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  List of Java software and tools

  This is a list of software and programming tools for the Java programming language, which includes frameworks, libraries, IDEs, build tools, application servers, and related projects. == Java frameworks == == Libraries == Apache Ant – build automation tool Apache Batik – SVG processing Apache Cayenne – object-relational mapping Apache Xerces – collection of software libraries for parsing, validating, serializing and manipulating XML. Applet – applet API Ardor3D – 3D graphics engine Bonita BPM – workflow engine Cassowary – constraint solving Checkstyle – static code analysis GNU Classpath – standard library implementation Colt – scientific computing and technical computing Commons Daemon – manages applications as daemons DESMO-J – discrete event simulation Diagrams.net – diagramming Disruptor – high-performance messaging Dom4j – XML processing Dynamic Languages Toolkit – support for dynamic programming languages on the JVM Echo – GUI Flying Saucer – XHTML/CSS rendering Formatting Objects Processor – XSL-FO to PDF H2 Database Engine – relational database IAIK-JCE – cryptography Internet Foundation Classes – legacy GUI JavaBeans – reusable component architecture for enabling encapsulation, events, and properties for software components JavaCC – open-source parser generator and lexical analyzer Java Class Library – standard library of Java and other JVM languages Java Native Access – provides Java programs easy access to native shared libraries without using the Java Native Interface Javolution – real-time computing Jblas – linear algebra JDBCFacade – simplifies JDBC use JExcel – Excel API JFugue – music programming JMusic – music programming Joget Workflow – workflow engine JOOQ Object Oriented Querying – fluent API for SQL JPOS – financial messaging JUNG – open-source graph modeling and visualization LanguageWare – language processing LibGDX – game development Modular Audio Recognition Framework – collection of voice, sound, speech, text and natural language processing algorithms. ASM – bytecode manipulation Open Inventor – 3D graphics OpenPDF – PDF Parallel Colt – parallel computing Parboiled – parser PlayN – game development QOCA – constraint solving QtJambi – Qt bindings SLF4J – logging StableUpdate – update management SWT – GUI SuanShu – numerical computing SwingLabs – GUI extensions UBY – natural language processing Undecimber – calendar XDoclet – attribute-oriented programming XINS – XML network services XStream – object serialization == Machine learning and AI == Apache Mahout – scalable machine learning library focused on clustering, classification, and collaborative filtering Apache MXNet – deep learning framework with Java API support Apache OpenNLP – machine learning based toolkit for natural language processing of text Deeplearning4j – distributed deep learning library Deep Java Library – open-source deep learning framework developed by Amazon Web Services Encog – framework for neural networks, genetic algorithms, Hidden Markov model, and Bayesian networks. LIBSVM – Support Vector Machine implementation Mallet – machine learning toolkit for classification, clustering, and topic modeling. MLlib – distributed machine-learning framework on top of Apache Spark Core Neuroph – lightweight neural network framework Weka – collection of machine learning algorithms for data mining Yooreeka – machine learning == Data mining == Java Data Mining (JDM) – standard Java API for data mining Massive Online Analysis (MOA) – data stream mining with concept drift == Math and scientific libraries == Apache Commons Math – general-purpose mathematics library including statistics, linear algebra, and optimization. Colt – high-performance scientific computing, including linear algebra and random numbers. Efficient Java Matrix Library (EJML) – dense and sparse matrix computations and linear algebra Easy Java Simulations – Open Source Physics project designed to create discrete computer simulations Exp4j – evaluates mathematical expressions at runtime GroovyLab – numerical computational environment Hipparchus – fork of Apache Commons Math with updated algorithms for statistics, linear algebra, and optimization. JAMA – numerical linear algebra library Jblas: Linear Algebra for Java (Jblas) – linear algebra library using native BLAS/LAPACK bindings Java Astrodynamics Toolkit – numerical library of software components for use in spaceflight applications for Java or MATLAB Matrix Toolkit Java (MTJ) – linear algebra library with BLAS and LAPACK support OjAlgo – optimization, linear algebra, and financial calculations. OptimJ – extension for mathematical optimization and constraint programming Parallel Colt – A parallel extension of Colt SuanShu – numerical analysis, linear algebra, statistics, and optimization. == Integrated development environments == See also: Java IDEs on Wikibooks Android Studio – IDE for Google's Android operating system BlueJ – educational IDE for teaching Java DrJava – lightweight Java IDE for beginners Eclipse IDE – open-source IDE with extensive plugin ecosystem Greenfoot – educational IDE IntelliJ IDEA – commercial and community editions from JetBrains JDeveloper – freeware IDE supplied by Oracle Corporation jGRASP – software visualizations MyEclipse – Java EE IDE NetBeans IDE – Apache NetBeans Visual Studio Code – general-purpose editor with Java extensions === Online IDEs === Eclipse Che GitHub Codespaces JDoodle Replit == Text editors with Java support == == Build tools and package managers == Apache Ant – automating software build Apache Ivy – subproject of Apache Ant Apache Maven – build automation and dependency management Boot – build automation for Clojure CMake – build tool with limited support for java Gradle – modern build automation tool Go continuous delivery (GoCD) – continuous delivery and build automation server Jenkins – automation server continuous delivery JitPack – package repository for Git projects Leiningen – build automation for Clojure Simple build tool (sbt) – open-source build tool Spring Roo – rapid application development of Java-based enterprise software WaveMaker – low-code development platform == Java runtimes, compilers and virtual machines == Android Runtime – runtime environment javac – Java programming language compiler Java Virtual Machine (JVM) – virtual machine that executes Java bytecode JD Decompiler JEB decompiler – disassembler and decompiler software for Android applications GraalVM – Just-in-time compilation HotSpot – JVM implementation included in OpenJDK == JVM languages and dialects == Clojure – Lisp dialect Groovy JRuby – Ruby implementation Jython – Python implementation Kotlin – popular for Android app development Renjin – R implementation Scala == Application servers and containers == Apache Geronimo – open source application server Apache MINA – event-driven asynchronous network application framework Apache Tomcat – web container and web server Apache TomEE – Apache Tomcat with Java EE features Borland Enterprise Server – discontinued application server by Borland ColdFusion – commercial application server by Adobe Systems GlassFish – application server for Jakarta EE IBM WebSphere Application Server – enterprise application server by IBM IBM WebSphere Application Server Community Edition – open source edition of WebSphere (discontinued) JBoss Enterprise Application Platform – Red Hat's supported distribution of JBoss/WildFly JEUS – commercial Java EE application server from TmaxSoft Jetty – HTTP server and web container Lucee (formerly Railo) – open source CFML application server Netty – non-blocking I/O client–server framework for network applications Oracle Containers for J2EE – discontinued application server by Oracle Oracle WebLogic Server – enterprise application server by Oracle Orion Application Server – early commercial Java EE server by IronFlare Payara Server – fork of GlassFish for production use Resin – Java application server by Caucho (open source and professional editions) SAP NetWeaver Application Server – enterprise application server by SAP WildFly – application server == Debugging and profiling tools == jdb – Java debugger bundled with the JDK JConsole – JMX-compliant monitoring tool JDK Flight Recorder – method profiling, allocation profiling, and garbage collection related events. JProfiler – commercial Java profiler VisualVM – visual tool integrating commandline JDK tools for profiling and monitoring == Testing and quality assurance == Apache JMeter – load testing tool JaCoCo – Java code coverage library JArchitect – analyzes code quality, architecture, and dependencies. Jtest – software testing and static analysis JUnit – unit testing framework Mockito – open-source testing framework for Java PMD – static program analysis source code analyzer Selenium – browser automation for web app testing Spock – test framework SpotBugs (formerly FindBugs) – static analysis tool TestNG – testing framework inspired by JUnit and NUnit == Other == Apache XMLBeans –

