AI Face Live

AI Face Live — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Infogram

  Infogram is a web-based data visualization and infographics platform, created in Riga, Latvia. It allows people to make and share digital charts, infographics and maps. Infogram offers an intuitive WYSIWYG editor that converts users’ data into infographics that can be published, embedded or shared. Users do not need coding skills to use this tool; users include newsrooms, marketing teams, governments, educators and students. The company that created Infogram, also called Infogram, was founded in 2012 in Riga, Latvia and has another office in San Francisco. As of October 2017, Infogram says it has 3 million users who have created charts and infographics that have been viewed more than 1.5 billion times. Infogram was bought by Prezi, a web-based presentation software company, in May 2017. == History == Infogram was founded in February 2012 in Riga, Latvia by Uldis Leiterts, Raimonds Kaže and Alise Dīrika. In January 2013, Infogram won the international Hy Berlin pitch contest. During his pitch, Infogram CEO Uldis Leiterts announced that the company had created more templates and was working with Microsoft to integrate its platform with the contemporaneous version of Microsoft Office. The company also won the 2013 Kantar Information Is Beautiful Award, which “celebrates excellence and beauty in data visualizations, infographics, interactives & information art.” In December 2014, Infogram acquired the Brazil-based data visualization blog, Visualoop. In an effort to expand sales and marketing in the U.S., Infogram secured $1.8 million in funding in February 2014. The announcement was made at TechChill, a startup conference for the Baltics in Riga, Latvia. At the time, the funding was believed to be the largest to date for the company. Infogram won the 2017 National Design Award of Latvia. == Acquisition by Prezi == Prezi, a web-based presentation software company, acquired Infogram in May 2017. Infogram is now a wholly owned subsidiary of Prezi. Infogram was rated #1 on Forbes’ list of “The Best Infographic Tools for 2017,” which was published in September 2017. In October 2017, Infogram announced a new version of its data visualization platform, including a drag-and-drop editor, over 40 new designer templates and social media support.

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  Top 10 AI Subtitle Generators Compared (2026)

  Curious about the best AI subtitle generator? An AI subtitle generator is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI subtitle generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  Markov chain central limit theorem

