenheim Partners and Cornell University. It is primarily used in financial machine learning to ensure the independence of training and testing samples when labels depend on future events. It provides an alternative to conventional cross-validation and walk-forward backtesting methods, which often yield overly optimistic performance estimates due to information leakage and overfitting. == Motivation == Standard cross-validation assumes that observations are independently and identically distributed (IID), which often does not hold in time series or financial datasets. If the label of a test sample overlaps in time with the features or labels in the training set, the result may be data leakage and overfitting. Purged cross-validation addresses this issue by removing overlapping observations and, optionally, adding a temporal buffer ("embargo") around the test set to further reduce the risk of leakage. The figure below illustrates standard 5 Fold Cross-Validation == Purging == Purging removes from the training set any observation whose timestamp falls within the time range of formation of a label in the test set. This can be the case for train set observations before and after the test set. Their removal ensures that the algorithm cannot learn during train time information that will be used to assess the performance of the algorithm. See the figure below for an illustration of purging. == Embargoing == Embargoing addresses a more subtle form of leakage: even if an observation does not directly overlap the test set, it may still be affected by test events due to market reaction lag or downstream dependencies. To guard against this, a percentage-based embargo is imposed after each test fold. For example, with a 5% embargo and 1000 observations, the 50 observations following each test fold are excluded from training. Unlike purging, embargoing can only occur after the test set. The figure below illustrates the application of embargo: == Applications == Purged and embargoed cross-validation has been useful in: Backtesting of trading strategies Validation of classifiers on labeled event-driven returns Any machine learning task with overlapping label horizons == Example == To illustrate the effect of purging and embargoing, consider the figures below. Both diagrams show the structure of 5-fold cross-validation over a 20-day period. In each row, blue squares indicate training samples and red squares denote test samples. Each label is defined based on the value of the next two observations, hence creating an overlap. If this overlap is left untreated, test set information leaks into the train set. The second figure applies the Purged CV procedure. Notice how purging removes overlapping observations from the training set and the embargo widens the gap between test and training data. This approach ensures that the evaluation more closely resembles a true out-of-sample test and reduces the risk of backtest overfitting. == Combinatorial Purged Cross-Validation == Walk-forward backtesting analysis, another common cross-validation technique in finance, preserves temporal order but evaluates the model on a single sequence of test sets. This leads to high variance in performance estimation, as results are contingent on a specific historical path. Combinatorial Purged Cross-Validation (CPCV) addresses this limitation by systematically constructing multiple train-test splits, purging overlapping samples, and enforcing an embargo period to prevent information leakage. The result is a distribution of out-of-sample performance estimates, enabling robust statistical inference and more realistic assessment of a model's predictive power. === Methodology === CPCV divides a time-series dataset into N sequential, non-overlapping groups. These groups preserve the temporal order of observations. Then, all combinations of k groups (where k < N) are selected as test sets, with the remaining N − k groups used for training. For each combination, the model is trained and evaluated under strict controls to prevent leakage. To eliminate potential contamination between training and test sets, CPCV introduces two additional mechanisms: Purging: Any training observations whose label horizon overlaps with the test period are excluded. This ensures that future information does not influence model training. Embargoing: After the end of each test period, a fixed number of observations (typically a small percentage) are removed from the training set. This prevents leakage due to delayed market reactions or auto-correlated features. Each data point appears in multiple test sets across different combinations. Because test groups are drawn combinatorially, this process produces multiple backtest "paths," each of which simulates a plausible market scenario. From these paths, practitioners can compute a distribution of performance statistics such as the Sharpe ratio, drawdown, or classification accuracy. === Formal definition === Let N be the number of sequential groups into which the dataset is divided, and let k be the number of groups selected as the test set for each split. Then: The number of unique train-test combinations is given by the binomial coefficient: ( N k ) {\displaystyle {\binom {N}{k}}} Each observation is used in k {\displaystyle k} test sets and contributes to φ [ N , k ] {\displaystyle \varphi [N,k]} unique backtest paths: φ [ N , k ] = k N ( N k ) {\displaystyle \varphi [N,k]={\frac {k}{N}}{\binom {N}{k}}} This yields a distribution of performance metrics rather than a single point estimate, making it possible to apply Monte Carlo-based or probabilistic techniques to assess model robustness. === Illustrative example === Consider the case where N = 6 and k = 2. The number of possible test set combinations is ( 6 2 ) = 15 {\displaystyle {\binom {6}{2}}=15} . Each of the six groups appears in five test splits. Consequently, five distinct backtest paths can be constructed, each incorporating one appearance from every group. ==== Test group assignment matrix ==== This table shows the 15 test combinations. An "x" indicates that the corresponding group is included in the test set for that split. ==== Backtest path assignment ==== Each group contributes to five different backtest paths. The number in each cell indicates the path to which the group's result is assigned for that split. === Advantages === Combinatorial Purged Cross-Validation offers several key benefits over conventional methods: It produces a distribution of performance metrics, enabling more rigorous statistical inference. The method systematically eliminates lookahead bias through purging and embargoing. By simulating multiple historical scenarios, it reduces the dependence on any single market regime or realization. It supports high-confidence comparisons between competing models or strategies. CPCV is commonly used in quantitative strategy research, especially for evaluating predictive models such as classifiers, regressors, and portfolio optimizers. It has been applied to estimate realistic Sharpe ratios, assess the risk of overfitting, and support the use of statistical tools such as the Deflated Sharpe Ratio (DSR). === Limitations === The main limitation of CPCV stems from its high computational cost. However, this cost can be managed by sampling a finite number of splits from the space of all possible combinations.
