The study of image formation encompasses the radiometric and geometric processes by which 2D images of 3D objects are formed. In the case of digital images, the image formation process also includes analog to digital conversion and sampling. == Imaging == The imaging process is a mapping of an object to an image plane. Each point on the image corresponds to a point on the object. An illuminated object will scatter light toward a lens and the lens will collect and focus the light to create the image. The ratio of the height of the image to the height of the object is the magnification. The spatial extent of the image surface and the focal length of the lens determines the field of view of the lens. Image formation of mirror these have a center of curvature and its focal length of the mirror is half of the center of curvature. == Illumination == An object may be illuminated by the light from an emitting source such as the sun, a light bulb or a Light Emitting Diode. The light incident on the object is reflected in a manner dependent on the surface properties of the object. For rough surfaces, the reflected light is scattered in a manner described by the Bi-directional Reflectance Distribution Function (BRDF) of the surface. The BRDF of a surface is the ratio of the exiting power per square meter per steradian (radiance) to the incident power per square meter (irradiance). The BRDF typically varies with angle and may vary with wavelength, but a specific important case is a surface that has constant BRDF. This surface type is referred to as Lambertian and the magnitude of the BRDF is R/π, where R is the reflectivity of the surface. The portion of scattered light that propagates toward the lens is collected by the entrance pupil of the imaging lens over the field of view. == Field of view and imagery == The Field of view of a lens is limited by the size of the image plane and the focal length of the lens. The relationship between a location on the image and a location on the object is y = ftan(θ), where y is the max extent of the image plane, f is the focal length of the lens and θ is the field of view. If y is the max radial size of the image then θ is the field of view of the lens. While the image created by a lens is continuous, it can be modeled as a set of discrete field points, each representing a point on the object. The quality of the image is limited by the aberrations in the lens and the diffraction created by the finite aperture stop. == Pupils and stops == The aperture stop of a lens is a mechanical aperture which limits the light collection for each field point. The entrance pupil is the image of the aperture stop created by the optical elements on the object side of the lens. The light scattered by an object is collected by the entrance pupil and focused onto the image plane via a series of refractive elements. The cone of the focused light at the image plane is set by the size of the entrance pupil and the focal length of the lens. This is often referred to as the f-stop or f-number of the lens. f/# = f/D where D is the diameter of the entrance pupil. == Pixelation and color vs. monochrome == In typical digital imaging systems, a sensor is placed at the image plane. The light is focused on to the sensor and the continuous image is pixelated. The light incident on each pixel in the sensor will be integrated within the pixel and a proportional electronic signal will be generated. The angular geometric resolution of a pixel is given by atan(p/f), where p is the pitch of the pixel. This is also called the pixel field of view. The sensor may be monochrome or color. In the case of a monochrome sensor, the light incident on each pixel is integrated and the resulting image is a grayscale like picture. For color images, a mosaic color filter is typically placed over the pixels to create a color image. An example is a Bayer filter. The signal incident on each pixel is then digitized to a bit stream. == Image quality == The quality of an image is dependent upon both geometric and physical items. Geometrically, higher density of pixels across an image will give less blocky pixelation and thus a better geometric image quality. Lens aberrations also contribute to the quality of the image. Physically, diffraction due to the aperture stop will limit the resolvable spatial frequencies as a function of f-number. In the frequency domain, Modulation Transfer Function (MTF) is a measure of the quality of the imaging system. The MTF is a measure of the visibility of a sinusoidal variation in irradiance on the image plane as a function of the frequency of the sinusoid. It includes the effects of diffraction, aberrations and pixelation. For the lens, the MTF is the autocorrelation of the pupil function, so it accounts for the finite pupil extent and the lens aberrations. The sensor MTF is the Fourier Transform of the pixel geometry. For a square pixel, MTF(ξ) = sin(πξp)/πξp where p is the pixel width and ξ is the spatial frequency. The MTF of the combination of the lens and detector is the product of the two component MTFs. == Perception == Color images can be perceived via two means. In the case of computer vision the light incident on the sensor comprises the image. In the case of visual perception, the human eye has a color dependent response to light so this must be accounted for. This is important consideration when converting to grayscale. == Image formation in eye == The principal difference between the lens of the eye and an ordinary optical lens is that the former is flexible. The radius of the curvature of the anterior surface of the lens is greater than the radius of its posterior surface. The shape of the lens is controlled by tension in the fibers of the ciliary body. To focus on distant objects, the controlling muscles cause the lens to be relatively flattened. Similarly, these muscles allow the lens to become thicker in order to focus on objects near the eye. The distance between the center of the lens and the retina (focal length) varies from approximately 17 mm to about 14 mm, as the refractive power of the lens increases from its minimum to its maximum. When the eye focuses on an object farther away than about 3 m, the lens exhibits its lowest refractive power. When the eye focuses on a close object, the lens is most strongly refractive.