  In the mathematical theory of random processes, the Markov chain central limit theorem has a conclusion somewhat similar in form to that of the classic central limit theorem (CLT) of probability theory, but the quantity in the role taken by the variance in the classic CLT has a more complicated definition. See also the general form of Bienaymé's identity. == Statement == Suppose that: the sequence X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } of random elements of some set is a Markov chain that has a stationary probability distribution; and the initial distribution of the process, i.e. the distribution of X 1 {\textstyle X_{1}} , is the stationary distribution, so that X 1 , X 2 , X 3 , … {\textstyle X_{1},X_{2},X_{3},\ldots } are identically distributed. In the classic central limit theorem these random variables would be assumed to be independent, but here we have only the weaker assumption that the process has the Markov property; and g {\textstyle g} is some (measurable) real-valued function for which var ⁡ ( g ( X 1 ) ) < + ∞ . {\textstyle \operatorname {var} (g(X_{1}))<+\infty .} Now let μ = E ⁡ ( g ( X 1 ) ) , μ ^ n = 1 n ∑ k = 1 n g ( X k ) σ 2 := lim n → ∞ var ⁡ ( n μ ^ n ) = lim n → ∞ n var ⁡ ( μ ^ n ) = var ⁡ ( g ( X 1 ) ) + 2 ∑ k = 1 ∞ cov ⁡ ( g ( X 1 ) , g ( X 1 + k ) ) . {\displaystyle {\begin{aligned}\mu &=\operatorname {E} (g(X_{1})),\\{\widehat {\mu }}_{n}&={\frac {1}{n}}\sum _{k=1}^{n}g(X_{k})\\\sigma ^{2}&:=\lim _{n\to \infty }\operatorname {var} ({\sqrt {n}}{\widehat {\mu }}_{n})=\lim _{n\to \infty }n\operatorname {var} ({\widehat {\mu }}_{n})=\operatorname {var} (g(X_{1}))+2\sum _{k=1}^{\infty }\operatorname {cov} (g(X_{1}),g(X_{1+k})).\end{aligned}}} Then as n → ∞ , {\textstyle n\to \infty ,} we have n ( μ ^ n − μ ) → D Normal ( 0 , σ 2 ) , {\displaystyle {\sqrt {n}}({\hat {\mu }}_{n}-\mu )\ {\xrightarrow {\mathcal {D}}}\ {\text{Normal}}(0,\sigma ^{2}),} where the decorated arrow indicates convergence in distribution. == Monte Carlo Setting == The Markov chain central limit theorem can be guaranteed for functionals of general state space Markov chains under certain conditions. In particular, this can be done with a focus on Monte Carlo settings. An example of the application in a MCMC (Markov Chain Monte Carlo) setting is the following: Consider a simple hard spheres model on a grid. Suppose X = { 1 , … , n 1 } × { 1 , … , n 2 } ⊆ Z 2 {\displaystyle X=\{1,\ldots ,n_{1}\}\times \{1,\ldots ,n_{2}\}\subseteq Z^{2}} . A proper configuration on X {\displaystyle X} consists of coloring each point either black or white in such a way that no two adjacent points are white. Let χ {\displaystyle \chi } denote the set of all proper configurations on X {\displaystyle X} , N χ ( n 1 , n 2 ) {\displaystyle N_{\chi }(n_{1},n_{2})} be the total number of proper configurations and π be the uniform distribution on χ {\displaystyle \chi } so that each proper configuration is equally likely. Suppose our goal is to calculate the typical number of white points in a proper configuration; that is, if W ( x ) {\displaystyle W(x)} is the number of white points in x ∈ χ {\displaystyle x\in \chi } then we want the value of E π W = ∑ x ∈ χ W ( x ) N χ ( n 1 , n 2 ) {\displaystyle E_{\pi }W=\sum _{x\in \chi }{\frac {W(x)}{N_{\chi }{\bigl (}n_{1},n_{2}{\bigr )}}}} If n 1 {\displaystyle n_{1}} and n 2 {\displaystyle n_{2}} are even moderately large then we will have to resort to an approximation to E π W {\displaystyle E_{\pi }W} . Consider the following Markov chain on χ {\displaystyle \chi } . Fix p ∈ ( 0 , 1 ) {\displaystyle p\in (0,1)} and set X 1 = x 1 {\displaystyle X_{1}=x_{1}} where x 1 ∈ χ {\displaystyle x_{1}\in \chi } is an arbitrary proper configuration. Randomly choose a point ( x , y ) ∈ X {\displaystyle (x,y)\in X} and independently draw U ∼ U n i f o r m ( 0 , 1 ) {\displaystyle U\sim \mathrm {Uniform} (0,1)} . If u ≤ p {\displaystyle u\leq p} and all of the adjacent points are black then color ( x , y ) {\displaystyle (x,y)} white leaving all other points alone. Otherwise, color ( x , y ) {\displaystyle (x,y)} black and leave all other points alone. Call the resulting configuration X 1 {\displaystyle X_{1}} . Continuing in this fashion yields a Harris ergodic Markov chain { X 1 , X 2 , X 3 , … } {\displaystyle \{X_{1},X_{2},X_{3},\ldots \}} having π {\displaystyle \pi } as its invariant distribution. It is now a simple matter to estimate E π W {\displaystyle E_{\pi }W} with w n ¯ = ∑ i = 1 n W ( X i ) / n {\displaystyle {\overline {w_{n}}}=\sum _{i=1}^{n}W(X_{i})/n} . Also, since χ {\displaystyle \chi } is finite (albeit potentially large) it is well known that X {\displaystyle X} will converge exponentially fast to π {\displaystyle \pi } which implies that a CLT holds for w n ¯ {\displaystyle {\overline {w_{n}}}} . == Implications == Not taking into account the additional terms in the variance which stem from correlations (e.g. serial correlations in markov chain monte carlo simulations) can result in the problem of pseudoreplication when computing e.g. the confidence intervals for the sample mean.