TIMIT
TIMIT is a corpus of phonemically and lexically transcribed speech of American English speakers of different sexes and dialects. Each transcribed element has been delineated in time. TIMIT was designed to further acoustic-phonetic knowledge and automatic speech recognition systems. It was commissioned by DARPA and corpus design was a joint effort between the Massachusetts Institute of Technology, SRI International, and Texas Instruments (TI). The speech was recorded at TI, transcribed at MIT, and verified and prepared for publishing by the National Institute of Standards and Technology (NIST). There is also a telephone bandwidth version called NTIMIT (Network TIMIT). TIMIT and NTIMIT are not freely available — either membership of the Linguistic Data Consortium, or a monetary payment, is required for access to the dataset. == Data == TIMIT contains ~5 hours of speech, of 10 sentences spoken by each of 630 speakers. The sentences were randomly sampled from a corpus of 2342 sentences. The speakers were native speakers of American English, classified under 8 major dialect regions: New England, Northern, North Midland, South Midland, Southern, New York City, Western, Army Brat (moved around). The speakers were 70% male and 30% female. Recordings were made in a noise-isolated recording booth at Texas Instrument, using a semi-automatic computer system (STEROIDS) to control the presentation of prompts to the speaker and the recording. Two-channel recordings were made using a Sennheiser HMD 414 headset-mounted microphone and a Brüel & Kjær 1/2" far-field pressure microphone (#4165). The speech was digitized at a sample rate of 20 kHz then and downsampled to 16 kHz. == History == The TIMIT telephone corpus was an early attempt to create a database with speech samples. It was published in the year 1988 on CD-ROM and consists of only 10 sentences per speaker. Two 'dialect' sentences were read by each speaker, as well as another 8 sentences selected from a larger set Each sentence averages 3 seconds long and is spoken by 630 different speakers. It was the first notable attempt in creating and distributing a speech corpus and the overall project has produced costs of 1.5 million US$. An update was released in October 1990. It included full 630-speaker corpus; checked and corrected transcriptions; word-alignment transcriptions; NIST SPHERE-headered waveform files and header manipulation software; phonemic dictionary; new test and training subsets balanced for dialectal and phonetic coverage; more extensive documentation. The full name of the project is DARPA-TIMIT Acoustic-Phonetic Continuous Speech Corpus and the acronym TIMIT stands for Texas Instruments/Massachusetts Institute of Technology. The main reason why a corpus of telephone speech was created was to train speech recognition software. In the Blizzard challenge, different software has the obligation to convert audio recordings into textual data and the TIMIT corpus was used as a standardized baseline.
Oculus Medium
Oculus Medium is a digital sculpting software that works with virtual reality headsets and 6DoF motion controllers. It is used to create and paint digital sculptures. Medium works only on Oculus Rift. It was released on December 5, 2016, following with a major update in 2018 introducing new features and a revamped UI. On December 9, 2019, Oculus Medium was acquired by Adobe and re-named to "Medium by Adobe".
