The KoalaPad is a graphics tablet, released in 1983 by US company Koala Technologies Corporation, for the Apple II, TRS-80 Color Computer (as the TRS-80 Touch Pad), Atari 8-bit computers, Commodore 64, and IBM PC compatibles. Originally designed by Dr. David Thornburg as a low-cost computer drawing tool for schools, the Koala Pad and the bundled drawing program, KoalaPainter, was popular with home users as well. KoalaPainter was called KoalaPaint in some versions for the Apple II, and PC Design for the IBM PC. A program called Graphics Exhibitor was included for creating slideshow presentations from KoalaPainter drawings. == Description == The pad was four inches square (i.e. roughly 10×10 cm) and mounted on a slightly inclined base with the back of the pad higher than the front. At the top, "behind" the pad, were two buttons. The pad hooked into the computer using the analog signals of the joystick ports (the so-called paddle inputs), which meant that it had a low resolution and tended to jostle the cursor if moved during use. As an alternative to the drawing stylus, the pad could as easily be operated by the user's fingers for tasks that demanded less precision, such as selecting between menu items (thus using the pad as a kind of "indirect touch screen"). The top-mounted buttons tended to be somewhat frustrating to use, as the user had to "reach around" the stylus to push the buttons in order to start or stop drawing. A similar tablet from Atari, the Atari CX77 Touch Tablet, addressed this with a built-in button on the stylus, which some enterprising users adapted for use with their KoalaPad. == KoalaPainter == The pad shipped with a simple bitmap graphics editor developed by Audio Light called KoalaPainter, PC Design or Micro Illustrator depending on the target machine (see release history). Although bundled with the pad, KoalaPainter could also be operated using an ordinary digital joystick. One unique feature of the program, for its time, was that it held two pictures in the computer's memory, allowing the user to flip from one to the other—a function commonly used in order to study the differences between an original and a modified picture, and to copy and paste between two different pictures. Some third-party bitmap editors could also be used with the KoalaPad, such as Broderbund's Dazzle Draw for the Apple II. === Release history === KoalaPainter for Commodore 64 (1983) and Atari 8-bit computers (1983) PC Design for the IBM PC (1983) Micro Illustrator for the Apple II (1983), Atari 8-bit computers (1983) and Commodore Plus/4 (1984) KoalaPainter II for Commodore 64 (1984) === Reception === Ahoy! called KoalaPainter "a very powerful and effective color drawing package", and concluded that it and the KoalaPad were "excellent in ease of use, a fine choice for a beginner as well as young children". BYTE's reviewer stated in December 1984 that he made far fewer errors when using an Apple Mouse with MousePaint than with a KoalaPad and its software. He found that MousePaint was easier to use and more efficient, predicting that the mouse would receive more software support than the pad. Cassie Stahl in InfoWorld's Essential Guide to Atari Computers praised the tablet and its documentation, rating it "Excellent" among all categories and stating that "Playing with the KoalaPad becomes addictive. It does everything it claims to, and it does it well". She also liked Micro Illustrator, rating it "Excellent" except for "Good" for Performance. While criticizing the limited erase function, Stahl reported an undocumented feature enabling exporting pictures to other software. === File format === The Commodore 64 version of KoalaPainter used a fairly simple file format corresponding directly to the way bitmapped graphics are handled on the computer: A two-byte load address, followed immediately by 8,000 bytes of raw bitmap data, 1,000 bytes of raw "Video Matrix" data, 1,000 bytes of raw "Color RAM" data, and a one-byte Background Color field. == KoalaWare == Koala Technologies offered more software beyond the bundled KoalaPainter and Graphics Exhibitor for use with the pad. Among these applications, marketed under the moniker KoalaWare (like KoalaPainter itself), was educational software for use with customized keypads and overlays, such as spelling tools, music programs, and mathematics instruction software, as well as software for "translating" graphical designs into Logo programs.