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  Krohn–Rhodes theory

  In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and finite simple groups that are combined in a feedback-free manner (called a "wreath product" or "cascade"). Krohn and Rhodes found a general decomposition for finite automata. The authors discovered and proved an unexpected major result in finite semigroup theory, revealing a deep connection between finite automata and semigroups. Decidability of Krohn-Rhodes complexity long motivated much work in semigroup theory. In June 2024, Stuart Margolis, John Rhodes, and Anne Schilling announced a proof that the complexity is decidable. == Definitions and description of the Krohn–Rhodes theorem == Let T {\displaystyle T} be a semigroup. A semigroup S {\displaystyle S} that is a homomorphic image of a subsemigroup of T {\displaystyle T} is said to be a divisor of T {\displaystyle T} . The Krohn–Rhodes theorem for finite semigroups states that every finite semigroup S {\displaystyle S} is a divisor of a finite alternating wreath product of finite simple groups, each a divisor of S {\displaystyle S} , and finite aperiodic semigroups (which contain no nontrivial subgroups). In the automata formulation, the Krohn–Rhodes theorem for finite automata states that given a finite automaton A {\displaystyle A} with states Q {\displaystyle Q} and input alphabet I {\displaystyle I} , output alphabet U {\displaystyle U} , then one can expand the states to Q ′ {\displaystyle Q'} such that the new automaton A ′ {\displaystyle A'} embeds into a cascade of "simple", irreducible automata: In particular, A {\displaystyle A} is emulated by a feed-forward cascade of (1) automata whose transformation semigroups are finite simple groups and (2) automata that are banks of flip-flops running in parallel. The new automaton A ′ {\displaystyle A'} has the same input and output symbols as A {\displaystyle A} . Here, both the states and inputs of the cascaded automata have a very special hierarchical coordinate form. Moreover, each simple group (prime) or non-group irreducible semigroup (subsemigroup of the flip-flop monoid) that divides the transformation semigroup of A {\displaystyle A} must divide the transformation semigroup of some component of the cascade, and only the primes that must occur as divisors of the components are those that divide A {\displaystyle A} 's transformation semigroup. == Group complexity == The Krohn–Rhodes complexity (also called group complexity or just complexity) of a finite semigroup S is the least number of groups in a wreath product of finite groups and finite aperiodic semigroups of which S is a divisor. All finite aperiodic semigroups have complexity 0, while non-trivial finite groups have complexity 1. In fact, there are semigroups of every non-negative integer complexity. For example, for any n greater than 1, the multiplicative semigroup of all (n+1) × (n+1) upper-triangular matrices over any fixed finite field has complexity n (Kambites, 2007). A major open problem in finite semigroup theory is the decidability of complexity: is there an algorithm that will compute the Krohn–Rhodes complexity of a finite semigroup, given its multiplication table? Upper bounds and ever more precise lower bounds on complexity have been obtained (see, e.g. Rhodes & Steinberg, 2009). Rhodes has conjectured that the problem is decidable. In June 2024, Stuart Margolis, John Rhodes, and Anne Schilling announced a proof in the affirmative of the conjecture, though as of 2025 the result has yet to be confirmed. == History and applications == At a conference in 1962, Kenneth Krohn and John Rhodes announced a method for decomposing a (deterministic) finite automaton into "simple" components that are themselves finite automata. This joint work, which has implications for philosophy, comprised both Krohn's doctoral thesis at Harvard University and Rhodes' doctoral thesis at MIT. Simpler proofs, and generalizations of the theorem to infinite structures, have been published since then (see Chapter 4 of Rhodes and