Algorithmic inference
Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst. Cornerstones in this field are computational learning theory, granular computing, bioinformatics, and, long ago, structural probability (Fraser 1966). The main focus is on the algorithms which compute statistics rooting the study of a random phenomenon, along with the amount of data they must feed on to produce reliable results. This shifts the interest of mathematicians from the study of the distribution laws to the functional properties of the statistics, and the interest of computer scientists from the algorithms for processing data to the information they process. == The Fisher parametric inference problem == Concerning the identification of the parameters of a distribution law, the mature reader may recall lengthy disputes in the mid 20th century about the interpretation of their variability in terms of fiducial distribution (Fisher 1956), structural probabilities (Fraser 1966), priors/posteriors (Ramsey 1925), and so on. From an epistemology viewpoint, this entailed a companion dispute as to the nature of probability: is it a physical feature of phenomena to be described through random variables or a way of synthesizing data about a phenomenon? Opting for the latter, Fisher defines a fiducial distribution law of parameters of a given random variable that he deduces from a sample of its specifications. With this law he computes, for instance "the probability that μ (mean of a Gaussian variable – omeur note) is less than any assigned value, or the probability that it lies between any assigned values, or, in short, its probability distribution, in the light of the sample observed". == The classic solution == Fisher fought hard to defend the difference and superiority of his notion of parameter distribution in comparison to analogous notions, such as Bayes' posterior distribution, Fraser's constructive probability and Neyman's confidence intervals. For half a century, Neyman's confidence intervals won out for all practical purposes, crediting the phenomenological nature of probability. With this perspective, when you deal with a Gaussian variable, its mean μ is fixed by the physical features of the phenomenon you are observing, where the observations are random operators, hence the observed values are specifications of a random sample. Because of their randomness, you may compute from the sample specific intervals containing the fixed μ with a given probability that you denote confidence. === Example === Let X be a Gaussian variable with parameters μ {\displaystyle \mu } and σ 2 {\displaystyle \sigma ^{2}} and { X 1 , … , X m } {\displaystyle \{X_{1},\ldots ,X_{m}\}} a sample drawn from it. Working with statistics S μ = ∑ i = 1 m X i {\displaystyle S_{\mu }=\sum _{i=1}^{m}X_{i}} and S σ 2 = ∑ i = 1 m ( X i − X ¯ ) 2 , where X ¯ = S μ m {\displaystyle S_{\sigma ^{2}}=\sum _{i=1}^{m}(X_{i}-{\overline {X}})^{2},{\text{ where }}{\overline {X}}={\frac {S_{\mu }}{m}}} is the sample mean, we recognize that T = S μ − m μ S σ 2 m − 1 m = X ¯ − μ S σ 2 / ( m ( m − 1 ) ) {\displaystyle T={\frac {S_{\mu }-m\mu }{\sqrt {S_{\sigma ^{2}}}}}{\sqrt {\frac {m-1}{m}}}={\frac {{\overline {X}}-\mu }{\sqrt {S_{\sigma ^{2}}/(m(m-1))}}}} follows a Student's t distribution (Wilks 1962) with parameter (degrees of freedom) m − 1, so that f T ( t ) = Γ ( m / 2 ) Γ ( ( m − 1 ) / 2 ) 1 π ( m − 1 ) ( 1 + t 2 m − 1 ) m / 2 . {\displaystyle f_{T}(t)={\frac {\Gamma (m/2)}{\Gamma ((m-1)/2)}}{\frac {1}{\sqrt {\pi (m-1)}}}\left(1+{\frac {t^{2}}{m-1}}\right)^{m/2}.} Gauging T between two quantiles and inverting its expression as a function of μ {\displaystyle \mu } you obtain confidence intervals for μ {\displaystyle \mu } . With the sample specification: x = { 7.14 , 6.3 , 3.9 , 6.46 , 0.2 , 2.94 , 4.14 , 4.69 , 6.02 , 1.58 } {\displaystyle \mathbf {x} =\{7.14,6.3,3.9,6.46,0.2,2.94,4.14,4.69,6.02,1.58\}} having size m = 10, you compute the statistics s μ = 43.37 {\displaystyle s_{\mu }=43.37} and s σ 2 = 46.07 {\displaystyle s_{\sigma ^{2}}=46.07} , and obtain a 0.90 confidence interval for μ {\displaystyle \mu } with extremes (3.03, 5.65). == Inferring functions with the help of a computer == From a modeling perspective the entire dispute looks like a chicken-egg dilemma: either fixed data by first and probability distribution of their properties as a consequence, or fixed properties by first and probability distribution of the observed data as a corollary. The classic solution has one benefit and one drawback. The former was appreciated particularly back when people still did computations with sheet and pencil. Per se, the task of computing a Neyman confidence