AI agent
In the context of generative artificial intelligence, AI agents (also referred to as compound AI systems or agentic AI) are a class of intelligent agents that can pursue goals, use tools, and take actions with varying degrees of autonomy. In practice, they usually operate within human-defined objectives, constraints, and available tools. == Overview == AI agents possess several key attributes, including goal-directed behavior, natural language interfaces, the capacity to use external tools, and the ability to perform multi-step tasks. Their control flow is frequently driven by large language models (LLMs). Agent systems may also include memory components, planning logic, tool interfaces, and orchestration software for coordinating agent components. AI agents do not have a standard definition. NIST describes agentic AI as an emerging area requiring standards for secure operation, interoperability, and reliable interaction with external systems. A common application of AI agents is task automation: for example, booking travel plans based on a user's prompted request. Companies such as Google, Microsoft and Amazon Web Services have offered platforms for deploying pre-built AI agents. Several protocols have been proposed for standardizing inter-agent communication, with examples including the Model Context Protocol, Gibberlink, and many others. Some of these protocols are also used for connecting agents to external applications. In December 2025, Linux Foundation announced the formation of the Agentic AI Foundation (AAIF), with the goal of ensuring agentic AI evolves transparently and collaboratively. == History == AI agents have been traced back to research from the 1990s, with Harvard professor Milind Tambe noting that the definition of an AI agent was not clear at the time. Researcher Andrew Ng has been credited with spreading the term "agentic" to a wider audience in 2024. == Training and testing == Researchers have attempted to build world models and reinforcement learning environments to train or evaluate AI agents. For example, video games such as Minecraft and No Man's Sky as well as replicas of company websites, have also been used for training such agents. == Autonomous capabilities == The Financial Times compared the autonomy of AI agents to the SAE classification of self-driving cars, likening most applications to level 2 or level 3, with some achieving level 4 in highly specialized circumstances, and level 5 being theoretical. == Cognitive architecture == The following are some internal design options for reasoning within an agent: Retrieval-augmented generation ReAct (Reason + Act) pattern is an iterative process in which an AI agent alternates between reasoning and taking actions, receives observations from the environment or external tools, and integrates these observations into subsequent reasoning steps. Reflexion, which uses an LLM to create feedback on the agent's plan of action and stores that feedback in a memory cache. A tool/agent registry, for organizing software functions or other agents that the agent can use. One-shot model querying, which queries the model once to create the plan of action. === Reference architecture === Ken Huang proposed an AI agent reference architecture, which consists of seven interconnected layers, with each layer building on the functionality of the layers beneath it: Layer 1: Foundation models - provide the core AI engines to power agent capabilities. Layer 2: Data operations - manage the complex data infrastructure required for AI agent operations, including Vector database, data loaders, RAG. Layer 3: Agent frameworks - sophisticated software and tools that simplify the development and management of the AI agents. Layer 4: Deployment and infrastructure - provide the robust technical foundation for running AI agents. Layer 5: Evaluation and observability - focus on assessing the safety and performance of AI agents. Layer 6: Security and compliance - a crucial protective framework ensuring AI agents operate safely, securely, and conform to regulatory boundaries. At this layer security and compliance features embedded into all the AI agent stack layers are integrated together. Layer 7: Agent ecosystem - represents the AI agents' interface with real-world applications and users. == Orchestration patterns == To execute complex tasks, autonomous agents are often integrated with other agents or specialized tools. These configurations, known as orchestration patterns or workflows, include the following: Prompt chaining: A sequence where the output of one step serves as the input for the next. Routing: The classification of an input to direct it to a specialized downstream task or tool. Parallelization: The simultaneous execution of multiple tasks. Sequential processing: A fixed, linear progression of tasks through a predefined pipeline. Planner-critic: An iterative pattern where one agent generates a proposal and another evaluates it to provide feedback for refinement. == Multimodal AI agents == In addition to large language models (LLMs), vision-language models (VLMs) and multimodal foundation models can be used as the basis for agents. In September 2024, Allen Institute for AI released an open-source vision-language model. Nvidia released a framework for developers to use VLMs, LLMs and retrieval-augmented generation for building AI agents that can analyze images and videos, including video search and video summarization. Microsoft released a multimodal agent model – trained on images, video, software user interface interactions, and robotics data – that