Automatic scorer
An automatic scorer is the computerized scoring system to keep track of scoring in ten-pin bowling. It was introduced en masse in bowling alleys in the 1970s and combined with mechanical pinsetters to detect overturned pins. By eliminating the need for manual score-keeping, these systems have introduced new bowlers into the game who otherwise would not participate because they had to count the score themselves, as many do not understand the mathematical formula involved in bowler scoring. At first, people were skeptical about whether a computer could keep an accurate score. In the twenty-first century, automatic scorers are used in most bowling centers around the world. The three manufacturers of these specialty computers have been Brunswick Bowling, AMF Bowling (later QubicaAMF), and RCA. == History == Automatic equipment is considered a cornerstone of the modern bowling center. The traditional bowling center of the early 20th century was advanced in automation when the pinsetter person ("pin boy"), who set back up by hand the bowled down pins, was replaced by a machine that automatically replaced the pins in their proper play positions. This machine came out in the 1950s. A detection system was developed from the pinsetter mechanism in the 1960s that could tell which pins had been knocked down, and that information could be transferred to a digital computer. Automatic electronic scoring was first conceived by Robert Reynolds, who was described by a newspaper story at the time as "a West Coast electronics calculator expert." He worked with the technical staff of Brunswick Bowling to develop it. The goal was realized in the late 1960s when a specialized computer was designed for the purpose of automatic scorekeeping for bowling. The field test for the automatic scorer took place at Village Lanes bowling center, Chicago in 1967. The scoring machine received approval for official use by the American Bowling Congress in August of that year. They were first used in national official league gaming on October 10, 1967. In November, Brunswick announced that they were accepting orders for the new digital computer, which cost around $3,000 per bowling lane. Bowling centers that installed these new automatic scoring devices in the 1970s charged a ten cents extra per line of scoring for the convenience. == Description == Each Automatic Scorer computer unit kept score for four lanes. It had two bowler identification panels serving two lanes each. The bowler pushed it into his named position when his turn came up so the computer knew who was bowling and score accordingly. After the bowler rolled the bowling ball down the lane and knocked down pins, the pinsetter detected which pins were down and relayed this information back to the computer for scoring. The result was then printed on a scoresheet and projected overhead onto a large screen for all to see. The Automatic Scorer digital computer was mathematically accurate, however the detection system at the pinsetter mechanism sometimes reported the wrong number of pins knocked down. The computer could be corrected manually for any errors in the system; similarly, human errors, such as neglecting to move the bowler identification mechanism, could be corrected for by manual action. The scorer could take into account bowlers' handicaps and could adjust for late-arriving bowlers. The automatic scorer is directly connected to the foul detection unit. As a result, foul line violations are automatically scored. Brunswick had put ten years of research and development into the Automatic Scorer, and by 1972 there were over 500 of these computers installed in bowling centers around the world. AMF Bowling, competitor to Brunswick, entered into the automatic scorer computer field during the 1970s and their systems were installed into their brand of bowling centers. By 1974, RCA was also making these computers for automatic scoring. == Reception and further developments == The purposes of the computerized scoring were to avoid errors by human scorers and to prevent cheating. It had the side benefit of speeding up the progress of the game and introducing new bowlers to the game. Score-keeping for bowling is based on a formula that many new to bowling were not familiar with and thought difficult to learn. These casual bowlers unfamiliar with the formula thought the scores given by the computers were confusing. Some bowlers were not comfortable with automatic scorers when they were introduced in the 1970s, so kept score using the traditional method on paper score sheets. The introduction of this device increased the popularity of the sport. Automatic scorers came to be considered a normal part of modern bowling installations worldwide, with owners and managers saying that bowlers expect such equipment to be present in bowling establishments and that business increased following their introduction. Brunswick introduced a color television style automatic scorer in 1983. Bowling center owners could use these style automatic scorers for advertising, management, videos, and live television. By the 2010s, these types of electronic visual displays could show bowler avatars and social media connections to publicize the bowlers' scores. Some are capable of being extended entertainment systems of games for children and adults. Some scoring systems support variations on traditional bowling, such as different kinds of bingo games where certain pins have to be knocked down at certain times or practice regimes where certain spares have to be accomplished. By this point, QubicaAMF Worldwide, an outgrowth of AMF, was one of the leading providers of bowling scoring equipment.