interval for the fixed parameter θ is hard: you do not know θ, but you look for disposing around it an interval with a possibly very low probability of failing. The analytical solution is allowed for a very limited number of theoretical cases. Vice versa a large variety of instances may be quickly solved in an approximate way via the central limit theorem in terms of confidence interval around a Gaussian distribution – that's the benefit. The drawback is that the central limit theorem is applicable when the sample size is sufficiently large. Therefore, it is less and less applicable with the sample involved in modern inference instances. The fault is not in the sample size on its own part. Rather, this size is not sufficiently large because of the complexity of the inference problem. With the availability of large computing facilities, scientists refocused from isolated parameters inference to complex functions inference, i.e. re sets of highly nested parameters identifying functions. In these cases we speak about learning of functions (in terms for instance of regression, neuro-fuzzy system or computational learning) on the basis of highly informative samples. A first effect of having a complex structure linking data is the reduction of the number of sample degrees of freedom, i.e. the burning of a part of sample points, so that the effective sample size to be considered in the central limit theorem is too small. Focusing on the sample size ensuring a limited learning error with a given confidence level, the consequence is that the lower bound on this size grows with complexity indices such as VC dimension or detail of a class to which the function we want to learn belongs. === Example === A sample of 1,000 independent bits is enough to ensure an absolute error of at most 0.081 on the estimation of the parameter p of the underlying Bernoulli variable with a confidence of at least 0.99. The same size cannot guarantee a threshold less than 0.088 with the same confidence 0.99 when the error is identified with the probability that a 20-year-old man living in New York does not fit the ranges of height, weight and waistline observed on 1,000 Big Apple inhabitants. The accuracy shortage occurs because both the VC dimension and the detail of the class of parallelepipeds, among which the one observed from the 1,000 inhabitants' ranges falls, are equal to 6. == The general inversion problem solving the Fisher question == With insufficiently large samples, the approach: fixed sample – random properties suggests inference procedures in three steps: === Definition === For a random variable and a sample drawn from it a compatible distribution is a distribution having the same sampling mechanism M X = ( Z , g θ ) {\displaystyle {\mathcal {M}}_{X}=(Z,g_{\boldsymbol {\theta }})} of X with a value θ {\displaystyle {\boldsymbol {\theta }}} of the random parameter Θ {\displaystyle \mathbf {\Theta } } derived from a master equation rooted on a well-behaved statistic s. === Example === You may find the distribution law of the Pareto parameters A and K as an implementation example of the population bootstrap method as in the figure on the left. Implementing the twisting argument method, you get the distribution law F M ( μ ) {\displaystyle F_{M}(\mu )} of the mean M of a Gaussian variable X on the basis of the statistic s M = ∑ i = 1 m x i {\textstyle s_{M}=\sum _{i=1}^{m}x_{i}} when Σ 2 {\displaystyle \Sigma ^{2}} is known to be equal to σ 2 {\displaystyle \sigma ^{2}} (Apolloni, Malchiodi & Gaito 2006). Its expression is: F M ( μ ) = Φ ( m μ − s M σ m ) , {\displaystyle F_{M}(\mu )=\Phi {\left({\frac {m\mu -s_{M}}{\sigma {\sqrt {m}}}}\right)},} shown in the figure on the right, where Φ {\displaystyle \Phi } is the cumulative distribution function of a standard normal distribution. Computing a confidence interval for M given its distribution function is straightforward: we need only find two quantiles (for instance δ / 2 {\displaystyle \delta /2} and 1 − δ / 2 {\displaystyle 1-\delta /2} quantiles in case we are interested in a confidence interval of level δ symmetric in the tail's probabilities) as indicated on the left in the diagram showing the behavior of
Futuresport