the company claimed can manipulate software and robots. == Applications == As of April 2025, per the Associated Press, there are few real-world applications of AI agents. As of June 2025, per Fortune, many companies are primarily experimenting with AI agents. The Information divided AI agents into seven archetypes: business-task agents, for acting within enterprise software; conversational agents, which act as chatbots for customer support; research agents, for querying and analyzing information (such as OpenAI Deep Research); analytics agents, for analyzing data to create reports; software developer or coding agents (such as Cursor); domain-specific agents, which include specific subject matter knowledge; and web browser agents (such as OpenAI Operator). By mid-2025, AI agents have been used in video game development, gambling (including sports betting), cryptocurrency wallets (including cryptocurrency trading and meme coins) and social media. In August 2025, New York Magazine described software development as the most definitive use case of AI agents. Likewise, by October 2025, noting a decline in expectations, The Information noted AI coding agents and customer support as the primary use cases by businesses. In November 2025, The Wall Street Journal reported that few companies that deployed AI agents have received a return on investment. === Applications in government === Several government bodies in the United States and United Kingdom have deployed or announced the deployment of agents, at the local and national level. The city of Kyle, Texas deployed an AI agent from Salesforce in March 2025 for 311 customer service. In November 2025, the Internal Revenue Service stated that it would use Agentforce, AI agents from Salesforce, for the Office of Chief Counsel, Taxpayer Advocate Services and the Office of Appeals. That same month, Staffordshire Police announced that they would trial Agentforce agents for handling non-emergency 101 calls in the United Kingdom starting in 2026. In December 2025, the Department of Neighborhoods in Detroit, Michigan, in partnership with a local business, deployed a pilot project in two Detroit districts for an AI agent to be used for customer service calls. In February 2025, Thomas Shedd, the director of the Technology Transformation Services, proposed using AI coding agents across the United States federal government. A recruiter for the Department of Government Efficiency proposed in April 2025 to use AI agents to automate the work of about 70,000 United States federal government employees, as part of a startup with funding from OpenAI and a partnership agreement with Palantir. This proposal was criticized by experts for its impracticality, if not impossibility, and the lack of corresponding widespread adoption by businesses. In December 2025, the Food and Drug Administration announced that it would offer "agentic AI capabilities" to its staff for "meeting management, pre-market reviews, review validation, post-market surveillance, inspections and compliance and administrative functions." That same month, the United States Department of Defense launched GenAI.mil, an internal platform for American military personnel to use generative AI-based applications based on Google Gemini, including "intelligent agentic workflows". Defense Secretary Pete Hegseth listed applications such as "[conducting] deep r
Content as a service
Content as a service (CaaS) or managed content as a service (MCaaS) is a service-oriented model, where the service provider delivers the content on demand to the service consumer via web services that are licensed under subscription. The content is hosted by the service provider centrally in the cloud and offered to a number of consumers that need the content delivered into any applications or system, hence content can be demanded by the consumers as and when required. Content as a Service is a way to provide raw content (in other words, without the need for a specific human compatible representation, such as HTML) in a way that other systems can make use of it. Content as a Service is not meant for direct human consumption, but rather for other platforms to consume and make use of the content according to their particular needs. This happens usually on the cloud, with a centralized platform which can be globally accessible and provides a standard format for your content. With Content as a Service, you centralize your content into a single repository, where you can manage it, categorize it, make it available to others, search for it, or do whatever you wish with it. == Overview == The content delivered typically could be one or more of the following The technical terminology related to equipment or spares that is required to procure or design the materials The industrial terminology of the equipment or spares Technical values pertaining to various types, specifications, applications, characteristics of equipment or spares Sourcing information which will help in procurement or supply-chain management of equipment or spares Descriptive specifications of equipment or spares based on the product reference number or identifier UNSPSC codes or industry practiced classifications ISO, IEC compliant terminology Ontology or Technical Dictionary of products & services Predefined content for specific business needs The term "Content as a service" (CaaS) is considered to be part of the nomenclature of cloud computing service models & Service-oriented architecture along with Software as a service (SaaS), Infrastructure as a service (IaaS), and Platform as a service (PaaS).
