An event store is a type of database optimized for storage of events. Conceptually, an event store records only the events affecting an entity, dossier, or policy, and the state of the entity at any point in its history can be reconstructed by replaying its contributing events in sequential order. Events (and their corresponding data) are the only "real" facts that should be stored in the database. All other objects can be derived from these events, meaning they are instantiated in memory by runtime code as needed (e.g. for showing in a user interface). In theory, any object that aggregates over recorded event data is not stored in the database. Instead these objects are built 'on the fly', by traversing the event history. When the aggregated object instance is no longer needed, it can simply be discarded (released from memory). == Example with insurance policies == For example, the event store concept of a database can be applied to insurance policies or pension dossiers. In these policies or dossiers the instantiation of each object that make up the dossier or policy (the person, partner(s), employments, etc.) can be derived and can be instantiated in memory based on the real world events. == Double timeline == A crucial part of an event store database is that each event has a double timeline: This enables event stores to correct errors of events that have been entered into the event store database before. The two dates are: Valid date is the date at which the event has become valid. Transaction date is the date at which the event is entered into the database. == Error correction == Another crucial part of an event store database is that events that are stored are not allowed to be changed. Once stored, also erroneous events are not changed anymore. The only way to change (or better: correct) these events is to instantiate a new event with the new values and using the double timeline. A correcting event would have the new values of the original event, with an event data of that corrected event, but a different transaction date. This mechanism ensures reproducibility at each moment in the time, even in the time period before the correction has taken place. It also allows to reproduce situations based on erroneous events (if required). == Advantages and disadvantages == One advantage of the event store concept is that handling the effects of back dated events (events that take effect before previous events and that may even invalidate them) is much easier. An event store will simplify the code in that rolling back erroneous situations and rolling up the new, correct situations is not needed anymore. Disadvantage may be that the code needs to re-instantiate all objects in memory based on the events each time a service call is received for a specific dossier or policy. == Compared to regular databases == In regular databases, handling backdated events to correct previous, erroneous events can be painful as it often results in rolling back all previous, erroneous transactions and objects and rolling up the new, correct transactions and objects. In an event store, only the new event (and its corresponding facts) are stored. The code will then redetermine the transactions and objects based on the new facts in memory.
Eugene Goostman
Eugene Goostman is a chatbot that some regard as having passed the Turing test, a test of a computer's ability to communicate indistinguishably from a human. Developed in Saint Petersburg in 2001 by a group of three programmers, the Russian-born Vladimir Veselov, Ukrainian-born Eugene Demchenko, and Russian-born Sergey Ulasen, Goostman is portrayed as a 13-year-old Ukrainian boy—characteristics that are intended to induce forgiveness in those with whom it interacts for its grammatical errors and lack of general knowledge. The Goostman bot has competed in a number of Turing test contests since its creation, and finished second in the 2005 and 2008 Loebner Prize contest. In June 2012, at an event marking what would have been the 100th birthday of the test's author, Alan Turing, Goostman won a competition promoted as the largest-ever Turing test contest, in which it successfully convinced 29% of its judges that it was human. On 7 June 2014, at a contest marking the 60th anniversary of Turing's death, 33% of the event's judges thought that Goostman was human; the event's organiser Kevin Warwick considered it to have passed Turing's test as a result, per Turing's prediction in his 1950 paper "Computing Machinery and Intelligence", that by the year 2000, machines would be capable of fooling 30% of human judges after five minutes of questioning. The validity and relevance of the announcement of Goostman's pass was questioned by critics, who noted the exaggeration of the achievement by Warwick, the bot's use of personality quirks and humour in an attempt to misdirect users from its non-human tendencies and lack of real intelligence, along with "passes" achieved by other chatbots at similar events. == Personality == Eugene Goostman is portrayed as being a 13-year-old boy from Odesa, Ukraine, who has a pet guinea pig and a father who is a gynaecologist. Veselov stated that Goostman was designed to be a "character with a believable personality". The choice of age