Futuresport is a 1998 American made-for-television sports film directed by Ernest Dickerson, starring Dean Cain, Vanessa Williams, and Wesley Snipes. It originally aired on ABC in October 1998, was released on VHS and DVD in March 1999 and then distributed outside of the U.S. by Minerva Pictures. == Plot == The film is set in 2025, and centers on a sport called "Futuresport" (a combination of basketball, baseball and hockey that uses hoverboards and rollerblades) created as a non-lethal way to reduce gang warfare. Tre Ramzey (Dean Cain) along with his ex-girlfriend Alex Torres (Vanessa Williams) and his old coach Obike Fixx (Wesley Snipes) must prevent an all out war between the North American Alliance and the Pan-Pacific Commonwealth (The Com). At stake is who rules over the Hawaiian Islands—which are being terrorized by Eric Sythe (JR Bourne) and his gang the Hawaiian Liberation Organization (Hilo). It takes a revolutionary sport to stop a revolution. == Cast ==
Smartglasses
Smartglasses or smart glasses are eye or head-worn wearable computers. Many smartglasses include displays that add information alongside or to what the wearer sees. Alternatively, smartglasses are sometimes defined as glasses that are able to change their optical properties, such as smart sunglasses that are programmed to change tint by electronic means. Alternatively, smartglasses are sometimes defined as glasses that include headphone functionality. A pair of smartglasses can be considered an augmented reality device if it performs pose tracking. Superimposing information onto a field of view is achieved through an optical head-mounted display (OHMD) or embedded wireless glasses with transparent heads-up display (HUD) or augmented reality (AR) overlay. These systems have the capability to reflect projected digital images as well as allowing the user to see through it or see better with it. While early models can perform basic tasks, such as serving as a front end display for a remote system, as in the case of smartglasses utilizing cellular technology or Wi-Fi, modern smart glasses are effectively wearable computers which can run self-contained mobile apps. Some are handsfree and can communicate with the Internet via natural language voice commands, while others use touch buttons. Like other computers, smartglasses may collect information from internal or external sensors. It may control or retrieve data from other instruments or computers. In most cases, it supports wireless technologies like Bluetooth, Wi-Fi, and GPS. A small number of models run a mobile operating system and function as portable media players to send audio and video files to the user via a Bluetooth or WiFi headset. Some smartglasses models also feature full lifelogging and activity tracker capability. Smartglasses devices may also have features found on a smartphone. Some have activity tracker functionality features (also known as "fitness tracker") as seen in some GPS watches. == Features and applications == As with other lifelogging and activity tracking devices, the GPS tracking unit and digital camera of some smartglasses can be used to record historical data. For example, after the completion of a workout, data can be uploaded into a computer or online to create a log of exercise activities for analysis. Some smart watches can serve as full GPS navigation devices, displaying maps and current coordinates. Users can "mark" their current location and then edit the entry's name and coordinates, which enables navigation to those new coordinates. Although some smartglasses models manufactured in the 21st century are completely functional as standalone products, most manufacturers recommend or even require that consumers purchase mobile phone handsets that run the same operating system so that the two devices can be synchronized for additional and enhanced functionality. The smartglasses can work as an extension, for head-up display (HUD) or remote control of the phone and alert the user to communication data such as calls, SMS messages, emails, and calendar invites. === Security applications === Smart glasses could be used as a body camera. In 2018, Chinese police in Zhengzhou and Beijing were using smart glasses to take photos which are compared against a government database using facial recognition to identify suspects, retrieve an address, and track people moving beyond their home areas. === Sport applications === Smart glasses are used in sports like cycling, running, skiing, golf, tennis, or sailing, giving athletes real-time, heads-up data without looking down at the screen of a watch or smartphone. In 2025, Meta has announced a new partnership with sports eyewear brand Oakley. === Healthcare applications === Several proofs of concept for Google Glasses have been proposed in healthcare. In July 2013, Lucien Engelen started research on the usability and impact of Google Glass in health care. Engelen, who is based at Singularity University and in Europe at Radboud University Medical Center, is participating in the Glass Explorer program. Key findings of Engelen's research included: The quality of pictures