Toolchain
A toolchain is a set of software development tools used to build and otherwise develop software. Often, the tools are executed sequentially and form a pipeline such that the output of one tool is the input for the next. Sometimes the term is used for a set of related tools that are not necessarily executed sequentially. A relatively common and simple toolchain consists of the tools to build for a particular operating system (OS) and CPU architecture: a compiler, a linker, and a debugger. With a cross-compiler, a toolchain can support cross-platform development. For building more complex software systems, many other tools may be in the toolchain. For example, for a video game, the toolchain may include tools for preparing sound effects, music, textures, 3-dimensional models and animations, and for combining these resources into the finished product.
C-RAN
C-RAN (Cloud-RAN), also referred to as Centralized-RAN, is an architecture for cellular networks. C-RAN is a centralized, cloud computing-based architecture for radio access networks that supports 2G, 3G, 4G, 5G and future wireless communication standards. Its name comes from the four 'C's in the main characteristics of C-RAN system, "Clean, Centralized processing, Collaborative radio, and a real-time Cloud Radio Access Network". == Background == Traditional cellular, or Radio Access Networks (RAN), consist of many stand-alone base stations (BTS). Each BTS covers a small area, whereas a group BTS provides coverage over a continuous area. Each BTS processes and transmits its own signal to and from the mobile terminal, and forwards the data payload to and from the mobile terminal and out to the core network via the backhaul. Each BTS has its own cooling, back haul transportation, backup battery, monitoring system, and so on. Because of limited spectral resources, network operators 'reuse' the frequency among different base stations, which can cause interference between neighboring cells. There are several limitations in the traditional cellular architecture. First, each BTS is costly to build and operate. Moore's law helps reduce the size and power of an electrical system, but the supporting facilities of the BTS are not improved quite as well. Second, when more BTS are added to a system to improve its capacity, interference among BTS is more severe as BTS are closer to each other and more of them are using the same frequency. Third, because users are mobile, the traffic of each BTS fluctuates (called 'tide effect'), and as a result, the average utilization rate of individual BTS is pretty low. However, these processing resources cannot be shared with other BTS. Therefore, all BTS are designed to handle the maximum traffic, not average traffic, resulting in a waste of processing resources and power at idle times. == Evolution of base station architecture == === All-in-one macro base station === In the 1G and 2G cellular networks, base stations had an all-in-one architecture. Analog, digital, and power functions were housed in a single cabinet as large as a refrigerator. Usually the base station cabinet was placed in a dedicated room along with all necessary supporting facilitates such as power, backup battery, air conditioning, environment surveillance, and backhaul transmission equipment. The RF signal is generated by the base station RF unit and propagates through pairs of RF cables up to the antennas on the top of a base station tower or other mounting points. This all-in-one architecture was mostly found in macro cell deployments. === Distributed base station === For 3G, a distributed base station architecture was introduced by Ericsson, Nokia, Huawei, and other leading telecom equipment vendors. In this architecture the radio function unit, also known as the remote radio head (RRH), is separated from the digital function unit, or baseband unit (BBU) by fiber. Digital baseband signals are carried over fiber, using the Open Base Station Architecture Initiative (OBSAI) or Common Public Radio Interface (CPRI) standard. The RRH can be installed on the top of tower close to the antenna, reducing the loss compared to the traditional base station where the RF signal has to travel through a long cable from the base station cabinet to the antenna at the top of the tower. The fiber link between RRH and BBU also allows more flexibility in network planning and deployment as they can be placed a few hundred meters or a few kilometers away. Most modern base stations now use this decoupled architecture. === C-RAN/Cloud-RAN === C-RAN may be viewed as an architectural evolution of the above distributed base station system. It takes advantage of many technological advances in wireless, optical and IT communications systems. For example, it uses the latest CPRI standard, low cost Coarse or Dense Wavelength Division Multiplexing (CWDM/ DWDM) technology, and mmWave to allow transmission of baseband signal over long distance thus