Steinberg's 2009 book The q-Theory of Finite Semigroups for an overview). In the 1965 paper by Krohn and Rhodes, the proof of the theorem on the decomposition of finite automata (or, equivalently sequential machines) made extensive use of the algebraic semigroup structure. Later proofs contained major simplifications using finite wreath products of finite transformation semigroups. The theorem generalizes the Jordan–Hölder decomposition for finite groups (in which the primes are the finite simple groups), to all finite transformation semigroups (for which the primes are again the finite simple groups plus all subsemigroups of the "flip-flop" (see above)). Both the group and more general finite automata decomposition require expanding the state-set of the general, but allow for the same number of input symbols. In the general case, these are embedded in a larger structure with a hierarchical "coordinate system". One must be careful in understanding the notion of "prime" as Krohn and Rhodes explicitly refer to their theorem as a "prime decomposition theorem" for automata. The components in the decomposition, however, are not prime automata (with prime defined in a naïve way); rather, the notion of prime is more sophisticated and algebraic: the semigroups and groups associated to the constituent automata of the decomposition are prime (or irreducible) in a strict and natural algebraic sense with respect to the wreath product (Eilenberg, 1976). Also, unlike earlier decomposition theorems, the Krohn–Rhodes decompositions usually require expansion of the state-set, so that the expanded automaton covers (emulates) the one being decomposed. These facts have made the theorem difficult to understand and challenging to apply in a practical way—until recently, when computational implementations became available (Egri-Nagy & Nehaniv 2005, 2008). H.P. Zeiger (1967) proved an important variant called the holonomy decomposition (Eilenberg 1976). The holonomy method appears to be relatively efficient and has been implemented computationally by A. Egri-Nagy (Egri-Nagy & Nehaniv 2005). Meyer and Thompson (1969) give a version of Krohn–Rhodes decomposition for finite automata that is equivalent to the decomposition previously developed by Hartmanis and Stearns, but for useful decompositions, the notion of expanding the state-set of the original automaton is essential (for the non-permutation automata case). Many proofs and constructions now exist of Krohn–Rhodes decompositions (e.g., [Krohn, Rhodes & Tilson 1968], [Ésik 2000], [Diekert et al. 2012]), with the holonomy method the most popular and efficient in general (although not in all cases). [Zimmermann 2010] gives an elementary proof of the theorem. Owing to the close relation between monoids and categories, a version of the Krohn–Rhodes theorem is applicable to category theory. This observation and a proof of an analogous result were offered by Wells (1980). The Krohn–Rhodes theorem for semigroups/monoids is an analogue of the Jordan–Hölder theorem for finite groups (for semigroups/monoids rather than groups). As such, the theorem is a deep and important result in semigroup/monoid theory. The theorem was also surprising to many mathematicians and computer scientists since it had previously been widely believed that the semigroup/monoid axioms were too weak to admit a structure theorem of any strength, and prior work (Hartmanis & Stearns) was only able to show much more rigid and less general decomposition results for finite automata. Work by Egri-Nagy and Nehaniv (2005, 2008–) continues to further automate the holonomy version of the Krohn–Rhodes decomposition extended with the related decomposition for finite groups (so-called Frobenius–Lagrange coordinates) using the computer algebra system GAP. Applications outside of the semigroup and monoid theories are now computationally feasible. They include computations in biology and biochemical systems (e.g. Egri-Nagy & Nehaniv 2008), artificial intelligence, finite-state physics, psychology, and game theory (see, for example, Rhodes 2009).