and video are usable for healthcare education, reference, and remote consultation. The camera needs to be tilted to different angle for most of the operative procedures Tele-consultation is possible—depending on the available bandwidth—during operative procedures. A stabilizer should be added to the video function to prevent choppy transmission when a surgeon looks to screens or colleagues. Battery life can be easily extended with the use of an external battery. Controlling the device and/or programs from another device is needed for some features because of a sterile environment. Text-to-speech ("Take a Note" to Evernote) exhibited a correction rate of 60 percent, without the addition of a medical thesaurus. A protocol or checklist displayed on the screen of Google Glass can be helpful during procedures. Dr. Phil Haslam and Dr. Sebastian Mafeld demonstrated the first concept for Google Glass in the field of interventional radiology. They demonstrated the manner in which the concept of Google Glass could assist a liver biopsy and fistulaplasty, and the pair stated that Google Glass has the potential to improve patient safety, operator comfort, and procedure efficiency in the field of interventional radiology. In June 2013, surgeon Dr. Rafael Grossmann was the first person to integrate Google Glass into the operating theater, when he wore the device during a PEG (percutaneous endoscopic gastrostomy) procedure. In August 2013, Google Glass was also used at Wexner Medical Center at Ohio State University. Surgeon Dr. Christopher Kaeding used Google Glass to consult with a colleague in a distant part of Columbus, Ohio. A group of students at The Ohio State University College of Medicine also observed the operation on their laptop computers. Following the procedure, Kaeding stated, "To be honest, once we got into the surgery, I often forgot the device was there. It just seemed very intuitive and fit seamlessly." 16 November 2013, in Santiago de Chile, the maxillofacial team led by Dr.gn Antonio Marino conducted the first orthognathic surgery assisted with Google Glass in Latin America, interacting with them and working with simultaneous three-dimensional navigation. The surgical team was interviewed by ADN radio. In January 2014, Indian Orthopedic Surgeon Selene G. Parekh conducted the foot and ankle surgery using Google Glass in Jaipur, which was broadcast live on Google website via the internet. The surgery was held during a three-day annual Indo-US conference attended by a team of experts from the US and co-organized by Ashish Sharma. Sharma said Google Glass allows looking at an X-Ray or MRI without taking the eye off of the patient and allows a doctor to communicate with a patient's family or friends during a procedure. In Australia, during January 2014, Melbourne tech startup Small World Social collaborated with the Australian Breastfeeding Association to create the first hands-free breastfeeding Google Glass application for new mothers. The application, named Google Glass Breastfeeding app trial, allows mothers to nurse their baby while viewing instructions about common breastfeeding issues (latching on, posture etc.) or call a lactation consultant via a secure Google Hangout, who can view the issue through the mother's Google Glass camera. The trial was successfully concluded in Melbourne in April 2014, and 100% of participants were breastfeeding confidently. == Display types == Various techniques have existed for see-through HMDs. Most of these techniques can be summarized into two main families: "Curved Mirror" (or Curved Combiner) based and "Waveguide" or "Light-guide" based. The mirror technique has been used in EyeTaps, by Meta in their Meta 1, by Vuzix in their Star 1200 product, by Olympus, and by Laster Technologies. Various waveguide techniques have existed for some time. These techniques include diffraction optics, holographic optics, polarized optics, reflective optics, and projection: Diffractive waveguide – slanted diffraction grating elements (nanometric 10E-9). Nokia technique now licensed to Vuzix. Holographic waveguide – 3 holographic optical elements (HOE) sandwiched together (RGB). Used by Sony and Konica Minolta. Reflective waveguide – A thick light guide with single semi-reflective mirror is used by Epson in their Moverio product. A curved light guide with partial-reflective segmented mirror array to out-couple the light is used by tooz technologies GmbH. Virtual retinal display (VRD) – Also known as a retinal scan display (RSD) or retinal projector (RP), is a display technology that draws a raster display (like a television) directly onto the retina of the eye - developed by MicroVision, Inc. OLED microdisplays for near-eye applications (outdoor optical equipment, night vision glasses, ocular equipment for medical devices, augme