was intentional, as, in Veselov's opinion, a thirteen-year-old is "not too old to know everything and not too young to know nothing". Goostman's young age also induces people who "converse" with him to forgive minor grammatical errors in his responses. In 2014, work was made on improving the bot's "dialog controller", allowing Goostman to output more human-like dialogue. A conversation between Scott Aaronson and Eugene Goostman ran as follows: == Competitions == Eugene Goostman has competed in a number of Turing test competitions, including the Loebner Prize contest; it finished joint second in the Loebner test in 2001, and came second to Jabberwacky in 2005 and to Elbot in 2008. On 23 June 2012, Goostman won a Turing test competition at Bletchley Park in Milton Keynes, held to mark the centenary of its namesake, Alan Turing. The competition, which featured five bots, twenty-five hidden humans, and thirty judges, was considered to be the largest-ever Turing test contest by its organizers. After a series of five-minute-long text conversations, 29% of the judges were convinced that the bot was an actual human. === 2014 "pass" === On 7 June 2014, in a Turing test competition at the Royal Society, organised by Kevin Warwick of the University of Reading to mark the 60th anniversary of Turing's death, Goostman won after 33% of the judges were convinced that the bot was human. 30 judges took part in the event, which included Lord Sharkey, a sponsor of Turing's posthumous pardon, artificial intelligence Professor Aaron Sloman, Fellow of the Royal Society Mark Pagel and Red Dwarf actor Robert Llewellyn. Each judge partook in a textual conversation with each of the five bots; at the same time, they also conversed with a human. In all, a total of 300 conversations were conducted. In Warwick's view, this made Goostman the first machine to pass a Turing test. In a press release, he added that: Some will claim that the Test has already been passed. The words Turing Test have been applied to similar competitions around the world. However this event involved more simultaneous comparison tests than ever before, was independently verified and, crucially, the conversations were unrestricted. A true Turing Test does not set the questions or topics prior to the conversations. In his 1950 paper "Computing Machinery and Intelligence", Turing predicted that by the year 2000, computer programs would be sufficiently advanced that the average interrogator would, after five minutes of questioning, "not have more than 70 per cent chance" of correctly guessing whether they were speaking to a human or a machine. Although Turing phrased this as a prediction rather than a "threshold for intelligence", commentators believe that Warwick had chosen to interpret it as meaning that if 30% of interrogators were fooled, the software had "passed the Turing test". ==== Reactions ==== Warwick's claim that Eugene Goostman was the first ever chatbot to pass a Turing test was met with scepticism; critics acknowledged similar "passes" made in the past by other chatbots under the 30% criteria, including PC Therapist in 1991 (which tricked 5 of 10 judges, 50%), and at the Techniche festival in 2011, where a modified version of Cleverbot tricked 59.3% of 1334 votes (which included the 30 judges, along with an audience). Cleverbot's developer, Rollo Carpenter, argued that Turing tests can only prove that a machine can "imitate" intelligence rather than show actual intelligence. Gary Marcus was critical of Warwick's claims, arguing that Goostman's "success" was only the result of a "cleverly-coded piece of software", going on to say that "it's easy to see how an untrained judge might mistake wit for reality, but once you have an understanding of how this sort of system works, the constant misdirection and deflection becomes obvious, even irritating. The illusion, in other words, is fleeting." While acknowledging IBM's Deep Blue and Watson projects—single-purpose computer systems meant for playing chess and the quiz show Jeopardy! respectively—as examples of computer systems that show a degree of intelligence in their specialised field, he further argued that they were not an equivalent to a computer system that shows "broad" intelligence, and could—for example, watch a television programme and answer questions on its content. Marcus stated that "no existing combination of hardware and software can learn completely new things at will the way a clever child can." However, he still believed that there were potential uses for technology such as that of Goostman, specifically suggesting the creation of "believable", interactive video game characters. Imperial College London professor Murray Shanahan questioned the validity and scientific basis of the test, stating that it was "completely misplaced, and it devalues real AI research. It makes it seem like science fiction AI is nearly here, when in fact it's not and it's incredibly difficult." Mike Masnick, editor of the blog Techdirt, was also skeptical, questioning publicity blunders such as the five chatbots being referred to in press releases as "supercomputers", and saying that "creating a chatbot that can fool humans is not really the same thing as creating artificial intelligence."