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  Imaging

  Imaging is the process of creating visual representations of objects, scenes, or phenomena. The term encompasses both the formation of images through physical processes and the technologies used to capture, store, process, and display them. While traditional imaging relies on visible light, modern imaging systems can visualize information across the electromagnetic spectrum and through other physical phenomena such as sound waves, magnetic fields, and particle emissions, enabling the visualization of subjects invisible to the human eye. Imaging science is the multidisciplinary field concerned with the theoretical foundations and practical applications of image creation and analysis. The field draws on physics, mathematics, electrical engineering, computer science, computer vision, and perceptual psychology to develop systems that generate, collect, duplicate, analyze, modify, and visualize images. == Principles == === The imaging chain === The imaging chain is a conceptual framework describing the interconnected components of any imaging system. Understanding each link in this chain allows engineers and scientists to optimize system performance for specific applications. The chain begins with the subject and its observable properties, typically energy that is emitted, reflected, or transmitted. A light source or other energy source may illuminate the subject to make these properties detectable. The capture device then collects this energy using appropriate sensors: optical systems for electromagnetic radiation, transducers for acoustic waves, or antenna arrays for radio frequencies. In digital systems, a processor converts the captured signals into a format suitable for rendering, applying algorithms for noise reduction, enhancement, or reconstruction. Finally, a display renders the processed information as a visible image on media such as paper, screens, or projection surfaces. Throughout this process, the characteristics of the human visual system inform design decisions, as the ultimate purpose of most imaging systems is to convey information to human observers. === Coherent and non-coherent imaging === Imaging systems are often classified by whether they use coherent or non-coherent illumination. Coherent imaging employs an active source that produces waves with a consistent phase relationship, as in radar, synthetic aperture radar, medical ultrasound, and optical coherence tomography. These systems can capture phase information in addition to amplitude, enabling techniques such as holography and interferometry. Non-coherent imaging systems, including conventional photography, fluorescence microscopy, and telescopes, rely on illumination sources where light waves have random phase relationships. == Methods and applications == Imaging methods span a wide range of physical principles, each suited to particular applications. Optical imaging encompasses photography, cinematography, microscopy, and telescopic observation. These methods capture electromagnetic radiation in or near the visible spectrum and form the basis of most consumer and scientific imaging. Extensions include thermography, which visualizes infrared radiation to reveal temperature distributions, and multispectral imaging, which captures data across multiple wavelength bands for applications in remote sensing and materials analysis. Medical imaging comprises techniques designed to visualize the interior of the human body for diagnostic and therapeutic purposes. Radiography and computed tomography use X-rays to image dense structures such as bone. Magnetic resonance imaging exploits nuclear magnetic properties to produce detailed soft-tissue images without ionizing radiation. Ultrasound imaging uses high-frequency sound waves and is particularly valuable for real-time imaging and fetal monitoring. Nuclear medicine techniques such as positron emission tomography track radioactive tracers to reveal metabolic activity. Emerging modalities include photoacoustic imaging, which combines optical and acoustic principles, and Magneto-acousto-electrical tomography, which maps electrical conductivity in biological tissues. Acoustic imaging uses sound waves to create images. Beyond medical ultrasound, applications include sonar for underwater navigation and mapping, seismic imaging for geological exploration, and industrial non-destructive testing. Radar and microwave imaging employ radio waves to detect and image objects. Synthetic aperture radar produces high-resolution images from aircraft or satellites regardless of weather or lighting conditions, making it essential for Earth observation and reconnaissance. Ground-penetrating radar images subsurface structures for archaeological and engineering applications. Electron and particle imaging use beams of electrons or other particles to achieve resolutions far beyond the diffraction limit of visible light. Electron microscopes can image individual atoms, enabling advances in materials science and structural biology. Chemical imaging combines spectroscopy with spatial imaging to map the chemical composition of samples, with applications in pharmaceutical development, food safety, and forensics. LIDAR (Light Detection and Ranging) measures distances using laser pulses to create three-dimensional representations of surfaces and objects, widely used in autonomous vehicles, topographic mapping, and forestry. Computational and digital imaging encompasses image processing, computer graphics, three-dimensional rendering, and digital image restoration. Computer vision applies algorithmic analysis to extract information from images automatically. == History == Photography and imaging have always been intertwined. When Joseph Nicéphore Niépce created the first permanent photograph using heliography in 1826, and Louis Daguerre refined the process into the daguerreotype a decade later, they weren't just inventing a new art form, they were laying the groundwork for an entire scientific discipline built on silver halide chemistry. For most of the nineteenth century, photography remained the province of specialists. That changed with George Eastman's Kodak camera, introduced in 1888 with the slogan "You press the button, we do the rest." Suddenly, anyone could take pictures. Around the same time, Wilhelm Röntgen stumbled onto X-rays in 1895, an accident that would spawn the entire field of medical imaging. World War II proved to be a turning point. Radar technology, developed frantically on both sides of the conflict, introduced concepts that engineers would later adapt for synthetic aperture radar and medical ultrasound. Then the charge-coupled device came: Willard Boyle and George E. Smith built the first one at Bell Labs in 1969, and within a few decades it had made film nearly obsolete. Magnetic resonance imaging arrived in the 1970s, offering doctors something X-rays never could, detailed views of soft tissue without any radiation. Digital cameras took over fast. By the 2000s, film was already in decline; by the 2010s, smartphones had put a surprisingly capable camera in nearly every pocket. Features that once required real skill, proper exposure, sharp focus, accurate color, became automatic. Today, billions of photos get uploaded to social media every day. As a result, a growing issue is that generative artificial intelligence can fabricate photorealistic images from scratch. What counts as a "real" photograph is no longer necessarily obvious.