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  Oracle Cloud

  Oracle Cloud is a cloud computing service offered by Oracle Corporation providing servers, storage, network, applications and services through a global network of Oracle Corporation managed data centers. The company allows these services to be provisioned on demand over the Internet. Oracle Cloud provides infrastructure as a service (IaaS), platform as a service (PaaS), software as a service (SaaS), and data as a service (DaaS). These services are used to build, deploy, integrate, and extend applications in the cloud. This platform supports numerous open standards (SQL, HTML5, REST, etc.), open-source applications (Kubernetes, Spark, Hadoop, Kafka, MySQL, Terraform, etc.), and a variety of programming languages, databases, tools, and frameworks including Oracle-specific, open source, and third-party software and systems. == Services == === Infrastructure as a Service (IaaS) and Platform as a Service (PaaS) === Oracle's cloud infrastructure was made generally available (GA) on October 20, 2016 under the name "Oracle Bare Metal Cloud Services". Oracle Bare Metal Cloud Services was rebranded as Oracle Cloud Infrastructure in 2018 and dubbed Oracle's "Generation 2 Cloud" at Oracle OpenWorld 2018. Oracle Cloud Infrastructure offerings include the following services: Compute: The company provides Virtual Machine Instances to provide different shapes (VM sizes) catering to different types of workloads and performance characteristics. They also provide on-demand Bare metal servers and Bare metal GPU servers, without a hypervisor. In 2016, Oracle Cloud Infrastructure launched with bare metal instances with Intel processors. These first bare metal instances offered were powered by Intel servers. In 2018, Oracle Cloud added bare metal instances powered by AMD processors, followed by Ampere Cloud-native processors in 2021. In 2021, Oracle also released its first VM-based compute instances based on Arm processors. Storage: The platform provides block volumes, file storage, object storage, and archive storage for database, analytics, content, and other applications across common protocols and APIs. Networking: This cloud platform provides network with fully configurable IP addresses, subnets, routing, and firewalls to support new or existing private networks with end-to-end security. Governance: For auditing, identity and access management, the platform has data integrity checks, traceability, and access management features. Database Management / Data Management: Oracle offers a data management platform for database workloads as well as hyper-scale big data and streaming workloads including OLTP, data warehousing, Spark, machine learning, text search, image analytics, data catalog, and deep learning. The platform allows Oracle, MySQL, and NoSQL databases to be deployed on demand as managed cloud services. Oracle Databases uniquely offer the Oracle Autonomous Database (optimized for data warehouse, transaction processing, or JSON), the Exadata shape, as well as Real Application Clusters (RAC). Load Balancing: The cloud platform offers load balancing capability to automatically route traffic across fault domains and availability domains for high availability and fault-tolerance for hosted applications. Edge Services: These services can monitor the path between users and resources and adapt to changes and outages. They include Domain Name System (DNS) services from Oracle's acquisition of Dyn. FastConnect: The cloud platform provides private connectivity across on-premises and cloud networks through providers like Equinix, AT&T, and Colt. Application Development: For application development, the company's cloud offers an open, standards-based application development platform to build, deploy, and manage API-first, mobile-first cloud applications. This platform supports container-native, cloud-native, and low code development. This platform also provides a DevOps platform for CI/CD, diagnostics for Java applications, and integration with SaaS and on-prem applications. Services include Java, mobile, digital assistants (evolution from chatbots), messaging, application container cloud, developer cloud, visual builder, API catalog, AI platform, DataScience.com (Oracle acquired) and blockchain. Integration: This is a platform offering with adapters to integrate on-premise and cloud applications. Capabilities include data integration and replication, API management, integration analytics, along with data migration and integration. They offer services such as data integration platform cloud, data integrator cloud service, GoldenGate cloud service, integration cloud, process cloud service, API platform cloud service, apiary cloud service, and SOA cloud service. Business Analytics: The company provides this business analytics platform which can analyze and generate insights from data across various applications, data warehouses, and data lakes. The services offered include analytics cloud, business