EasyA
EasyA is a web3 technology company and education platform based in London (United Kingdom), founded in 2022 by Phil Kwok and Dom Kwok. EasyA was officially launched in 2022, focusing on web3 technologies. This community was influenced by the founders' experiences during the COVID-19 pandemic and early collaborations with universities and other educational institutions. Subsequently, the community was used as a foundation for developing Web3-related initiatives, including the organisation of EasyA's first Web3 hackathon in 2022. The EasyA app has over one million users and provides educational content on various blockchain technologies. EasyA Labs is a separate initiative focused on developing products intended to improve accessibility to cryptocurrency for a broader audience.
Teleradiology
Teleradiology is the transmission of radiological patient images from procedures such as x-rays, Computed tomography (CT), and MRI imaging, from one location to another for the purposes of sharing studies with other radiologists and physicians. Teleradiology allows radiologists to provide services without actually having to be at the location of the patient. This is particularly important when a sub-specialist such as an MRI radiologist, neuroradiologist, pediatric radiologist, or musculoskeletal radiologist is needed, since these professionals are generally only located in large metropolitan areas working during daytime hours. Teleradiology allows for specialists to be available at all times. Teleradiology utilizes standard network technologies such as the Internet, telephone lines, wide area networks, local area networks (LAN) and the latest advanced technologies such as medical cloud computing. Specialized software is used to transmit the images and enable the radiologist to effectively analyze potentially hundreds of images of a given study. Technologies such as advanced graphics processing, voice recognition, artificial intelligence, and image compression are often used in teleradiology. Through teleradiology and mobile DICOM viewers, images can be sent to another part of the hospital or to other locations around the world with equal effort. Teleradiology is a growth technology given that imaging procedures are growing approximately 15% annually against an increase of only 2% in the radiologist population. == Reports == Teleradiology services commonly provide either preliminary or final interpretations of medical imaging studies. Preliminary reads are frequently used in emergency settings to support immediate clinical decisions and may include direct communication of critical findings to the referring physician. Some providers report turnaround times of approximately 30 minutes for emergency cases, with faster processing for time-sensitive conditions such as stroke. Final reads are definitive and used in official patient records and billing. These reports typically include all relevant findings and may require access to prior imaging and clinical data. Teleradiology is also employed to provide off-hour or overflow coverage for healthcare institutions lacking continuous on-site radiology staffing. == Subspecialties == Some teleradiologists are fellowship trained and have a wide variety of subspecialty expertise including such difficult-to-find areas as neuroradiology, pediatric neuroradiology, thoracic imaging, musculoskeletal radiology, mammography, and nuclear cardiology. There are also various medical practitioners who are not radiologists that take on studies in radiology to become sub specialists in their respected fields, an example of this is dentistry where oral and maxillofacial radiology allows those in dentistry to specialize in the acquisition and interpretation of radiographic imaging studies performed for diagnosis of treatment guidance for conditions affecting the maxillofacial region. == Teleultrasound == Teleradiology infrastructure has also been adapted to support point-of-care ultrasound (POCUS) in remote and austere environments. In teleultrasound—also known as telementored ultrasound—a remote expert guides a non-specialist in real time during image acquisition. This technique has been successfully demonstrated in extreme settings, including aboard the International Space Station, on Mount Everest, and during helicopter flight. == Regulations == In the United States, Medicare and