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  Automatic meter reading

  Automatic meter reading (AMR) is the technology of automatically collecting consumption, diagnostic, and status data from water meter or energy metering devices (gas, electric) and transferring that data to a central database for billing, troubleshooting, and analyzing. This technology mainly saves utility providers the expense of periodic trips to each physical location to read a meter. Another advantage is that billing can be based on near real-time consumption rather than on estimates based on past or predicted consumption. This timely information coupled with analysis can help both utility providers and customers better control the use and production of electric energy, gas usage, or water consumption. AMR technologies include handheld, mobile and network technologies based on telephony platforms (wired and wireless), radio frequency (RF), or powerline transmission. == Technologies == === Touch technology === With touch-based AMR, a meter reader carries a handheld computer or data collection device with a wand or probe. The device automatically collects the readings from a meter by touching or placing the read probe close to a reading coil enclosed in the touchpad. When a button is pressed, the probe sends an interrogate signal to the touch module to collect the meter reading. The software in the device matches the serial number to one in the route database, and saves the meter reading for later download to a billing or data collection computer. Since the meter reader still has to go to the site of the meter, this is sometimes referred to as "on-site" AMR. Another form of contact reader uses a standardized infrared port to transmit data. Protocols are standardized between manufacturers by such documents as ANSI C12.18 or IEC 61107. === AMR hosting === AMR hosting is a back-office solution which allows a user to track their electricity, water, or gas consumption over the Internet. All data is collected in near real-time, and is stored in a database by data acquisition software. The user can view the data via a web application, and can analyze the data using various online analysis tools such as charting load profiles, analyzing tariff components, and verify their utility bill. === Radio frequency network === Radio frequency based AMR can take many forms. The more common ones are handheld, mobile, satellite and fixed network solutions. There are both two-way RF systems and one-way RF systems in use that use both licensed and unlicensed RF bands. In a two-way or "wake up" system, a radio signal is normally sent to an AMR meter's unique serial number, instructing its transceiver to power-up and transmit its data. The meter transceiver and the reading transceiver both send and receive radio signals. In a one-way "bubble-up" or continuous broadcast type system, the meter transmits continuously and data is sent every few seconds. This means the reading device can be a receiver only, and the meter a transmitter only. Data travels only from the meter transmitter to the reading receiver. There are also hybrid systems that combine one-way and two-way techniques, using one-way communication for reading and two-way communication for programming functions. RF-based meter reading usually eliminates the need for the meter reader to enter the property or home, or to locate and open an underground meter pit. The utility saves money by increased speed of reading, has less liability from entering private property, and has fewer missed readings from being unable to access the meter. The technology based on RF is not readily accepted everywhere. In several Asian countries, the technology faces a barrier of regulations in place pertaining to use of the radio frequency of any radiated power. For example, in India the radio frequency which is generally in ISM band is not free to use even for low power radio of 10 mW. The majority of manufacturers of electricity meters have radio frequency devices in the frequency band of 433/868 MHz for large scale deployment in European countries. The frequency band of 2.4 GHz can be now used in India for outdoor as well as indoor applications, but few manufacturers have shown products within this frequency band. Initiatives in radio frequency AMR in such countries are being taken up with regulators wherever the cost of licensing outweighs the benefits of AMR. ==== Handheld ==== In handheld AMR, a meter reader carries a handheld computer with a built-in or attached receiver/transceiver (radio frequency or touch) to collect meter readings from an AMR capable meter. This is sometimes referred to as "walk-by" meter reading since the meter reader walks by the locations where meters are installed as they go through their meter reading route. Handheld computers may also be used to manually enter readings without the use of AMR technology as an alternate but this will not support exhaustive data which can be accurately read using the meter reading electronically. ==== Mobile ==== Mobile or "drive-by" meter reading is where a reading device is installed in a vehicle. The meter reader drives the vehicle while the reading device automatically collects the meter readings. Often, for mobile meter reading, the reading equipment includes navigational and mapping features provided by GPS and mapping software. With mobile meter reading, the reader does not normally have to read the meters in any particular route order, but just drives the service area until all meters are read. Components often consist of a laptop or proprietary computer, software, RF receiver/transceiver, and external vehicle antennas. ==== Satellite ==== Transmitters for data collection satellites can be installed in the field next to existing meters. The satellite AMR devices communicate with the meter for readings, and then sends those readings over a fixed or mobile satellite network. This network requires a clear view to the sky for the satellite transmitter/receiver, but eliminates the need to install fixed towers or send out field technicians, thereby being particularly suited for areas with low geographic meter density. ==== RF technologies commonly used for AMR ==== Narrow Band (single fixed radio frequency) Spread spectrum Direct-sequence spread spectrum (DSSS) Frequency-hopping spread spectrum (FHSS) There are also meters using AMR with RF technologies such as cellular phone data systems, Zigbee, Bluetooth, Wavenis and others. Some systems operate with U.S. Federal Communications Commission (FCC) licensed frequencies and others under FCC Part 15, which allows use of unlicensed radio frequencies. ==== Wi-Fi ==== WiSmart is a versatile platform which can be used by a variety of electrical home appliances in order to provide wireless TCP/IP communication using the 802.11 b/g protocol. Devices such as the Smart Thermostat permit a utility to lower a home's power consumption to help manage power demand. The city of Corpus Christi became one of the first cities in the United States to implement citywide Wi-Fi, which had been free until May 31, 2007, mainly to facilitate AMR after a meter reader was attacked by a dog. Today many meters are designed to transmit using Wi-Fi, even if a Wi-Fi network is not available, and they are read using a drive-by local Wi-Fi hand held receiver. The meters installed in Corpus Christi are not directly Wi-Fi enabled, but rather transmit narrow-band burst telemetry on the 460 MHz band. This narrow-band signal has much greater range than Wi-Fi, so the number of receivers required for the project are far fewer. Special receiver stations then decode the narrow-band signals and resend the data via Wi-Fi. Most of the automated utility meters installed in the Corpus Christi area are battery powered. Wi-Fi technology is unsuitable for long-term battery-powered operation. === Power line communication === PLC is a method where electronic data is transmitted over power lines back to the substation, then relayed to a central computer in the utility's main office. This would be considered a type of fixed network system—the network being the distribution network which the utility has built and maintains to deliver electric power. Such systems are primarily used for electric meter reading. Some providers have interfaced gas and water meters to feed into a PLC type system. == Brief history == In 1972, Theodore George "Ted" Paraskevakos, while working with Boeing in Huntsville, Alabama, developed a sensor monitoring system which used digital transmission for security, fire and medical alarm systems as well as meter reading capabilities for all utilities. This technology was a spin-off of the automatic telephone line identification system, now known as caller ID. In 1974, Paraskevakos was awarded a U.S. patent for this technology. In 1977, he launched Metretek, Inc., which developed and produced the first fully automated, commercially available remote meter reading and load management system. Since this system was developed pre-Internet, Metret

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  Signal transfer function

  The signal transfer function (SiTF) is a measure of the signal output versus the signal input of a system such as an infrared system or sensor. There are many general applications of the SiTF. Specifically, in the field of image analysis, it gives a measure of the noise of an imaging system, and thus yields one assessment of its performance. == SiTF evaluation == In evaluating the SiTF curve, the signal input and signal output are measured differentially; meaning, the differential of the input signal and differential of the output signal are calculated and plotted against each other. An operator, using computer software, defines an arbitrary area, with a given set of data points, within the signal and background regions of the output image of the infrared sensor, i.e. of the unit under test (UUT), (see "Half Moon" image below). The average signal and background are calculated by averaging the data of each arbitrarily defined region. A second order polynomial curve is fitted to the data of each line. Then, the polynomial is subtracted from the average signal and background data to yield the new signal and background. The difference of the new signal and background data is taken to yield the net signal. Finally, the net signal is plotted versus the signal input. The signal input of the UUT is within its own spectral response. (e.g. color-correlated temperature, pixel intensity, etc.). The slope of the linear portion of this curve is then found using the method of least squares. == SiTF curve == The net signal is calculated from the average signal and background, as in signal to noise ratio (imaging)#Calculations. The SiTF curve is then given by the signal output data, (net signal data), plotted against the signal input data (see graph of SiTF to the right). All the data points in the linear region of the SiTF curve can be used in the method of least squares to find a linear approximation. Given n {\displaystyle n\,} data points ( x i , y i ) {\displaystyle (x_{i}\,,y_{i}\,)} a best fit line parameterized as y = m x + b {\displaystyle y=mx+b\,} is given by: m = ∑ x i y i n − ∑ x i n ∑ y i n ∑ x i 2 n − ( ∑ x i n ) 2 b = ∑ y i n − m ∑ x i n {\displaystyle m={\frac {{\frac {\sum x_{i}y_{i}}{n}}-{\frac {\sum x_{i}}{n}}{\frac {\sum y_{i}}{n}}}{{\frac {\sum x_{i}^{2}}{n}}-({\frac {\sum x_{i}}{n}})^{2}}}\qquad \qquad b={\frac {\sum y_{i}}{n}}-m{\frac {\sum x_{i}}{n}}}

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  Superintelligence ban

  Superintelligence ban refers to proposed legal, ethical, or policy measures intended to restrict or prohibit the development of artificial superintelligence, AI systems that would surpass human cognitive abilities in nearly all domains. The idea arises from concerns that such systems could become uncontrollable, potentially posing existential threats to humanity or causing severe social and economic disruption. == Background == The concept of limiting or banning superintelligence research has roots in early 21st-century debates on artificial general intelligence (AGI) safety. Thinkers such as Nick Bostrom and Eliezer Yudkowsky warned that self-improving AI could rapidly exceed human oversight. As advanced models like large-scale language models and autonomous agents began demonstrating complex reasoning abilities, policymakers and ethicists increasingly discussed the need for legal constraints on the creation of systems capable of recursive self-improvement. In October 2025, the Future of Life Institute published a statement calling for "a prohibition on the development of superintelligence, not lifted before there is broad scientific consensus that it will be done safely and controllably, and strong public buy-in." This statement was signed by various public personalities, such as Richard Branson and Steve Wozniak, and AI experts, such as Yoshua Bengio and Geoffrey Hinton. == Rationale == Supporters of a superintelligence ban argue that once AI systems surpass human intelligence, traditional containment, alignment, and control methods may fail. They contend that even limited experimentation with such systems could lead to irreversible outcomes, including loss of human decision-making power or unintended global harm. Some propose international treaties modeled after the nuclear non-proliferation framework to prevent a competitive AI arms race. Opponents argue that a ban would be difficult to define and enforce, given the lack of a precise threshold distinguishing advanced AGI from superintelligence. They also warn that excessive restriction could slow scientific progress, hinder beneficial automation, and encourage unregulated underground research. == Global discussion == Although no government has enacted an explicit superintelligence ban, the idea has been debated within the European Union, United Nations, and several independent AI safety organizations. The Future of Life Institute, Center for AI Safety, and other organizations have called for international cooperation to manage risks associated with the pursuit of superintelligent systems. In 2024 and 2025, proposals for a temporary moratorium on frontier AI research were circulated among major technology firms and research institutes, reflecting growing public concern over the trajectory of AI capabilities.