Sourcegraph
Sourcegraph Inc. is a company developing code search and code intelligence tools that semantically index and analyze large codebases so that they can be searched across commercial, open-source, local, and cloud-based repositories. The company has two core products: Code Search and Amp. A previous core product, Cody, retains limited legacy support for existing customers. Code Search was initially released in 2013 under the name Sourcegraph, but was rebranded to Code Search when the company unveiled Cody in 2023. As of 2021, the platform has around 800,000 developers and has indexed around 54 billion lines of code. In July 2025, new accounts for Cody were discontinued, and a new AI coding project, Amp, was released. In December 2025, Amp was spun-off to become a separate company. == History == Sourcegraph Inc. was founded by Stanford graduates Quinn Slack and Beyang Liu to drive the development of a code search and code intelligence tool, formerly called Sourcegraph. It was first released in 2013 but was rebranded to Code Search in 2023. It was partly inspired by Liu's experience using Google Code Search while he was a Google intern, It was designed to "tackle the big code problem" by enabling developers to manage large codebases that span multiple repositories, programming languages, file formats, and projects. Code Search was initially self-hosted by each customer on their own infrastructure. Early customers included Uber, Dropbox, and Lyft. In 2016, Code Search was criticized for being provided with a Fair Source License with the developers explaining that "all of Sourcegraph's source code is publicly available and hackable" and was intended to "help open sourcers strike a balance between getting paid and preserving their values". In 2018, Code Search was licensed under the Apache License 2.0, and Sourcegraph OSS has since been released under the Apache License 2.0. The commercial version, Code Search Enterprise, has been released under its own license. In 2023, Code Search was criticized for dropping the Apache license for most of its code, leaving it public but only available under its Enterprise license. In 2024, the main repository was made completely private. In 2019, Code Search was integrated into the GitLab codebase, giving GitLab users access to a browser-based developer platform. In 2021, a browser-based portal became available, allowing users to browse open-source projects and personal private code for free. In 2022, Sourcegraph Cloud, a commercial single-tenant cloud solution for organizations with more than 100 developers, was launched. Sourcegraph has raised a total of $223 million in financing to date. Its most recent $125 million Series D investment in 2021 valued the company at $2.625 billion, a 300% growth from its previous valuation in 2020. In 2023 Sourcegraph Inc. unveiled their new product Cody, and rebranded Sourcegraph to Code Search. In 2025, Sourcegraph announced the discontinuation of Cody Free, Pro, and Enterprise Starter plans, effective July 23, 2025, and launched Amp, a new AI coding agent. == Products == The company has three major products: Code Search, Amp, and Cody. === Sourcegraph Code Search === Code Search tool is used to search and summarize code. It supports over 30 programming languages and integrates with GitHub and GitLab for code hosting, Codecov for code coverage, and Jira Software for project management. Sourcegraph's Code Search uses a variant of Google's PageRank algorithm to rank results by relevance. While it was originally launched under the Apache License, on June 13, 2023, it was relicensed to the non-open-source "Sourcegraph Enterprise" license. Then, on August 22, 2024, the source code was moved to a private repository, and thus no longer source-available. === Sourcegraph Amp === Launched in 2025, Amp can generate code, generate documentation, write tests, and perform refactoring operations on projects. The tool operates on a credit-based pricing model and is available through web interfaces, command-line tools, and IDE extensions. In December 2025, Sourcegraph announced that Amp would be spun-off to become a separate company. === Sourcegraph Cody === Cody is an AI coding application for writing and maintaining code. Cody was released in December 2023 and was available for Microsoft Visual Studio Code and most JetBrains IDEs. As of July 2025, Cody Free, Pro, and Enterprise Starter plans have been discontinued, with only Cody Enterprise remaining available for existing enterprise customers.