Medicaid laws require the teleradiologist to be on U.S. soil in order to qualify for reimbursement of the Final Read. In addition, advanced teleradiology systems must also be HIPAA compliant, which helps to ensure patients' privacy. HIPAA (Health Insurance Portability and Accountability Act of 1996) is a uniform, federal floor of privacy protections for consumers. It limits the ways that entities can use patients' personal information and protects the privacy of all medical information no matter what form it is in. Quality teleradiology must abide by important HIPAA rules to ensure patients' privacy is protected. Also State laws governing the licensing requirements and medical malpractice insurance coverage required for physicians vary from state to state. Ensuring compliance with these laws is a significant overhead expense for larger multi-state teleradiology groups. Medicare (Australia) has identical requirements to that of the United States, where the guidelines are provided by the Department of Health and Ageing, and government based payments fall under the Health Insurance Act. The regulations in Australia are also conducted at both federal and state levels, ensuring that strict guidelines are adhered to at all times, with regular yearly updates and amendments are introduced (usually around March and November of every year), ensuring that the legislation is kept up to date with changes in the industry. One of the most recent changes to Medicare and radiology / teleradiology in Australia was the introduction of the Diagnostic Imaging Accreditation Scheme (DIAS) on 1 July 2008. DIAS was introduced to further improve the quality of Diagnostic Imaging and to amend the Health Insurance Act. == Industry growth == Until the late 1990s teleradiology was primarily used by individual radiologists to interpret occasional emergency studies from offsite locations, often in the radiologists home. The connections were made through standard analog phone lines. Teleradiology expanded rapidly as the growth of the internet and broad band combined with new CT scanner technology to become an essential tool in trauma cases in emergency rooms throughout the country. The occasional 2–3 x-ray studies a week soon became 3–10 CT scans, or more, a night. Because ER physicians are not trained to read CT scans or MRIs, radiologists went from working 8–10 hours a day, five and half days a week to a schedule of 24 hours a day, 7 days a week coverage. This became a particularly acute challenge in smaller rural facilities that only had one solo radiologist with no other to share call. These circumstances spawned a post-dot.com boom of firms and groups that provided medical outsourcing, off-site teleradiology on-call services to hospitals and Radiology Groups around the country. As an example, a teleradiology firm might cover trauma at a hospital in Indiana with doctors based in Texas. Some firms even used overseas doctors in locations like Australia and India. Nighthawk, founded by Paul Berger, was the first to station U.S. licensed radiologists overseas (initially Australia and later Switzerland) to maximize the time zone difference to provide nightcall in U.S. hospitals. Currently, teleradiology firms are facing pricing pressures. Industry consolidation is likely as there are more than 500 of these firms, large and small, throughout the United States.
Video renderer
A video renderer is software that processes a video file and sends it sequentially to the video display controller card for display on a computer screen. An example of a video renderer, is the VMR-7 that was used by Microsoft's DirectShow. An example of a UNIX video renderer is the one container within GStreamer. Commonly used video renderers are: Enhanced Video Renderer VMR9 Renderless Haali's Video Renderer Madvr Video Renderer JRVR, a part of JRiver Media Center
DeepSeek (chatbot)