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  Reconstruction from projections

  The problem of reconstructing a multidimensional signal from its projection is uniquely multidimensional, having no 1-D counterpart. It has applications that range from computer-aided tomography to geophysical signal processing. It is a problem which can be explored from several points of view—as a deconvolution problem, a modeling problem, an estimation problem, or an interpolation problem. == Motivation and applications == Many fields in science and engineering use reconstruction from projections, especially in imaging. It is widely applied geophysical tomography, medical imaging and industrial radiography. For example, in a CT scanner, the 3D structure of the patient’s body being scanned is measured with beams going through the tissue and hitting a detector, giving a flat projection of the body from that angle. Multiple projections are put together to get an image of the position and shape of structures inside in 3D. == Problem statement and basics == A projection is a linear mapping of an M {\displaystyle M} dimensional signal into an N {\displaystyle N} dimensional one, where N ≤ M {\displaystyle N\leq M} . And the objective of reconstruction is to restore the M {\displaystyle M} dimensional signal based on the N {\displaystyle N} dimensional signal. The following case is a 2-D signal projected into 1D signal. The signal in the original coordinate is denoted as d ( u , v ) {\displaystyle d(u,v)} . Now consider a collimated beam of radiation coming from the opposite orientation of v ^ {\displaystyle {\hat {v}}} , producing a projection along u ^ {\displaystyle {\hat {u}}} . v ^ {\displaystyle {\hat {v}}} and u ^ {\displaystyle {\hat {u}}} are normal to each other, and the angle between u {\displaystyle u} and u ^ {\displaystyle {\hat {u}}} is theta. The signal obtained along u ^ {\displaystyle {\hat {u}}} axis is defined to be p θ ( u ^ ) {\displaystyle p_{\theta }({\hat {u}})} . The relationship between the original coordinate and the rotated coordinate is given by [ u ^ v ^ ] = [ cos ⁡ θ sin ⁡ θ − sin ⁡ θ cos ⁡ θ ] [ u v ] {\displaystyle {\begin{bmatrix}{\hat {u}}\\{\hat {v}}\end{bmatrix}}={\begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}u\\v\end{bmatrix}}} or inversely, [ u v ] = [ cos ⁡ θ − sin ⁡ θ sin ⁡ θ cos ⁡ θ ] [ u ^ v ^ ] {\displaystyle {\begin{bmatrix}u\\v\end{bmatrix}}={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}{\hat {u}}\\{\hat {v}}\end{bmatrix}}} Then we have p θ ( u ^ ) = ∫ − ∞ ∞ d ( u , v ) d v ^ = ∫ − ∞ ∞ d ( u ^ cos ⁡ ( θ ) − v ^ sin ⁡ ( θ ) , u ^ sin ⁡ ( θ ) + v ^ cos ⁡ ( θ ) ) d v ^ {\displaystyle p_{\theta }({\hat {u}})=\int _{-\infty }^{\infty }d(u,v)\,\mathrm {d} {\hat {v}}=\int _{-\infty }^{\infty }d({\hat {u}}\cos(\theta )-{\hat {v}}\sin(\theta ),{\hat {u}}\sin(\theta )+{\hat {v}}\cos(\theta ))\,\mathrm {d} {\hat {v}}} By varying theta, a large number of projections can be obtained. Given the projection-slice theorem, D ( Ω , θ ) {\displaystyle D(\Omega ,\theta )} ,the slice of the Fourier transform of d ( u , v ) {\displaystyle d(u,v)} at angle theta, is equivalent to P θ ( Ω ) {\displaystyle P_{\theta }(\Omega )} , the Fourier Transform of the projection p θ ( u ^ ) {\displaystyle p_{\theta }({\hat {u}})} . Therefore, the unknown d ( u , v ) {\displaystyle d(u,v)} can be obtained from its Fourier transform by means of the Fourier transform inversion integral d ( u , v ) = 1 4 π 2 ∫ − ∞ ∞ ∫ − ∞ ∞ D ( Ω 1 , Ω 2 ) e j Ω 1 u e j Ω 2 v d Ω 1 , Ω 2 {\displaystyle \mathrm {d} (u,v)={\frac {1}{4\pi ^{2}}}\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }D(\Omega _{1},\Omega _{2})e^{j\Omega _{1}u}e^{j\Omega _{2}v}\,\mathrm {d} \Omega _{1},\Omega _{2}} = 1 4 π 2 ∫ 0 ∞ ∫ − π π D ( Ω , θ ) e j Ω u cos ⁡ ( θ ) e j Ω v s i n θ | Ω | d Ω d θ {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{0}^{\infty }\int _{-\pi }^{\pi }D(\Omega ,\theta )e^{j\Omega u\cos(\theta )}e^{j\Omega vsin\theta }{\begin{vmatrix}\Omega \end{vmatrix}}\,\mathrm {d} \Omega \mathrm {d} \theta } = 1 4 π 2 ∫ − π π ∫ 0 ∞ P θ ( Ω ) e j Ω ( u cos ⁡ θ + v sin ⁡ θ ) | Ω | d Ω d θ {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{-\pi }^{\pi }\int _{0}^{\infty }P_{\theta }(\Omega )e^{j}\Omega (u\cos \theta +v\sin \theta ){\begin{vmatrix}\Omega \end{vmatrix}}\,\mathrm {d} \Omega \mathrm {d} \theta } = 1 4 π 2 ∫ 0 π ( ∫ − ∞ ∞ P θ ( Ω ) | Ω | {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{0}^{\pi }(\int _{-\infty }^{\infty }P_{\theta }(\Omega ){\begin{vmatrix}\Omega \end{vmatrix}}} e j Ω u ^ d Ω ) d θ {\displaystyle e^{j\Omega {\hat {u}}}\mathrm {d} \Omega )\mathrm {d} \theta } By taking the inverse Fourier Transform and assuming g ( u ^ ) = F − 1 ( | Ω | 2 ) {\displaystyle g({\hat {u}})={\mathcal {F}}^{-1}({{\begin{vmatrix}\Omega \end{vmatrix}}^{2}})} , we get d ( u , v ) = ∑ i △ θ i [ p θ ( u ^ ) ∗ g θ i ( u ^ ) ] {\displaystyle d(u,v)=\sum _{i}\vartriangle \theta _{i}[p_{\theta }({\hat {u}})g_{\theta i}({\hat {u}})]} == Approaches == In practice, there are a wide variety of methods that are utilized, most of which are reconstruct 3-D information (volume) from 2-D signals (image). Typically used methods are CT, MRI, PET and SPECT. And the filtered back projection based on the principles introduced above are commonly applied. === Computed Tomography (CT) === In CT, a volume is formed by stacking the axial slices. The software cuts the volume in a different plane (usually orthogonal). Commonly, slice data is generated using an X-ray source that rotates around the object. X-ray sensors are positioned on the opposite side of the circle from the X-ray source. === Magnetic resonance imaging (MRI) === In MRI, energy from an oscillating magnetic field is temporarily applied to the patient at the appropriate resonance frequency. The protons (hydrogen atoms) emit a radio frequency signal which is measured by a receiving coil. The radio signal can be made to encode position information by varying the main magnetic field using gradient coils. === Positron emission tomography (PET) === The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule. Three-dimensional images of tracer concentration within the body are then constructed by computer analysis. In modern PET-CT scanners, three dimensional imaging is often accomplished with the aid of a CT X-ray scan performed on the patient during the same session, in the same machine. === Single-photon emission computed tomography (SPECT) === SPECT imaging is performed by using a gamma camera to acquire multiple 2-D images (projections) from multiple angles. Multiple projections are used to yield a 3-D data set. This data set may then be manipulated to show thin slices along any chosen axis of the body. SPECT is similar to PET in its use of radioactive tracer material and detection of gamma rays, while the tracers used in SPECT emit gamma radiation that is measured more directly.

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  HTK Limited

  HTK Limited is a software-as-a-service company that provides mobile phone messaging and IVR services. Founded in 1996, HTK is headquartered in Ipswich, Suffolk, UK. HTK provide mass notification services. Specifically, the "Police Direct" messaging service to Suffolk and Norfolk Constabularies. In 2010 the HTK Horizon SaaS platform was selected by the Scottish Environment Protection Agency (SEPA) for their Floodline Warnings Direct service. == History == HTK was founded in 1996 by Marlon Bowser and Adrian Gregory and from the outset focused on what has now become commonly known as Software-as-a-Service. in 2004, according to the Deloitte Fast 50 (UK), HTK was the 17th fastest growing company in the East of England. In 2005 The Times listed HTK 65th nationally and 4th in the East of England in the Sunday Times & Microsoft "Tech Track 100" awards. In 2009 the company was approved as a supplier to UK Government under a new framework agreement. In 2010 HTK launched version 2.2 of its Horizon platform, with a feature set that signals a shift from mass notification into the customer service automation market.