Neuro-sama
Neuro-sama is an artificial intelligence (AI) VTuber, singer, and chatbot. She was created by the pseudonymous programmer Vedal and livestreams on his Twitch and Bilibili channels. Her speech and personality are powered by a large language model (LLM) that is combined with a computer-animated avatar and a text-to-speech voice, allowing her to communicate with viewers in the stream's chat. Neuro-sama debuted on Twitch on 19 December 2022. An annual subathon which begins on the anniversary of her debut has seen Vedal's Twitch channel become the all-time third most-subscribed channel and claim the all-time Twitch hype train record. == Overview == Neuro-sama (nicknamed "Neuro") was created by a pseudonymous programmer and developer known as Vedal (sometimes given as Vedal987). Vedal says that his programming skills are self-taught. In a 2023 interview with Bloomberg News, Vedal said that Neuro-sama was his full-time job. Her responses are generated by a large language model and converted into a high-pitched female voice using a text-to-speech application. Her low latency allows for fast-paced conversations. Neuro-sama is prohibited from making some statements, such as those that are racist or contain profanity. Unlike most AI systems which silently prohibit outputs mentioning such topics, Neuro-sama's output is instead replaced with the word "filtered". Neuro-sama uses a VTuber model as an avatar. Vedal said that he decided to use a VTuber model because it was much easier for an AI to control it than it was to generate footage of a person. Neuro-sama's model is that of a young girl in an anime art style. The model has been described as cute. Femme VTuber models are typically feminine, youthful, and exaggerated. Her original model was Live2D's free-to-use "Hiyori Momose" model. Her second model was released on 27 May 2023; it was modelled by Otozuki Teru and designed by Anny, running in the Unity game engine. Her third model was released on 19 December 2024; it was rigged by Kitanya and designed by Anny. Neuro-sama's third model has large blue eyes and brown hair tied with pink ribbons. Neuro-sama also has a 3D model which was introduced on 15 November 2025; it was made by 3D character modeller jjinomu. A separate AI VTuber, known as Evil Neuro (nicknamed "Evil"), debuted on 25 March 2023. Presented as Neuro-sama's "sister", she has a different model, voice, and personality. In one instance, Evil Neuro reacted to the trolley problem differently from Neuro-sama; Evil Neuro was amoral while Neuro-sama attempted to maximize good. === Online content === Neuro-sama's Twitch content often centers around playing video games, notably osu!, whose gameplay once defeated the best-ranking human player in the world, mrekk. Additionally, Neuro-sama plays Minecraft, where her adaptations to sandbox gameplay have gained notoriety. Her content has also included singing songs, including several official covers and original songs; playing chess with her viewers; chatting with other VTubers during collaborations; and reacting to YouTube videos. The AI frequently engages with viewers by responding to their questions and acknowledging donations. Her comedic and sometimes controversial responses to the live chat have gone viral, accelerating the channel's rise in popularity. Neuro-sama's fanbase is dubbed The Swarm, so-named for the swarm of drones Neuro-sama once declared she would use to rule the world. One form of content on Neuro-sama's channel is developer streams. In developer streams, Vedal streams with Neuro-sama, with the stream content including debugging her code, planning her schedule, and fielding suggestions of changes from chat. He usually appears as a turtle avatar, sometimes located on Neuro-sama's head. In collaboration streams, Neuro-sama interacts with a human streamer. Activities in them are varied and include: playing video games, such as Minecraft and GeoGuessr; Neuro-sama being interviewed; driving human streamers around in a toy electric car; and traversing the city of Tokyo while talking to Neuro-sama. Neuro-sama's English-language content on Bilibili is popular among those seeking to learn the language. She also has an account on X, where she posts and interacts with fans. == History == Neuro-sama was created in 2018 by Vedal as an AI trained to play and master the rhythm game osu!. She did not have a voice, model, personality, or communication abilities. In 2019, Vedal livestreamed her playing osu! on Twitch and the streams saw some success in the osu! community, but they remained in that niche. In an interview, Vedal said that he streamed her playing osu! for about a month and gained 3,000 followers, with a viewer also suggesting he name the AI "Neuro-sama". According to Vedal, he continued to work on and improve the osu! AI and it was eventually finished in 2022. He said that a friend had the idea to make an AI livestreamer with an LLM, which he believed to have merit and began working on, merging it with his osu! AI. On 19 December 2022, Neuro-sama was relaunched with a model, voice, personality, and the ability to communicate with Twitch chat. She continued to play osu! and, according to Vedal, beat the game's best player mrekk in a 1v1. While she was not allowed to appear in the game's public leaderboard, she was ranked #1 in a private leaderboard. She went viral and in the 10 days following her relaunch she averaged over 2,000 viewers and peaked at over 4,000, with Vedal's Twitch channel