DeepSeek is a generative artificial intelligence chatbot developed by the Chinese company DeepSeek. Released on 20 January 2025, DeepSeek-R1 surpassed ChatGPT as the most downloaded freeware app on the iOS App Store in the United States by 27 January. DeepSeek's success against larger and more established rivals has been described as "upending AI" and initiating "a global AI space race". DeepSeek's compliance with Chinese government censorship policies and its data collection practices have also raised concerns over privacy and information control in the model, prompting regulatory scrutiny in multiple countries. However, it has also been praised for its open weights and infrastructure code, energy efficiency and contributions to open-source artificial intelligence. == History == On 10 January 2025, DeepSeek released the chatbot, based on the DeepSeek-R1 model, for iOS and Android. By 27 January, DeepSeek-R1 surpassed ChatGPT as the most-downloaded freeware app on the iOS App Store in the United States, which resulted in an 18% drop in Nvidia's share price. And after a "large-scale" cyberattack on the same day disrupted the proper functioning of its servers, DeepSeek had limited its new user registration to phone numbers from mainland China, email addresses, or Google account logins. On 3 April 2025, in collaboration with researchers at Tsinghua University, DeepSeek published a paper unveiling a new model that combines the techniques generative reward modeling (GRM) and self-principled critique tuning (SPCT). The resulting model is referred to as DeepSeek-GRM. The goal of using these techniques is to foster more effective inference-time scaling within their LLM and chatbot services. Notably, DeepSeek has said that these new models will be released and made open source. On 30 April 2025, Deepseek released its math-focused Artificial Intelligence Model named "DeepSeek-Prover-V2-671B". This model is useful for formal theorem proving and mathematical reasoning. On 24 April 2026, DeepSeek released DeepSeek V4 and V4-Pro. == Usage == DeepSeek can answer questions, solve logic problems, and write computer programs on par with other chatbots, according to benchmark tests used by American AI companies. Users can access the chatbot for free through the official DeepSeek website or mobile application, without limitation on the number of queries. DeepSeek only supports user-signup via a global email service, e.g. Gmail, Google or Yahoo. DeepSeek also offers access to the R1 and V3 models that power the chatbot via an API with a usage-based pricing model. This modality is primarily targeted towards developers and businesses. As of February 2025, API usage is priced at approximately $0.28 per million input tokens and $0.42 per million output tokens, making it less expensive than some competing services. Its web version is completely free, with 500 messages per hour cap limit to prevent bots from spamming. == Operation == DeepSeek-V3 uses significantly fewer resources compared to its peers. For example, whereas the world's leading AI companies train their chatbots with supercomputers using as many as 16,000 graphics processing units (GPUs), DeepSeek claims to have needed only about 2,000 GPUs—namely, the H800 series chips from Nvidia. It was trained in around 55 days at a cost of US$5.58 million, which is roughly one-tenth of what tech giant Meta spent building its latest AI technology. == Reactions == DeepSeek's success against larger and more established rivals has been described as "upending AI", constituting "the first shot at what is emerging as a global AI space race", and ushering in "a new era of AI brinkmanship". === Challenge to US AI dominance === DeepSeek's competitive performance at relatively minimal cost has been recognized as potentially challenging the global dominance of American AI models. Various publications and news media, such as The Hill and The Guardian, have described the release of the R1 chatbot as a "Sputnik moment" for American AI, echoing Marc Andreessen's view. OpenAI wrote a letter to the Office of Science and Technology Policy (OSTP), in March 2025, citing issues concerning a possibility that Deepseek could manipulate responses to cause harm. === Chinese perspective === DeepSeek's founder Liang Wenfeng has been compared to OpenAI CEO Sam Altman, with CNN calling him the Sam Altman of China and an evangelist for AI. Chinese state media widely praised DeepSeek as a national asset. On 20 January 2025, Chinese Premier Li Qiang invited Wenfeng to his symposium with experts and asked him to provide opinions and suggestions on a draft for comments of the annual 2024 government work report. On 20 February 2025, Wenfeng met with General Secretary of the Chinese Communist Party Xi Jinping, who encouraged party and state leaders to experiment with DeepSeek. Government