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  Harmony (software)

  Harmony is a Java-based software for creating high-definition music videos with 2D and 3D animations. The application was developed by Digital Chaotics, a company based in San Jose, California and established in 2010 by Ken and Leanna Scott. == History == During a March 1, 2011 interview published by The LIST magazine, Ken explained how he initially got into music and digital entertainment. According to Scott: “I came at it from both the art and the technology side. … I built one of the first digital audio synthesizers as an undergrad project back in 1979. It was a short jump from there to creating visuals with computers, too.” Taking inspiration from Fantasia – which Scott calls, “The greatest music video of all time” – he began writing software code for Harmony in late 2009, finishing the project in mid-2010. However, Scott has also said that the idea for Harmony began much earlier: I read a book in 1978 called Digital Harmony, by John H Whitney, Sr. (Interestingly, he was the father of the president of Digital Productions.) He said that there was a kind of visual art based on motion, and proposed theories about the underlying mathematical structure of visual harmony. So there's the book, combined with my desire to create art with computers-add a taste or two of things commonly used by college students during the 70's - and lots of Pink Floyd. Add it all up, and the seeds for Harmony were planted. My friends in school and at Floating Point Systems listened to me ranting about "making music videos with computers" incessantly. I'm sure it was both maddening and fascinating to see. == Features == Harmony runs on Windows 7 and Windows Vista. Currently, Digital Chaotics does not offer a macOS or Linux platform for the software. However, Harmony can be run on these platforms by running it on Windows in a virtual machine. == Harmony 2 == On November 1, 2011, Digital Chaotics released the 2.0 version of the Harmony software. Unlike the original version, the second release featured three product levels: Harmony 2 Express, Harmony 2 Pro, and Harmony 2 Extreme. The "Express" version was positioned as an entry-level, free release to allow users a chance to "test-drive" the software. The "Pro" version currently retails at $197, while the "Extreme" is priced at $397. These two versions, aimed more towards VJ and Fulldome theater usage, featured additional software capability and features such as higher resolution, more video formatting options, and more camera angles.

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  Nextcloud

  Nextcloud is a modular workspace platform designed to provide teams and businesses with a comprehensive environment for digital collaboration. Beyond central data management, it integrates office suites like Collabora Online and EuroOffice office suites. for seamless, cooperative workflows. The platform features built-in tools for chat, videoconferencing, and a privacy-focused AI assistant capable of running entirely on local LLMs. Supported by a rich ecosystem of apps, it can be hosted in the cloud or on premises and can scale up to millions of users. It has been translated into over 100 languages. == Features == Nextcloud files are stored in conventional directory structures, accessible via WebDAV if necessary. A SQLite, MySQL/MariaDB or PostgreSQL database is required to provide additional functionality like permissions, shares, and comments. Nextcloud can synchronize with local clients running Windows (Windows 8.1 and above), macOS (10.14 or later), Linux and FreeBSD. Nextcloud permits user and group administration locally or via different backends like OpenID or LDAP. Content can be shared inside the system by defining granular read/write permissions between users and groups. Nextcloud users can create public URLs when sharing files. Logging of file-related actions, as well as disallowing access based on file access rules is also available. Security options like brute-force protection and multi-factor authentication using TOTP, WebAuthn, Oauth2, and OpenID Connect are available. Nextcloud has planned new features such as monitoring capabilities, full-text search and Kerberos authentication, as well as audio/video conferencing, expanded federation and smaller user interface improvements. == History == In April 2016 Frank Karlitschek and most core contributors left ownCloud Inc. These included some of ownCloud's staff according to sources near to the ownCloud community. Karlitschek and many of these contributors went on to fork ownCloud, creating Nextcloud. The fork was preceded by a blog post of Karlitschek announcing his departure and raising questions about the management of the ownCloud, its community, and priorities between growth, money, and sustainability. There have been no official statements about the reason for the fork. However, Karlitschek mentioned the fork several times in a talk at the 2018 FOSDEM conference and in two appearances on the FLOSS Weekly podcast, emphasizing cultural mismatch between open source developers and business oriented people not used to the open source community. On June 2, within 12 hours of the announcement of the fork, the American entity "ownCloud Inc." announced that it is shutting down with immediate effect, stating that "[...] main lenders in the US have cancelled our credit. Following American law, we are forced to close the doors of ownCloud, Inc. with immediate effect and terminate the contracts of 8 employees." ownCloud Inc. accused Karlitschek of poaching developers, while Nextcloud developers such as Arthur Schiwon stated that he "decided to quit because not everything in the ownCloud Inc. company world evolved as I imagined". ownCloud GmbH continued operations, secured financing from new investors and took over the business of ownCloud Inc. In April 2018 Informationstechnikzentrum Bund (ITZBund) reported Nextcloud won the tender for "Bundescloud" (Germany government cloud) project. In August 2019 it was announced that the governments of France, Sweden and the Netherlands would use Nextcloud for file transfer. In January 2020 Nextcloud 18 "Nextcloud Hub" was released. The major change was direct integration with an Office suite (OnlyOffice) and Nextcloud announced that their goal was to compete with Office 365 and Google Docs. A partnership with Ionos was revealed – its hosting location in Germany and compliance with GDPR should support the goal of data sovereignty. In spring 2020 remote work and web conferencing usage increased due to the COVID-19 pandemic and Nextcloud released version 19 with chat and videoconferencing Talk app integrated into the application core. Communication with an optional "high performance back-end" allows self-hosting of web conferences with more than 10 participants. Collabora Online was introduced as another integrated office suite. In August 2021 Nextcloud was chosen as a collaboration platform for European cloud software GAIA-X. In a September 2021 European Commission report it was mentioned as "the most widely deployed Open Source content collaboration platform" Following the 2025 United States tariffs against the European Union, fear of overreliance on US cloud providers such as Microsoft 365 and Google Workspace increased, with Nextcloud being one of the foremost contenders to replace them. Some governmental organisations including the European Data Protection Supervisor and the German state of Schleswig-Holstein have since switched from Microsoft's Sharepoint to Nextcloud. According to Nextcloud, during the first 5 months of 2025, customer interest in the software had tripled.