achieving large scale centralised base station deployment. It applies recent Data Centre Network technology to allow a low cost, high reliability, low latency and high bandwidth interconnect network in the BBU pool. It utilizes open platforms and real-time virtualization technology rooted in cloud computing to achieve dynamic shared resource allocation and support multi-vendor, multi-technology environments. == Architecture overview == C-RAN architecture has the following characteristics that are distinct from other cellular architectures: Large scale centralized deployment: Allows many RRHs to connect to a centralized BBU pool. The maximum distance can be 20km in fiber link for 4G (LTE/LTE-A) systems, and even longer distances (40~80km) for 3G (WCDMA/TD-SCDMA) and 2G (GSM/CDMA) systems. Native support to Collaborative Radio technologies: Any BBU can talk with any other BBU within the BBU pool with very high bandwidth (10 Gbit/s and above) and low latency (10 μs level). This is enabled by the interconnection of BBUs in the pool. This is one major difference from BBU Hotelling, or base station Hotelling; in the latter case, the BBUs of different base stations are simply stacked together and have no direct link between them to allow physical layer co-ordination. Real-time virtualization capability based on open platform: This is different from traditional base stations built on proprietary hardware, where the software and hardware are close-sourced and provided by single vendors. In contrast, a C-RAN BBU pool is built on open hardware, like x86/ARM CPU based servers, and interface cards that handle fiber links to RRHs and inter-connections in the pool. Real-time virtualization ensures that resources in the pool can be allocated dynamically to base station software stacks, say 4G/3G/2G function modules from different vendors, according to network load. However, to satisfy the strict timing requirements of wireless communication systems, the real-time performance for C-RAN is at the level of tens of microseconds, which is two orders of magnitude better than the millisecond level 'real-time' performance usually seen in Cloud Computing environments. == Similar architecture and systems == KT, a telecom operator in the Republic of Korea, introduced a Cloud Computing Center (CCC) system in their 3G (WCDMA/HSPA) and 4G (LTE/LTE-A) network in 2011 and 2012. The concept of CCC is basically the same as C-RAN. SK Telecom has also deployed Smart Cloud Access Network (SCAN) and Advanced-SCAN in their 4G (LTE/LTE-A) network in Korea no later than 2012. In 2014, Airvana (now CommScope) introduced OneCell, a C-RAN-based small cell system designed for enterprises and public spaces. == Competing architectures in cellular network evolution == === All-in-one BTS === One major alternative solution that is addressing similar challenges of RAN, is the small size, all-in-one outdoor BTS. Thanks to the achievements in the semiconductor industry, all the functionality of a BTS, including RF, baseband processing, MAC processing and package level processing, can now be implemented in a volume of <50 liters. This makes the system small and weatherproof, reduces the difficulty of BTS site choice and construction, eliminates the air conditioning requirement, and thus reduces operational costs. However, because each BTS is still working on its own, it cannot readily make use of the collaboration algorithms to reduce the interference between neighboring BTSs. It is also relatively hard to upgrade or repair because the all-in-one BTS units are usually mounted near the antenna. More processing units in less-protected environments also implies a higher failure rate compared to C-RAN, which only has the RRU deployed outdoors. The advantage of Cloud RAN lies in its ability to implement LTE-Advanced features such as Coordinated MultiPoint (CoMP) with very low latency between multiple radio heads. However, the economic benefit of improvements such as CoMP can be negated by the higher backhaul costs for some operators. === Small cell === The main competition between small cell and C-RAN occurs in two deployment scenarios: outdoor hotspot coverage and indoor coverage. == Academic research and publications == As one of the promising evolution paths for future cellular network architecture, C-RAN has attracted high academic research interest. Meanwhile, because the native support of cooperative radio capability built into the C-RAN architecture, it also enables many advanced algorithms that were hard to implement in cellular networks, including Cooperative Multi-Point Transmission/Receiving, Network Coding, etc. In October 2011, Wireless World Research Forum 27 was hosted in Germany, when China Mobile was invited to give a C-RAN presentation. In August 2012, IEEE C-RAN 2012 workshop was hosted in Kunming, China. CRC Press published a book, "Green Communications: Theore
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.