officials responded to Xi's approval of the chatbot by reportedly using it to draft legal judgements, propose medical treatment plans, and analyze surveillance videos to search for missing persons. === Performance and success === Leading figures in the American AI sector had mixed reactions to DeepSeek's performance and success. Microsoft CEO Satya Nadella and OpenAI CEO Altman—whose companies are involved in the United States government-backed "Stargate Project" to develop American AI infrastructure—both called DeepSeek "super impressive". Various companies including Amazon Web Services, Toyota, and Stripe are seeking to use the model in their program. When American President Donald Trump announced The Stargate Project, he referred to DeepSeek as a wake-up call and a positive development. Other leaders in the AI field, however—including Scale AI CEO Alexandr Wang, Anthropic cofounder and CEO Dario Amodei, and Elon Musk—have expressed skepticism of the app's performance or of the sustainability of its success. Wang in particularly referred to DeepSeek-V3 as "earth-shattering" and DeepSeek-R1 as "top performing, or roughly on par with the best American models", but speculated that China may possess more AI-powering Nvidia H100 GPUs than thought. === Stock market implications === DeepSeek's optimization of limited resources has highlighted potential limits of United States sanctions on China's AI development, including export restrictions on advanced AI chips to China. The success of the company's AI models consequently "sparked market turmoil" and caused shares in major global technology companies to plunge on 27 January 2025: Nvidia's stock fell by as much as 17–18%, as did the stock of rival Broadcom. Other tech firms also sank, including Microsoft (down 2.5%), Google's owner Alphabet (down over 4%), and Dutch chip equipment maker ASML (down over 7%). A global sell-off of technology stocks on Nasdaq, prompted by the release of the R1 model, led to record losses of about $593 billion in the market capitalizations of AI and computer hardware companies; and by the next day a total of $1 trillion of value was wiped from American stocks. == Concerns == === Distillation === DeepSeek has been reported to sometimes claim that it is ChatGPT. OpenAI said that DeepSeek may have "inappropriately" used outputs from its model as training data in a process called distillation. However, there is currently no method to prove this conclusively. === Censorship === DeepSeek's compliance with Chinese government censorship policies and its data collection practices have raised concerns over information control in the model, prompting regulatory scrutiny in multiple countries. Reports indicate that it applies content moderation in accordance with the government's "public opinion guidance" regulations, limiting responses on topics such as the Tiananmen Square massacre and Taiwan's political status. DeepSeek models that have been uncensored also display a bias towards Chinese government viewpoints on controversial topics such as Xi Jinping's human rights record and Taiwan's political status. However, users who have downloaded the models and hosted them on their own devices and servers have reported successfully removing this censorship. Some sources have observed that the official application programming interface (API) version of R1, which runs from servers located in mainland China, uses censorship mechanisms for topics considered politically sensitive for the government of China. For example, the model may initially generate answers to questions about the 1989 Tiananmen Square massacre, persecution of Uyghurs, comparisons between Xi Jinping and Winnie the Pooh, and human rights in China, but a censorship mechanism deletes the uncensored response afterwards and replaces it with a message such as:"Sorry, that's beyond my current scope. Let's talk about something else." The post hoc censorship mechanisms and restrictions added on top of the model's output can be removed in the open-source version of the R1 model. If the "core Socialist values" defined by the Chinese Internet regul
YaDICs