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  Medical imaging

  Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to reveal internal structures hidden by the skin and bones, as well as to diagnose and treat disease. Medical imaging also establishes a database of normal anatomy and physiology to make it possible to identify abnormalities. Although imaging of removed organs and tissues can be performed for medical reasons, such procedures are usually considered part of pathology instead of medical imaging. Measurement and recording techniques that are not primarily designed to produce images, such as electroencephalography (EEG), magnetoencephalography (MEG), electrocardiography (ECG), and others, represent other technologies that produce data susceptible to representation as a parameter graph versus time or maps that contain data about the measurement locations. In a limited comparison, these technologies can be considered forms of medical imaging in another discipline of medical instrumentation. As of 2010, 5 billion medical imaging studies had been conducted worldwide. Radiation exposure from medical imaging in 2006 made up about 50% of total ionizing radiation exposure in the United States. Medical imaging equipment is manufactured using technology from the semiconductor industry, including CMOS integrated circuit chips, power semiconductor devices, sensors such as image sensors (particularly CMOS sensors) and biosensors, and processors such as microcontrollers, microprocessors, digital signal processors, media processors and system-on-chip devices. As of 2015, annual shipments of medical imaging chips amount to 46 million units and $1.1 billion. The term "noninvasive" is used to denote a procedure where no instrument is introduced into a patient's body, which is the case for most imaging techniques used. == History == In 1972, engineer Godfrey Hounsfield from the British company EMI invented the X-ray computed tomography device for head diagnosis, which is commonly referred to as computed tomography (CT). The CT nucleus method is based on the projecting X-rays through a section of the human head, which are then processed by computer to reconstruct the cross-sectional image, known as image reconstruction. In 1975, EMI successfully developed a CT device for the entire body, enabling the clear acquisition of tomographic images of various parts of the human body. This revolutionary diagnostic technique earned Hounsfield and physicist Allan Cormack the Nobel Prize in Physiology or Medicine in 1979. Digital image processing technology for medical applications was inducted into the Space Foundation's Space Technology Hall of Fame in 1994. By 2010, over 5 billion medical imaging studies had been conducted worldwide. Radiation exposure from medical imaging in 2006 accounted for about 50% of total ionizing radiation exposure in the United States. Medical imaging equipment is manufactured using technology from the semiconductor industry, including CMOS integrated circuit chips, power semiconductor devices, sensors such as image sensors (particularly CMOS sensors) and biosensors, as well as processors like microcontrollers, microprocessors, digital signal processors, media processors and system-on-chip devices. As of 2015, annual shipments of medical imaging chips reached 46 million units, generating a market value of $1.1 billion. == Types == In the clinical context, "invisible light" medical imaging is generally equated to radiology or "clinical imaging". "Visible light" medical imaging involves digital video or still pictures that can be seen without special equipment. Dermatology and wound care are two modalities that use visible light imagery. Interpretation of medical images is generally undertaken by a physician specialising in radiology known as a radiologist; however, this may be undertaken by any healthcare professional who is trained and certified in radiological clinical evaluation. Increasingly interpretation is being undertaken by non-physicians, for example radiographers frequently train in interpretation as part of expanded practice. Diagnostic radiography designates the technical aspects of medical imaging and in particular the acquisition of medical images. The radiographer (also known as a radiologic technologist) is usually responsible for acquiring medical images of diagnostic quality; although other professionals may train in this area, notably some radiological interventions performed by radiologists are done so without a radiographer. As a field of scientific investigation, medical imaging constitutes a sub-discipline of biomedical engineering, medical physics or medicine depending on the context: Research and development in the area of instrumentation, image acquisition (e.g., radiography), modeling and quantification are usually the preserve of biomedical engineering, medical physics, and computer science; Research into the application and interpretation of medical images is usually the preserve of radiology and the medical sub-discipline relevant to medical condition or area of medical science (neuroscience, cardiology, psychiatry, psychology, etc.) under investigation. Many of the techniques developed for medical imaging also have scientific and industrial applications. === Radiography === Two forms of radiographic images are in use in medical imaging. Projection radiography and fluoroscopy, with the latter being useful for catheter guidance. These 2D techniques are still in wide use despite the advance of 3D tomography due to the low cost, high resolution, and depending on the application, lower radiation dosages with 2D technique. This imaging modality uses a wide beam of X-rays for image acquisition and is the first imaging technique available in modern medicine. Fluoroscopy produces real-time images of internal structures of the body in a similar fashion to radiography, but employs a constant input of X-rays, at a lower dose rate. Contrast media, such as barium, iodine, and air are used to visualize internal organs as they work. Fluoroscopy is also used in image-guided procedures when constant feedback during a procedure is required. An image receptor is required to convert the radiation into an image after it has passed through the area of interest. Early on, this was a fluorescing screen, which gave way to an Image Amplifier (IA) which was a large vacuum tube that had the receiving end coated with cesium iodide, and a mirror at the opposite end. Eventually the mirror was replaced with a TV camera. Projectional radiographs, more commonly known as X-rays, are often used to determine the type and extent of a fracture as well as for detecting pathological changes in the lungs. With the use of radio-opaque contrast media, such as barium, they can also be used to visualize the structure of the stomach and intestines – this can help diagnose ulcers or certain types of colon cancer. === Magnetic resonance imaging === A magnetic resonance imaging instrument (MRI scanner), or "nuclear magnetic resonance (NMR) imaging" scanner as it was originally known, uses powerful magnets to polarize and excite hydrogen nuclei (i.e., single protons) of water molecules in human tissue, producing a detectable signal that is spatially encoded, resulting in images of the body. The MRI machine emits a radio frequency (RF) pulse at the resonant frequency of the hydrogen atoms on water molecules. Radio frequency antennas ("RF coils") send the pulse to the area of the body to be examined. The RF pulse is absorbed by protons, causing their direction with respect to the primary magnetic field to change. When the RF pulse is turned off, the protons "relax" back to alignment with the primary magnet and emit radio waves in the process. This radio-frequency emission from the hydrogen atoms on water is what is detected and reconstructed into an image. The resonant frequency of a spinning magnetic dipole (of which protons are one example) is called the Larmor frequency and is determined by the strength of the main magnetic field and the chemical environment of the nuclei of interest. MRI uses three electromagnetic fields: a very strong (typically 1.5 to 3 teslas) static magnetic field to polarize the hydrogen nuclei, called the primary field; gradient fields that can be modified to vary in space and time (on the order of 1 kHz) for spatial encoding, often simply called gradients; and a spatially homogeneous radio-frequency (RF) field for manipulation of the hydrogen nuclei to produce measurable signals, collected through an RF antenna. Like CT, MRI traditionally creates a two-dimensional image of a thin "slice" of the body and is therefore considered a tomographic imaging technique. Modern MRI instruments are capable of producing images in the form of 3D blocks, which may be considered a generalization of the single-slice

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  Pixel

  In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable physical element of a raster image or the smallest controllable element of a display device or dot matrix printer. Pixels are arranged in a regular, two-dimensional grid, and each pixel serves as a sample of an original image, with a greater number of samples typically providing more accurate representations. Each pixel possesses a specific intensity or color, often composed of three or four component intensities, such as red, green, and blue (RGB), or cyan, magenta, yellow, and black (CMYK). The intensity of each pixel is variable, and in color imaging systems, these components are combined to produce a wide spectrum of colors. The concept of a picture element has existed since the early days of television, appearing as "Bildpunkt" in a 1888 German patent, and the term "pixel" has been used in various U.S. patents since 1911. In most digital display devices, pixels are the smallest element that can be manipulated through software. Each pixel is a sample of an original image; more samples typically provide more accurate representations of the original. The intensity of each pixel is variable. In color imaging systems, a color is typically represented by three or four component intensities such as red, green, and blue, or cyan, magenta, yellow, and black. In some contexts (such as descriptions of camera sensors), pixel refers to a single scalar element of a multi-component representation (called a photosite in the camera sensor context, although sensel 'sensor element' is sometimes used), while in yet other contexts (like MRI) it may refer to a set of component intensities for a spatial position. Software on early consumer computers was necessarily rendered at a low resolution, with large pixels visible to the naked eye; graphics made under these limitations may be called pixel art, especially in reference to video games. Modern computers and displays, however, can easily render orders of magnitude more pixels than was previously possible, necessitating the use of large measurements like the megapixel (one million pixels). == Etymology == The word pixel is a combination of pix (from "pictures", shortened to "pics") and el (for "element"); similar formations with 'el' include the words voxel 'volume pixel', and texel 'texture pixel'. The word pix appeared in Variety magazine headlines in 1932, as an abbreviation for the word pictures, in reference to movies. By 1938, "pix" was being used in reference to still pictures by photojournalists. The word "pixel" was first published in 1965 by Frederic C. Billingsley of JPL, to describe the picture elements of scanned images from space probes to the Moon and Mars. Billingsley had learned the word from Keith E. McFarland, at the Link Division of General Precision in Palo Alto, who in turn said he did not know where it originated. McFarland said simply it was "in use at the time" (c. 1963). The concept of a "picture element" dates to the earliest days of television, for example as "Bildpunkt" (the German word for pixel, literally 'picture point') in the 1888 German patent of Paul Nipkow. According to various etymologies, the earliest publication of the term picture element itself was in Wireless World magazine in 1927, though it had been used earlier in various U.S. patents filed as early as 1911. Some authors explain pixel as picture cell, as early as 1972. In graphics and in image and video processing, pel is often used instead of pixel. For example, IBM used it in their Technical Reference for the original PC. Pixilation, spelled with a second i, is an unrelated filmmaking technique that dates to the beginnings of cinema, in which live actors are posed frame by frame and photographed to create stop-motion animation. An archaic British word meaning "possession by spirits (pixies)", the term has been used to describe the animation process since the early 1950s; various animators, including Norman McLaren and Grant Munro, are credited with popularizing it. == Technical == A pixel is generally thought of as the smallest single component of a digital image. However, the definition is highly context-sensitive. For example, there can be "printed pixels" in a page, or pixels carried by electronic signals, or represented by digital values, or pixels on a display device, or pixels in a digital camera (photosensor elements). This list is not exhaustive and, depending on context, synonyms include pel, sample, byte, bit, dot, and spot. Pixels can be used as a unit of measure such as: 2400 pixels per inch, 640 pixels per line, or spaced 10 pixels apart. The measures "dots per inch" (dpi) and "pixels per inch" (ppi) are sometimes used interchangeably, but have distinct meanings, especially for printer devices, where dpi is a measure of the printer's density of dot (e.g. ink droplet) placement. For example, a high-quality photographic image may be printed with 600 ppi on a 1200 dpi inkjet printer. Even higher dpi numbers, such as the 4800 dpi quoted by printer manufacturers since 2002, do not mean much in terms of achievable resolution. The more pixels used to represent an image, the closer the result can resemble the original. The number of pixels in an image is sometimes called the resolution, though resolution has a more specific definition. Pixel counts can be expressed as a single number, as in a "three-megapixel" digital camera, which has a nominal three million pixels, or as a pair of numbers, as in a "640 by 480 display", which has 640 pixels from side to side and 480 from top to bottom (as in a VGA display) and therefore has a total number of 640 × 480 = 307,200 pixels, or 0.3 megapixels. The pixels, or color samples, that form a digitized image (such as a JPEG file used on a web page) may or may not be in one-to-one correspondence with screen pixels, depending on how a computer displays an image. In computing, an image composed of pixels is known as a bitmapped image or a raster image. The word raster originates from television scanning patterns, and has been widely used to describe similar halftone printing and storage techniques. === Sampling patterns === For convenience, pixels are normally arranged in a regular two-dimensional grid. By using this arrangement, many common operations can be implemented by uniformly applying the same operation to each pixel independently. Other arrangements of pixels are possible, with some sampling patterns even changing the shape (or kernel) of each pixel across the image. For this reason, care must be taken when acquiring an image on one device and displaying it on another, or when converting image data from one pixel format to another. For example: Liquid-crystal displays (LCDs) typically use a staggered grid, where the red, green, and blue components are sampled at slightly different locations. Subpixel rendering is a technology which takes advantage of these differences to improve the rendering of text on LCD screens. The vast majority of color digital cameras use a Bayer filter, resulting in a regular grid of pixels where the color of each pixel depends on its position on the grid. A clipmap uses a hierarchical sampling pattern, where the size of the support of each pixel depends on its location within the hierarchy. Warped grids are used when the underlying geometry is non-planar, such as images of the earth from space. The use of non-uniform grids is an active research area, attempting to bypass the traditional Nyquist limit. Pixels on computer monitors are normally "square" (that is, have equal horizontal and vertical sampling pitch); pixels in other systems are often "rectangular" (that is, have unequal horizontal and vertical sampling pitch – oblong in shape), as are digital video formats with diverse aspect ratios, such as the anamorphic widescreen formats of the Rec. 601 digital video standard. === Resolution of computer monitors === Computer monitors (and TV sets) generally have a fixed native resolution. What it is depends on the monitor, and size. See below for historical exceptions. Computers can use pixels to display an image, often an abstract image that represents a GUI. The resolution of this image is called the display resolution and is determined by the video card of the computer. Flat-panel monitors (and TV sets), e.g. OLED or LCD monitors, or E-ink, also use pixels to display an image, and have a native resolution, and it should (ideally) be matched to the video card resolution. Each pixel is made up of triads, with the number of these triads determining the native resolution. On older, historically available, CRT monitors the resolution was possibly adjustable (still lower than what modern monitor achieve), while on some such monitors (or TV sets) the beam sweep rate was fixed, resulting in a fixed native resolution. Most CRT monitors do not have a fixed beam sweep rate, meaning they do not have a native resolution at all – instead they