Box blur
A box blur (also known as a box linear filter) is a spatial domain linear filter in which each pixel in the resulting image has a value equal to the average value of its neighboring pixels in the input image. It is a form of low-pass ("blurring") filter. A 3 by 3 box blur ("radius 1") can be written as matrix 1 9 [ 1 1 1 1 1 1 1 1 1 ] . {\displaystyle {\frac {1}{9}}{\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}.} Due to its property of using equal weights, it can be implemented using a much simpler accumulation algorithm, which is significantly faster than using a sliding-window algorithm. Box blurs are frequently used to approximate a Gaussian blur. By the central limit theorem, repeated application of a box blur will approximate a Gaussian blur. In the frequency domain, a box blur has zeros and negative components. That is, a sine wave with a period equal to the size of the box will be blurred away entirely, and wavelengths shorter than the size of the box may be phase-reversed, as seen when two bokeh circles touch to form a bright spot where there would be a dark spot between two bright spots in the original image. == Extensions == Gwosdek, et al. has extended Box blur to take a fractional radius: the edges of the 1-D filter are expanded with a fraction. It makes slightly better gaussian approximation possible due to the elimination of integer-rounding error. Mario Klingemann has a "stack blur" that tries to better emulate gaussian's look in one pass by stacking weights: 1 9 [ 1 2 3 2 1 ] {\displaystyle {\frac {1}{9}}{\begin{bmatrix}1&2&3&2&1\end{bmatrix}}} The triangular impulse response it forms decomposes to two rounds of box blur. Stacked Integral Image by Bhatia et al. takes the weighted average of a few box blurs to fit the gaussian response curve. == Implementation == The following pseudocode implements a 3x3 box blur. The example does not handle the edges of the image, which would not fit inside the kernel, so that these areas remain unblurred. In practice, the issue is better handled by: Introducing an alpha channel to represent the absence of colors; Extending the boundary by filling in values, ranked by quality: Fill in a mirrored image at the border Fill in a constant color extending from the last pixel Pad in a fixed color A number of optimizations can be applied when implementing the box blur of a radius r and N pixels: The box blur is a separable filter, so that only two 1D passes of averaging 2 r + 1 pixels will be needed, one horizontal and one vertical, for each pixel. This lowers the complexity from O(Nr2) to O(Nr). In digital signal processing terminology, each pass is a moving-average filter. Accumulation. Instead of discarding the sum for each pixel, the algorithm re-uses the previous sum, and updates it by subtracting away the old pixel and adding the new pixel in the blurring range. A summed-area table can be used similarly. This lowers the complexity from O(Nr) to O(N). When being used in multiple passes to approximate a Gaussian blur, the cascaded integrator–comb filter construction allows for doing the equivalent operation in a single pass.
Age Of
Age Of is the eighth studio album by American electronic producer Oneohtrix Point Never, released on June 1, 2018, on Warp Records. Recorded over two years, it is the first Oneohtrix Point Never album to prominently feature Daniel Lopatin's own vocals. The album was accompanied by the MYRIAD tour, which premiered as a "conceptual concertscape" in 2018 at the Park Avenue Armory and ended its run in 2019. It features contributions from James Blake (who additionally produced and mixed the album), Anohni, Prurient, Kelsey Lu and Eli Keszler. The artwork, which employs Jim Shaw's "The Great Whatsit" as a central image, was designed by David Rudnick. While not entering the official United States Billboard 200 chart, it peaked at number 59 on the magazine's Top Current Albums chart. == Background == Lopatin produced Age Of in parts of a two-year period, during which he was also producing for other artists, including Anohni, FKA Twigs, Iggy Pop, and David Byrne. After composing the soundtrack for the Safdie Brothers' 2017 film Good Time, Lopatin moved to an Airbnb lodge in South Central Massachusetts, derived from his aspiration to live out the modern cliche of musicians moving to the woods to record albums; the eerie atmosphere in the lodge at nighttime influenced his desire to make "weird, little nightmare ballads". In addition to Lopatin's own singing, the album also features vocal performances from Anohni and Prurient, while instrumentalists Kelsey Lu and Eli Keszler contribute to several tracks. When the record was nearly finished, Lopatin reached out to musician James Blake to contribute to the mixing process, eventually traveling to Los Angeles to complete the album. The track "The Station" was originally composed as a demo for R&B singer Usher which was ultimately not used. On July 9, 2018, Lopatin released the original topline (vocal melody) demo for The Station through Sendspace. The track "Toys 2" imagines a theoretical sequel to the 1992 film Toys where actor Robin Williams' image has been recreated with CGI (as his will specifically forbade any usage of his image after his death), and pokes fun at the common electronic music trope of composing a soundtrack to a theoretical film (which Lopatin described as "horribly cliché"). == Concept and MYRIAD == Influences on Age Of included Stanley Kubrick's 1968 film 2001: A Space Odyssey, which inspired the narrative of the album's accompanying performance installation and tour MYRIAD, as well as William Strauss's The Fourth