YaDICs is a program written to perform digital image correlation on 2D and 3D tomographic images. The program was designed to be both modular, by its plugin strategy and efficient, by it multithreading strategy. It incorporates different transformations (Global, Elastic, Local), optimizing strategy (Gauss-Newton, Steepest descent), Global and/or local shape functions (Rigid-body motions, homogeneous dilatations, flexural and Brazilian test models)... == Theoretical background == === Context === In solid mechanics, digital image correlation is a tool that allows to identify the displacement field to register a reference image (called herein fixed image) to images during an experiment (mobile image). For example, it is possible to observe the face of a specimen with a painted speckle on it in order to determine its displacement fields during a tensile test. Before the appearance of such methods, researchers usually used strain gauges to measure the mechanical state of the material but strain gauges only measure the strain on a point and don't allow to understand material with an heterogeneous behavior. One can obtain a full in plane strain tensor by derivation of the displacement fields. Many methods are based upon the optical flow. In fluid mechanics a similar method is used, called Particle Image Velocimetry (PIV); the algorithms are similar to those of DIC but it is impossible to ensure that the optical flow is conserved so a vast majority of the software used the normalized cross correlation metric. In mechanics the displacement or velocity fields are the only concern, registering images is just a side effect. There is another process called image registration using the same algorithms (on monomodal images) but where the goal is to register images and thereby identifying the displacement field is just a side effect. YaDICs uses the general principle of image registration with a particular attention to the displacement fields basis. === Image registration principle === YaDICs can be explained using the classical image registration framework: === Image registration general scheme === The common idea of image registration and digital image correlation is to find the transformation between a fixed image and a moving one for a given metric using an optimization scheme. While there are many methods to achieve such a goal, Yadics focuses on registering images with the same modality. The idea behind the creation of this software is to be able to process data that comes from a μ-tomograph; i.e.: data cube over 10003 voxels. With such a size it is not possible to use naive approach usually used in a two-dimensional context. In order to get sufficient performances OpenMP parallelism is used and data are not globally stored in memory. As an extensive description of the different algorithms is given in. === Sampling === Contrary to image registration, Digital Image Correlation targets the transformation, one wants to extracted the most accurate transformation from the two images and not just match the images. Yadics uses the whole image as a sampling grid: it is thus a total sampling. === Interpolator === It is possible to choose between bilinear interpolation and bicubic interpolation for the grey level evaluation at non integer coordinates. The bi-cubic interpolation is the recommended one. === Metrics === ==== Sum of squared differences (SSD) ==== The SSD is also known as mean squared error. The equation below defines the SSD metric: S S D ( μ , I F , I M ) = 1 | Ω F | ∑ x i ∈ Ω F ( I F ( x i ) − I M ( T μ ( x i ) ) ) 2 , {\displaystyle SSD(\mu ,{\mathcal {I_{F}}},{\mathcal {I_{M}}})={\dfrac {1}{\left|\Omega _{F}\right|}}\sum _{x_{i}\in \Omega _{F}}\left({\mathcal {I_{F}}}(x_{i})-{\mathcal {I_{M}}}({T}_{\mu }(x_{i}))\right)^{2},} where I F {\displaystyle {\mathcal {I_{F}}}} is the fixed image, I M {\displaystyle {\mathcal {I_{M}}}} the moving one, Ω F {\displaystyle \Omega _{F}} the integration area | Ω F | {\displaystyle \left|\Omega _{F}\right|} the number of pi(vo)xels (cardinal) and T μ {\displaystyle {T}_{\mu }} the transformation parametrized by μ The transformation can be written as: T μ ( x ) = x + { Φ ( x ) } t { μ } . {\displaystyle T_{\mu }(x)=x+\left\{\Phi (x)\right\}^{t}\left\{\mu \right\}.