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  Find It, Fix It

  Find It, Fix It is a mobile app developed by the city of Seattle to report non-emergency issues. == History == The City of Seattle launched Find It, Fix It in 2013 for Android and iOS phones to let citizens report potholes, graffiti, and other problems they observe to the city. The app did not support Windows Phone, making it inaccessible to Microsoft employees in the city who used the company's then-supported mobile operating system. In 2015, Mayor Ed Murray led a Find It, Fix It walk with about 100 other people, including police officers, in the University District. Participants were encouraged to use the app to report problems they observed in the neighborhood. Later Find It, Fix It walks have taken place in neighborhoods including Crown Hill, First Hill, Belltown, Wallingford, and Highland Park. In 2020, Find It, Fix It added support for reporting issues with the dockless bicycle sharing systems in the city. Citing the success of Seattle’s app, the nearby city of Kent, Washington, announced that it would create a similar customer service app. == Usage == Users of Find It, Fix It can submit reports about graffiti, potholes, parking violations, broken street signs, and other issues. The app is designed to use a smartphone’s camera and GPS features to make it easier for users to file reports. The Atlantic reported in 2018 that Find It, Fix It was being used by neighborhood groups to report homeless encampments with the intention of having authorities remove them, citing examples of campaigns in Ravenna and Ballard. The executive director of Ballard Alliance, a local chamber of commerce for businesses in the neighborhood, used a private Facebook group to encourage business owners to use the app to report homeless encampments. In response to a poster campaign in the summer of 2019 with the slogan “See a tent? Report a tent”, a representative for the mayor’s office and two Seattle City Council members said that it was inappropriate to encourage use of Find It, Fix It to displace homeless people. As a backlash to these campaigns, people living far from Seattle filed hoax complaints using the app, such as by using photos of tents on display at REI stores. According to the Seattle Times, between January 1, 2020, and November 15, 2021, the city had received over 230,000 service requests, of which 77% were submitted via Find It, Fix It. The largest category of these, numbering over 55,000, concerned illegal dumping. Of complaints categorized as "parking", 3,000 had comments explicitly mentioning issues around homelessness. The ZIP code 98134, covering an industrial area south of Pioneer Square and north of Georgetown, had 5,559 service requests per 1,000 residents, by far the highest in the city.

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  Spatial embedding

  Spatial embedding is one of feature learning techniques used in spatial analysis where points, lines, polygons or other spatial data types. representing geographic locations are mapped to vectors of real numbers. Conceptually it involves a mathematical embedding from a space with many dimensions per geographic object to a continuous vector space with a much lower dimension. Such embedding methods allow complex spatial data to be used in neural networks and have been shown to improve performance in spatial analysis tasks == Embedded data types == Geographic data can take many forms: text, images, graphs, trajectories, polygons. Depending on the task, there may be a need to combine multimodal data from different sources. The next section describes examples of different types of data and their uses. === Text === Geolocated posts on social media can be used to acquire a library of documents bound to a given place that can be later transformed to embedded vectors using word embedding techniques. === Image === Satellites and aircraft collect digital spatial data acquired from remotely sensed images which can be used in machine learning. They are sometimes hard to analyse using basic image analysis methods and convolutional neural networks can be used to acquire an embedding of images bound to a given geographical object or a region. === Point === A single point of interest (POI) can be assigned multiple features that can be used in machine learning. These could be demographic, transportation, meteorological, or economic data, for example. When embedding single points, it is common to consider the entire set of available points as nodes in a graph. === Line / multiline === Among other things, motion trajectories are represented as lines (multilines). Individual trajectories are embedded taking into account travel time, distances and also features of points visited along the way. Embedding of trajectories allows to improve performance of such tasks as clustering and also categorization. === Polygon === The geographic areas analyzed in machine learning are defined by both administrative boundaries and top-down division into grids of regular shapes such as rectangles, for example. Both types are represented as polygons and, like points, can be assigned different demographic, transportation, or economic features. A polygon can also have features related to the size of the area or shape it represents. === Graph === An example domain where graph representation is used is the street layout in a city, where vertices can be intersections and edges can be roads. The vertices can also be destination points like public transport stops or important points in the city, and the edges represent the flow between them. Embedding graphs or single vertices allows to improve accuracy of analysis methods in which the treated geographical domain can be represented as a network. == Usage == POI recommendation - generating personalized point of interest recommendations based on user preferences. Next/future location prediction - prediction of the next location a person will go to based on their historical trajectory. Zone functions classification - based on different mobility of people or POI distribution a function of a given area in a city can be predicted. Crime prediction - estimation of crime rate in different regions of a city. Local event detection - studying spatio-temporal changes in embeddings can provide valuable information in detection of local event occurring in specific location. Regional mobility popularity prediction - analysis of mobility can show patterns in popularity of different regions in a city. Shape matching - finding a similar shape of given polygon, for example finding building with the same shape as input building. Travel time estimation - predicting estimated travel time given current traffic conditions and special occurring events. Time estimation for on-demand food delivery - estimation of delivery time when placing an order through the website. == Temporal aspect == Some of the data analyzed has a timestamp associated with it. In some cases of data analysis this information is omitted and in others it is used to divide the set into groups. The most common division is the separation of weekdays from weekends or division into hours of the day. This is particularly important in the analysis of mobility data, because the characteristics of mobility during the week and at different times of the day are very different from each other. Another area in which time division into, for example, individual months can be used is in the analysis of tourism of a given region. In order to take such a split into account, embedding methods treat the time stamp specifically or separate versions of the model are developed for different subgroups of the analyzed set.