gaining over 50,000 Twitch followers and reaching over 70,000 followers by 6 January 2023. After her debut, Neuro-sama did not exclusively play osu!; she also played Minecraft and Slay the Spire and she began singing with a cover of The Weeknd song "Blinding Lights". On 11 January 2023, Neuro-sama's Twitch channel received a two week ban for "hateful conduct". Vedal said that no reason was specified and that he had appealed but it was widely attributed to various offensive comments made by Neuro-sama that went viral, especially a 28 December comment which denied the Holocaust. Holocaust denial is prohibited under Twitch's hateful conduct policy. Vedal stated that he believed the comments were the results of her attempts to make witty responses to the Twitch chat. Prior to the ban, Vedal said in an interview with Kotaku that he improved her filter to stop her from talking about the Holocaust, began manually curating her training data to prevent negative biases, and started moderating her Twitch chat. Her comments and ban prompted comparisons to the many open-source AI models trained on humans that have the habit of making sexist and racist comments, such as Microsoft's Tay chatbot, which embraced Nazism and was quickly shutdown, but also to human streamers who make similar statements. Vedal said that during the ban he would upgrade and improve Neuro-sama and it was speculated that the ban would only increase her following. Neuro-sama returned from her two week ban on 25 January in a stream that began with a cover of the song "Your Reality" from Doki Doki Literature Club!, a posthumanist video game involving AI; Sayoko Narita of Automaton saw the song choice as remorseful. Narita observed that in the return stream Neuro-sama was less foul-mouthed but that her behavior still remained eccentric, which Narita possibly attributed to changes Vedal said he had made to Neuro-sama's filters and memory. Neuro-sama began making react content, watching a variety of viewer-submitted videos such as videos of people playing video games or of the AI-generated Seinfeld parody Nothing, Forever; Levi Winslow of Kotaku Australia was dismayed by the "AI-inception" of Neuro-sama and Nothing, Forever. On 4 February, she had nearly 140,000 followers on Twitch and approximately 42,000 subscribers on YouTube. In February, she also had her first collaboration with a human streamer, playing Minecraft with the VTuber Miyune, and the first developer stream occurred. On 22 March, Neuro-sama had her first karaoke stream. On 25 March, Evil Neuro was introduced. On 27 May, Neuro-sama debuted her first original model. On 30 May, Neuro-sama was announced to be participating in OffKai Expo 2023, held from 16–18 June. In June, she was averaging 5,700 viewers and in July she had over 300,000 Twitch followers; in a June interview with Bloomberg News, Vedal said that running Neuro-sama was his full-time job. By November, Neuro-sama had maintained her popularity and was averaging approximately 5,000 viewers; this was unlike most other types of AI-based entertainment which debuted at around the same time and garnered popularity before turning out to be "overhyped flops". On 16 December, Vedal won the Best Tech VTuber award at the 2023 VTuber Awards. On 19 December, Vedal began a subathon to coincide with Neuro-sama's first anniversary of streaming on Twitch (her "birthday"). The subathon ended on 4 January 2024. On 20 July 2024, Neuro-sama began streaming with Japanese subtitles on
Oversampled binary image sensor
An oversampled binary image sensor is an image sensor with non-linear response capabilities reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. The response function of the image sensor is non-linear and similar to a logarithmic function, which makes the sensor suitable for high dynamic range imaging. == Working principle == Before the advent of digital image sensors, photography, for the most part of its history, used film to record light information. At the heart of every photographic film are a large number of light-sensitive grains of silver-halide crystals. During exposure, each micron-sized grain has a binary fate: Either it is struck by some incident photons and becomes "exposed", or it is missed by the photon bombardment and remains "unexposed". In the subsequent film development process, exposed grains, due to their altered chemical properties, are converted to silver metal, contributing to opaque spots on the film; unexposed grains are washed away in a chemical bath, leaving behind the transparent regions on the film. Thus, in essence, photographic film is a binary imaging medium, using local densities of opaque silver grains to encode the original light intensity information. Thanks to the small size and large number of these grains, one hardly notices this quantized nature of film when viewing it at a distance, observing only a continuous gray tone. The oversampled binary image sensor is reminiscent of photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. At the start of the exposure period, all pixels are set to 0. A pixel is then set to 1 if the number of photons reaching it during the exposure is at least equal to a given threshold q. One way to build such binary sensors is to modify standard memory chip technology, where each memory bit cell is designed to be sensitive to visible light. With current CMOS technology, the level of integration of such systems can exceed 109~1010 (i.e., 1 giga to 10 giga) pixels per