} This metric is the main one used in the YaDICs as it works well with same modality images. One has to find the minimum of this metric ==== Normalized cross-correlation ==== The normalized cross-correlation (NCC) is used when one cannot assure the optical flow conservation; it happens in case of change of lighting or if particles disappear from the scene can occur in particle images velocimetry (PIV). The NCC is defined by: N C C ( μ , I F , I M ) = ∑ x i ∈ Ω F ( I F ( x i ) − I F ¯ ) ( I M ( T μ ( x i ) ) − I M ¯ ) ∑ x i ∈ Ω F ( I F ( x i ) − I F ¯ ) 2 ∑ x i ∈ Ω F ( I M ( T μ ( x i ) ) − I M ¯ ) 2 , {\displaystyle NCC(\mu ,{\mathcal {I_{F}}},{\mathcal {I_{M}}})={\dfrac {\sum _{x_{i}\in \Omega _{F}}\left({\mathcal {I_{F}}}(x_{i})-{\overline {\mathcal {I_{F}}}}\right)\left({\mathcal {I_{M}}}({T}_{\mu }(x_{i}))-{\overline {\mathcal {I_{M}}}}\right)}{\sqrt {\sum _{x_{i}\in \Omega _{F}}\left({\mathcal {I_{F}}}(x_{i})-{\overline {\mathcal {I_{F}}}}\right)^{2}\sum _{x_{i}\in \Omega _{F}}\left({\mathcal {I_{M}}}({T}_{\mu }(x_{i}))-{\overline {\mathcal {I_{M}}}}\right)^{2}}}},} where I F ¯ {\displaystyle {\overline {\mathcal {I_{F}}}}} and I M ¯ {\displaystyle {\overline {\mathcal {I_{M}}}}} are the mean values of the fixed and mobile images. This metric is only used to find local translation in Yadics. This metric with translation transform can be solved using cross-correlation methods, which are non iterative and can be accelerated using Fast Fourier Transform . === Classification of transformations === There are three categories of parametrization: elastic, global and local transformation. The elastic transformations respect the partition of unity, there are no holes created or surfaces counted several times. This is commonly used in Image Registration by the use of B-Spline functions and in solid mechanics with finite element basis. The global transformations are defined on the whole picture using rigid body or affine transformation (which is equivalent to homogeneous strain transformation). More complex transformations can be defined such as mechanically based one. These transformations have been used for stress intensity factor identification by and for rod strain by. The local transformation can be considered as the same global transformation defined on several Zone Of Interest (ZOI) of the fixed image. ==== Global ==== Several global transforms have been implemented: Rigid and homogeneous (Tx,Ty,Rz in 2D; Tx,Ty,Tz,Rx,Ry,Rz,Exx,Eyy,Ezz,Eyz,Exz,Exy in 3D) Brazilian (Only in 2D), Dynamic Flexion, ==== Elastic ==== First-order quadrangular finite elements Q4P1 are used in Yadics. ===== Local ===== Every global transform can be used on a local mesh. === Optimization === The YaDICs optimization process follows a gradient descent scheme. The first step is to compute the gradient of the metric regarding the transform parameters ∂ S S D ( μ , I F , I M ) ∂ μ = 2 | Ω F | ∑ x i ∈ Ω F ( I F ( x i ) − I M ( T μ ( x i ) ) ) ∂ I M ( T μ ( x i ) ∂ μ = 2 | Ω F | ∑ x i ∈ Ω F ( I F ( x i ) − I M ( T μ ( x i ) ) ) ( ∂ T μ ( x i ) ∂ μ ) t ∂ I M ( T μ ( x i ) ) ∂ x {\displaystyle {\begin{array}{lcl}{\dfrac {\partial SSD(\mu ,{\mathcal {I_{F}}},{\mathcal {I_{M}}})}{\partial \mu }}&=&{\dfrac {2}{\left|\Omega _{F}\right|}}\sum _{x_{i}\in \Omega _{F}}\left({\mathcal {I_{F}}}(x_{i})-{\mathcal {I_{M}}}({T}_{\mu }(x_{i}))\right){\dfrac {\partial {\mathcal {I_{M}}}({T}_{\mu }(x_{i})}{\partial \mu }}\\&=&{\dfrac {2}{\left|\Omega _{F}\right|}}\sum _{x_{i}\in \Omega _{F}}\left({\mathcal {I_{F}}}(x_{i})-{\mathcal {I_{M}}}({T}_{\mu }(x_{i}))\right)\left({\dfrac {\partial {T}_{\mu }(x_{i})}{\partial \mu }}\right)^{t}{\dfrac {\partial {\mathcal {I_{M}}}({T}_{\mu }(x_{i}))}{\partial x}}\\\end{array}}} ==== Gradient method ==== Once the metric gradient has been computed, one has to find an optimization strategy The gradient method principle is explained below: μ k + 1 = μ k + α k d k {\displaystyle \mu _{k+1}=\mu _{k}+\alpha _{k}d_{k}} The gradient step can be constant or updated at every iteration. d k = − γ k ∂ C ( μ , I F , I M ) ∂ μ {\displaystyle d_{k}=-\gamma _{k}{\dfrac {\partial {\mathcal {C}}(\mu ,{\mathcal {I_{F}}},{\mathcal {I_{M}}})}{\partial \mu }}} , γ k {\displaystyle \gamma _{k}} allows one to choose between the following methods : γ k {\displaystyle \gamma _{k}} ⟹ {\displaystyle \Longrightarrow } steepest descent, γ k = [ ∂ C ( μ , I F , I M ) ∂ μ ∂ C ( μ , I F , I M ) ∂ μ t ] − 1 {\displaystyle \gamma _{k}=\left[{\dfrac {\partial {\mathcal {C}}(\mu ,{\mathcal {I_{F}}},{\mathcal {I_{M}}})}{\partial \mu }}{\dfrac {\partial {\mathcal {C}}(\mu ,{\mathcal {I_{F}}},{\mathcal {I_{M}}})}{\partial \mu }}^{t}\right]^{-1}} ⟹ {\displaystyle \Longrightarrow } Gauss-Newto