Fatpaint
Fatpaint is a free, online (web-based) graphic design and desktop publishing software product and image editor. It includes integrated tools for creating page layout, painting, coloring and editing pictures and photos, drawing vector images, using dingbat vector clipart, writing rich text, creating ray traced 3D text logos and displaying graphics on products from Zazzle that can be purchased or sold. Fatpaint integrates desktop publishing features with brush painting, vector drawing and custom printed products in a single Flash application. It supports the use of a pressure-sensitive pen tablet and allows the user to add images by searching Wikimedia, Picasa, Flickr, Google, Yahoo, Bing, and Fatpaint's own collection of public domain images. The completed project can be saved on Fatpaint's server or locally. Fatpaint is affiliated with Zazzle, and owned by Mersica (also the developer of MakeWebVideo). == History == Fatpaint was launched in May 2010, after five years of development by Danish-Brazilian software developer, Mario Gomes Cavalcanti. After his departure, he was involved in the development of two of Denmark's most visited websites and is responsible for developing and running Fatpaint. Partner Kenneth Christensen mastered assembler and graphics programming on the Amiga computer. He spent years with Mario on the Amiga demo scene. According to the CEO, Kenneth helped him with the Linux servers while he handled the development, administration, promotion, video production, testing and content. The founder of Fatpaint also created "Make Web Video" (or Video Maker), a web application for creating video presentations for business, families and individuals. Video Maker allows users to give out the videos for personal or business use in a simple and affordable way. == Tools == Fatpaint provides free online logo maker, graphic design, vector drawing, photo editor and paint design in English, Danish and Portuguese. === Photo Editor === Users can change photo colours by manipulating R, G, B and A channels, saturation, contrast, brightness, hue, gamma, sharpness, tint and RGBA matrix. Users can also remove unwanted background and other artifacts by using the paint tools with added effects or by cloning. Multiple photos can be combined into a single image. Users can pick different blend modes and multiple layers. Users can also extract or change parts of the photo by cropping, resizing, skewing, bending, distorting and rotating in 2D and 3D. Hence, users' graphics can be printed on custom products that can be bought and sold for personal and business purposes. === Vector Drawing === Users can choose from 5000 vector images or draw vector graphics and art from scratch, using Fatpaint's vector shape creation tools. It also provides advanced symmetric vector transformation in 2D and 3D, as well as support for colour gradients. Multiple drawings can be combined to form complex vector shapes. Different blend modes and effects are supported. Vector drawings can be cropped, resized, skewed, distorted and rotated in 2D and 3D. Similar to Fatpaint's photo editor, vector graphics can be displayed on custom printed products that can be purchased and sold by the users for personal or business uses. === Paint Design === Fatpaint has full support for Pen Tablets and users can pick pen, brush, airbrush, paint bucket, clone painting, eraser and smudging tools. Fatpaint offers 8 palettes for painting, plus 13 palettes when clone painting. Fatpaint allows users to import or create their own brushes and thousands of free clipart drawings and brush sets that have dynamic brushes, effects and blend modes. Paintings can be combined in different layers and objects. Similarly, paintings can be cropped, resized, skewed, bent, distorted and rotated in 2D and 3D. Moreover, the graphics can be displayed on custom printed products, which users can buy or sell for personal or business uses. == Top Features == 3D Text objects: Create photorealistic, ray-traced 3D text logos and images. Image objects: Paint on multiple layers, import or create your own brushes, clone painting, and painting with effects. Vector drawing objects: Create vector images using multiple paths. Rich text objects with 981 fonts. Effect objects: Blur, Drop Shadow, Glow, Gradient Glow, Bevel, Gradient Bevel, Color manipulations. Page layout: Create multiple pages with a size limit of 64 megapixels, and arrange graphical objects on created pages (each object can be up to 7.8 megapixels in size). Nest graphical objects and transform them into 2D and 3D. Skew, bend and distort images and text. Design, purchase and sell custom-printed products. Fatpaint can send the projects to a printing company. Supports pressure-sensitive pen tablets. Fonts, public domain images, cliparts, and brushes. == Compatibility == Fatpaint supports Firefox, Google Chrome, Opera, and Internet Explorer with cookies and JavaScript enabled. Other browsers may not work correctly due to their support of Java Applets. Fatpaint requires Adobe's Flash 10 or newer and Sun's Java 6 or newer. It is recommended to run on Windows 7 and on Apple and Linux if Java has been disabled. The editor only works on Firefox on Linux. Java and Flash integration do not work on Linux and Apple browsers. WikiMedia search is disabled on those browsers. Fatpaint works best with at least 2 GB RAM and 1 GB video memory, as well as a decent graphics card.