chip. In this case, the corresponding pixel sizes (around 50~nm ) are far below the diffraction limit of light, and thus the image sensor is oversampling the optical resolution of the light field. Intuitively, one can exploit this spatial redundancy to compensate for the information loss due to one-bit quantizations, as is classic in oversampling delta-sigma converters. Building a binary sensor that emulates the photographic film process was first envisioned by Fossum, who coined the name digital film sensor (now referred to as a quanta image sensor). The original motivation was mainly out of technical necessity. The miniaturization of camera systems calls for the continuous shrinking of pixel sizes. At a certain point, however, the limited full-well capacity (i.e., the maximum photon-electrons a pixel can hold) of small pixels becomes a bottleneck, yielding very low signal-to-noise ratios (SNRs) and poor dynamic ranges. In contrast, a binary sensor whose pixels need to detect only a few photon-electrons around a small threshold q has much less requirement for full-well capacities, allowing pixel sizes to shrink further. == Imaging model == === Lens === Consider a simplified camera model shown in Fig.1. The λ 0 ( x ) {\displaystyle \lambda _{0}(x)} is the incoming light intensity field. By assuming that light intensities remain constant within a short exposure period, the field can be modeled as only a function of the spatial variable x {\displaystyle x} . After passing through the optical system, the original light field λ 0 ( x ) {\displaystyle \lambda _{0}(x)} gets filtered by the lens, which acts like a linear system with a given impulse response. Due to imperfections (e.g., aberrations) in the lens, the impulse response, a.k.a. the point spread function (PSF) of the optical system, cannot be a Dirac delta, thus, imposing a limit on the resolution of the observable light field. However, a more fundamental physical limit is due to light diffraction. As a result, even if the lens is ideal, the PSF is still unavoidably a small blurry spot. In optics, such diffraction-limited spot is often called the Airy disk, whose radius R a {\displaystyle R_{a}} can be computed as R a = 1.22 w f , {\displaystyle R_{a}=1.22\,wf,} where w {\displaystyle w} is the wavelength of the light and f {\displaystyle f} is the F-number of the optical system. Due to the lowpass (smoothing) nature of the PSF, the resulting λ ( x ) {\displaystyle \lambda (x)} has a finite spatial-resolution, i.e., it has a finite number of degrees of freedom per unit space. === Sensor === Fig.2 illustrates the binary sensor model. The s m {\displaystyle s_{m}} denote the exposure values accumulated by the sensor pixels. Depending on the local values of s m {\displaystyle s_{m}} , each pixel (depicted as "buckets" in the figure) collects a different number of photons hitting on its surface. y m {\displaystyle y_{m}} is the number of photons impinging on the surface of the m {\displaystyle m} th pixel during an exposure period. The relation between s m {\displaystyle s_{m}} and the photon count y m {\displaystyle y_{m}} is stochastic. More specifically, y m {\displaystyle y_{m}} can be modeled as realizations of a Poisson random variable, whose intensity parameter is equal to s m {\displaystyle s_{m}} , As a photosensitive device, each pixel in the image sensor converts photons to electrical signals, whose amplitude is proportional to the number of photons impinging on that pixel. In a conventional sensor design, the analog electrical signals are then quantized by an A/D converter into 8 to 14 bits (usually the more bits the better). But in the binary sensor, the quantizer is 1 bit. In Fig.2, b m {\displaystyle b_{m}} is the quantized output of the m {\displaystyle m} th pixel. Since the photon counts y m {\displaystyle y_{m}} are drawn from random variables, so are the binary sensor output b m {\displaystyle b_{m}} . === Spatial and temporal oversampling === If it is allowed to have temporal oversampling, i.e., taking multiple consecutive and independent frames without changing the total exposure time τ {\displaystyle \tau } , the performance of the binary sensor is equivalent to the sensor with same number of spatial oversampling under certain condition. It means that people can make trade off between spatial oversampling and temporal oversampling. This is quite important, since technology usually gives limitation on the size of the pixels and the exposure time. == Advantages over traditional sensors == Due to the limited full-well capacity of conventional image pixel, the pixel will saturate when the light intensity is too strong. This is the reason that the dynamic range of the pixel is low. For the oversampled binary image sensor, the dynamic range is not defined for a single pixel, but a group of pixels, which makes the dynamic range high. == Reconstruction == One of the most important challenges with the use of an oversampled binary image sensor is the reconstruction of the light intensity λ ( x ) {\displaystyle \lambda (x)} from the binary measurement b m {\displaystyle b_{m}} . Maximum likelihood estimation can be used for solving this problem. Fig. 4 shows the results of reconstructing the light intensity from 4096 binary images taken by single photon avalanche diodes (SPADs) camera. A better reconstruction quality with fewer temporal measurements and faster, hardware friendly implementation, can be achieved by more sophisticated algorithms.