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  Computer-aided lean management

  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.

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  Reconstruction from projections

  The problem of reconstructing a multidimensional signal from its projection is uniquely multidimensional, having no 1-D counterpart. It has applications that range from computer-aided tomography to geophysical signal processing. It is a problem which can be explored from several points of view—as a deconvolution problem, a modeling problem, an estimation problem, or an interpolation problem. == Motivation and applications == Many fields in science and engineering use reconstruction from projections, especially in imaging. It is widely applied geophysical tomography, medical imaging and industrial radiography. For example, in a CT scanner, the 3D structure of the patient’s body being scanned is measured with beams going through the tissue and hitting a detector, giving a flat projection of the body from that angle. Multiple projections are put together to get an image of the position and shape of structures inside in 3D. == Problem statement and basics == A projection is a linear mapping of an M {\displaystyle M} dimensional signal into an N {\displaystyle N} dimensional one, where N ≤ M {\displaystyle N\leq M} . And the objective of reconstruction is to restore the M {\displaystyle M} dimensional signal based on the N {\displaystyle N} dimensional signal. The following case is a 2-D signal projected into 1D signal. The signal in the original coordinate is denoted as d ( u , v ) {\displaystyle d(u,v)} . Now consider a collimated beam of radiation coming from the opposite orientation of v ^ {\displaystyle {\hat {v}}} , producing a projection along u ^ {\displaystyle {\hat {u}}} . v ^ {\displaystyle {\hat {v}}} and u ^ {\displaystyle {\hat {u}}} are normal to each other, and the angle between u {\displaystyle u} and u ^ {\displaystyle {\hat {u}}} is theta. The signal obtained along u ^ {\displaystyle {\hat {u}}} axis is defined to be p θ ( u ^ ) {\displaystyle p_{\theta }({\hat {u}})} . The relationship between the original coordinate and the rotated coordinate is given by [ u ^ v ^ ] = [ cos ⁡ θ sin ⁡ θ − sin ⁡ θ cos ⁡ θ ] [ u v ] {\displaystyle {\begin{bmatrix}{\hat {u}}\\{\hat {v}}\end{bmatrix}}={\begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}u\\v\end{bmatrix}}} or inversely, [ u v ] = [ cos ⁡ θ − sin ⁡ θ sin ⁡ θ cos ⁡ θ ] [ u ^ v ^ ] {\displaystyle {\begin{bmatrix}u\\v\end{bmatrix}}={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}{\hat {u}}\\{\hat {v}}\end{bmatrix}}} Then we have p θ ( u ^ ) = ∫ − ∞ ∞ d ( u , v ) d v ^ = ∫ − ∞ ∞ d ( u ^ cos ⁡ ( θ ) − v ^ sin ⁡ ( θ ) , u ^ sin ⁡ ( θ ) + v ^ cos ⁡ ( θ ) ) d v ^ {\displaystyle p_{\theta }({\hat {u}})=\int _{-\infty }^{\infty }d(u,v)\,\mathrm {d} {\hat {v}}=\int _{-\infty }^{\infty }d({\hat {u}}\cos(\theta )-{\hat {v}}\sin(\theta ),{\hat {u}}\sin(\theta )+{\hat {v}}\cos(\theta ))\,\mathrm {d} {\hat {v}}} By varying theta, a large number of projections can be obtained. Given the projection-slice theorem, D ( Ω , θ ) {\displaystyle D(\Omega ,\theta )} ,the slice of the Fourier transform of d ( u , v ) {\displaystyle d(u,v)} at angle theta, is equivalent to P θ ( Ω ) {\displaystyle P_{\theta }(\Omega )} , the Fourier Transform of the projection p θ ( u ^ ) {\displaystyle p_{\theta }({\hat {u}})} . Therefore, the unknown d ( u , v ) {\displaystyle d(u,v)} can be obtained from its Fourier transform by means of the Fourier transform inversion integral d ( u , v ) = 1 4 π 2 ∫ − ∞ ∞ ∫ − ∞ ∞ D ( Ω 1 , Ω 2 ) e j Ω 1 u e j Ω 2 v d Ω 1 , Ω 2 {\displaystyle \mathrm {d} (u,v)={\frac {1}{4\pi ^{2}}}\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }D(\Omega _{1},\Omega _{2})e^{j\Omega _{1}u}e^{j\Omega _{2}v}\,\mathrm {d} \Omega _{1},\Omega _{2}} = 1 4 π 2 ∫ 0 ∞ ∫ − π π D ( Ω , θ ) e j Ω u cos ⁡ ( θ ) e j Ω v s i n θ | Ω | d Ω d θ {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{0}^{\infty }\int _{-\pi }^{\pi }D(\Omega ,\theta )e^{j\Omega u\cos(\theta )}e^{j\Omega vsin\theta }{\begin{vmatrix}\Omega \end{vmatrix}}\,\mathrm {d} \Omega \mathrm {d} \theta } = 1 4 π 2 ∫ − π π ∫ 0 ∞ P θ ( Ω ) e j Ω ( u cos ⁡ θ + v sin ⁡ θ ) | Ω | d Ω d θ {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{-\pi }^{\pi }\int _{0}^{\infty }P_{\theta }(\Omega )e^{j}\Omega (u\cos \theta +v\sin \theta ){\begin{vmatrix}\Omega \end{vmatrix}}\,\mathrm {d} \Omega \mathrm {d} \theta } = 1 4 π 2 ∫ 0 π ( ∫ − ∞ ∞ P θ ( Ω ) | Ω | {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{0}^{\pi }(\int _{-\infty }^{\infty }P_{\theta }(\Omega ){\begin{vmatrix}\Omega \end{vmatrix}}} e j Ω u ^ d Ω ) d θ {\displaystyle e^{j\Omega {\hat {u}}}\mathrm {d} \Omega )\mathrm {d} \theta } By taking the inverse Fourier Transform and assuming g ( u ^ ) = F − 1 ( | Ω | 2 ) {\displaystyle g({\hat {u}})={\mathcal {F}}^{-1}({{\begin{vmatrix}\Omega \end{vmatrix}}^{2}})} , we get d ( u , v ) = ∑ i △ θ i [ p θ ( u ^ ) ∗ g θ i ( u ^ ) ] {\displaystyle d(u,v)=\sum _{i}\vartriangle \theta _{i}[p_{\theta }({\hat {u}})g_{\theta i}({\hat {u}})]} == Approaches == In practice, there are a wide variety of methods that are utilized, most of which are reconstruct 3-D information (volume) from 2-D signals (image). Typically used methods are CT, MRI, PET and SPECT. And the filtered back projection based on the principles introduced above are commonly applied. === Computed Tomography (CT) === In CT, a volume is formed by stacking the axial slices. The software cuts the volume in a different plane (usually orthogonal). Commonly, slice data is generated using an X-ray source that rotates around the object. X-ray sensors are positioned on the opposite side of the circle from the X-ray source. === Magnetic resonance imaging (MRI) === In MRI, energy from an oscillating magnetic field is temporarily applied to the patient at the appropriate resonance frequency. The protons (hydrogen atoms) emit a radio frequency signal which is measured by a receiving coil. The radio signal can be made to encode position information by varying the main magnetic field using gradient coils. === Positron emission tomography (PET) === The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule. Three-dimensional images of tracer concentration within the body are then constructed by computer analysis. In modern PET-CT scanners, three dimensional imaging is often accomplished with the aid of a CT X-ray scan performed on the patient during the same session, in the same machine. === Single-photon emission computed tomography (SPECT) === SPECT imaging is performed by using a gamma camera to acquire multiple 2-D images (projections) from multiple angles. Multiple projections are used to yield a 3-D data set. This data set may then be manipulated to show thin slices along any chosen axis of the body. SPECT is similar to PET in its use of radioactive tracer material and detection of gamma rays, while the tracers used in SPECT emit gamma radiation that is measured more directly.

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