Turning, a favorite book of former White House Chief Strategist Steve Bannon, which Lopatin described as "insidious, like the voice of a computer insisting on the truth about history without any sensitivity given to how complex and non-linear systems might be"; Lopatin was subsequently inspired to "[use] that sort of taxonomy as a kind of farce to then create these little frameworks for understanding". Other inspirations included the writings of the 1990s multidisciplinary collective Cybernetic Culture Research Unit and the works of singer-songwriters such as Bruce Cockburn, Bob Dylan, and Paul Simon. Around the time Lopatin began finalizing Age Of in his Airbnb lodge, he began working on the concept for MYRIAD, a conceptual concert performance which premiered at Park Avenue Armory. He described the concept as a four-part "epochal song cycle" showcasing the idiocy of previous generations of living organisms. The loose story concerns a group of artificial intelligences near the end of time named a "Limitless Living Informational Intelligence" (represented in the MYRIAD logo as nine squares) which, for leisurely purposes, attempt to replicate the cultures and behaviors of the previously existent human species. It does this by determining an "average" of human experiences through the species' "recorded output", and does so through imperfect, heuristic techniques. The show was consequently divided into four sections, each representing an epoch of the cycle concept loosely inspired by the Strauss–Howe generational theory: the Age of Ecco, the Age of Harvest, the Age of Excess, and the Age of Bondage. Ecco is "a phase of pre-evolutionary ignorance", Harvest is "living in agrarian harmony with the world", Excess is "the age of unchecked industrial ambition", and Bondage is "an era of engorgement, wherein "we keep making more and more shit until there's no space left." MYRIAD mainly featured "three-hundred pound sculptures that hang from the ceiling like kebabs that secrete ooze", and a full ensemble that toured to perform songs from Age Of, including Eli Keszler, Kelly Moran and Aaron David Ross. The sculptures, as well as the visuals displayed on five polygon panels, were created by frequent Oneohtrix Point Never collaborator Nate Boyce. Initially, Lopatin planned for each of the album's four epoches to be represented by fragrances, the more noisy epochs being pleasant to the nose to make a "weird dissonance". However, due to lack of time and resources, that part of the plan was scrapped. == Composition == Whereas previous Oneohtrix Point Never albums followed musical styles from only distinctive eras, Age Of is the first album by Lopatin to incorporate elements of unique genres from a variety of periods, hence the "incompleteness" of its title according to reviewer Heather Phares, and his first pop-song-oriented release since his work for Ford & Lopatin. The sound palettes it uses are those from a variety of styles such as chamber pop, "android"-like folk and country music, yacht rock, smooth jazz, R&B, Future-style soul, black metal, new age, and stadium pop, as well as post-industrial sounds on tracks like "Warning", "We'll Take It" and "Same", and, in particular, baroque music and medieval music on the opening title track, "Age Of". Critics also noted elements of Lopatin's past discography being present on Age Of. The instrumentation of Age Of is made up of MIDI harpsichords, guitars, pianos, brass and vocals, as well as Lopatin's trademark unorthodox sound design, samples and synth presets. The LP's use of the harpsichord shows its similarities "with Eastern instruments such as the koto and with rapid-fire electronic melodies", wrote Phares. == Critical reception == Age Of was critically well-received upon its distribution. Some reviewers praised the album's use of collaborators. Reviewing the album for AllMusic, Heather Phares called Age Of a "landmark work" for Lopatin. She praised it as his "widest-ranging" release, elaborating that he "matches the album's ambition with plenty of emotion" and "gives his music exciting new shapes." Ross Devlin of The Skinny, in a five-star review of the record, also highlighted the album's amount of ambition, particularly the "wealth of exquisitely baroque moments, exploring history as a pliable, multi-dimensional rift", that gave it "exceptional sonic depth". The Observer praised Age Of for continuing the "off-kilter composition and unexpected instrumentation" of Lopatin's previous releases, and critic Matt McDermott highlighted that the producer increased his musical range with the record: "It's a dizzying trip meant to shore up Lopatin's status as an avant-garde auteur while aiding his forays into mainstream pop culture." Age Of was ranked the 15th best release of the year in The Wire magazine's annual critics' poll. == Track listing == Notes "Myriad Industries" is stylized as "myriad.industries". Sample credits "Age Of" contains a sample of "Blow the Wind" by Jocelyn Pook. "Manifold" contains a sample from "Overture (Ararat the Border Crossing)" by Tayfun Erdem; and a sample from "Venice Beach in Winter" (listed in the liner notes as "a keyboard sample from Reharmonization") by Julian Bradley. "Myriad Industries" contains a sample of "EchoSpace" by Gil Trythall. == Accolades == == Personnel == Daniel Lopatin – production, lead vocals, album art, design James Blake – additional production, mixing, keyboards Gabriel Schuman, Joshua Smith and Evan Sutton – assistance Greg Calbi – mastering David Rudnick – album art, design Prurient – vocals Kelsey Lu – keyboards Anohni – vocals Eli Keszler – drums Shaun Trujillo – words == Charts ==