intelligence, big data discovery, big data preparation, data visualization, and essbase. Security: The Oracle Cloud Platform provides identity and security applications for providing secure access and monitoring of hybrid cloud environment and addressing IT governance and compliance requirements. This platform delivers an identity SOC (Security Operations Center) through a combined offering of SIEM, UEBA, CASB, and IDaaS. The services offered include Identity Cloud Service and CASB Cloud Service. Management: The platform provides an integrated monitoring, management, and analytics platform. This platform also uses machine learning and big data on the operational data set. The platform is used to improve IT stability, prevent application outages, improve DevOps, and harden security. Services offered include Application Performance Monitoring, Infrastructure Monitoring, Log Analytics, Orchestration, IT Analytics, Configuration and Compliance, Security Monitoring, and Analytics. Content and Experience: This is a platform for content, website, and workflow management. This service is used to provide content collaboration and web presence. This tool comes integrated with Oracle on-premise and SaaS services. The services offered are Content and Experience Cloud, WebCenter Portal Cloud, and DIVA Cloud. In 2016, Oracle acquired Dyn, an internet infrastructure company. On May 16, 2018 Oracle announced that it had acquired DataScience.com, a privately held cloud workspace platform for data science projects and workloads. In April 2020, Oracle became the cloud infrastructure provider for Zoom, an online and video meeting platform. The same month, Nissan announced its migration to Oracle Cloud for its high-performance computing (HPC) workloads used for simulating the structural impacts of a car design. Xerox announced a partnership with Oracle Cloud in 2021, where Xerox will use Oracle's cloud-computing capabilities within its business incubator. === Software as a Service (SaaS) === Oracle provides SaaS applications also known as Oracle Cloud Applications. These applications are offered across a variety of products, industrial sectors with various deployment options to adhere to compliance standards. The below list mentions Oracle Cloud Applications provided by Oracle Corporation. Customer Experience (CX) Human Capital Management (HCM) Enterprise Resource Planning (ERP) Supply Chain Management (SCM) Enterprise Performance Management (EPM) Internet of Things Applications (IoT) SaaS Analytics Data Industry Solutions (Communications, Financial Services, Consumer Goods, High Tech and Manufacturing, Higher Education, Hospitality, Utilities) Deployment (adhering to standards for sectors such as Financial Services, Retail Services, Public Sector, Defense) Block-Chain Cloud Service (in partnership with SAP, IBM and Microsoft) Blockchain Applications On July 28, 2016 Oracle bought NetSuite, the very first cloud company, for $9.3 billion. === Data as a Service (DaaS) === This platform is known as the Oracle Data Cloud. This platform aggregates and analyzes consumer data powered by Oracle ID Graph across channels and devices to create cross-channel consumer understanding. == Deployment models == Oracle Cloud is available in 44 regions as of July 2023, including North America, South America, UK, European Union, Middle East, Africa, India, Australia, Korea, and Japan. Oracle Cloud is available as a public cloud (Oracle-managed regions); to selected government agencies as an Oracle-managed government cloud in the United States (with FedRAMP High and DISA SRG IL5 compliance) and United Kingdom; and as a "private cloud" or "hybrid cloud" as an Oracle-managed database-only service or full-service dedicated region - what Oracle calls "Cloud at Customer". == Architecture == Oracle's public and government cloud is offered through a global network of Oracle-managed data centers, connected by an Oracle-managed backbone network. Oracle's Exadata Cloud at Customer leverages this network for contr

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  Tomáš Mikolov

  Tomáš Mikolov is a Czech computer scientist working in the field of machine learning. In March 2020, Mikolov became a senior research scientist at the Czech Institute of Informatics, Robotics and Cybernetics. == Career == Mikolov obtained his PhD in Computer Science from Brno University of Technology for his work on recurrent neural network-based language models. He is the lead author of the 2013 paper that introduced the Word2vec technique in natural language processing and is an author on the FastText architecture. Mikolov came up with the idea to generate text from neural language models in 2007 and his RNNLM toolkit was the first to demonstrate the capability to train language models on large corpora, resulting in large improvements over the state of the art. Prior to joining Facebook in 2014, Mikolov worked as a visiting researcher at Johns Hopkins University, Université de Montréal, Microsoft and Google. He left Facebook at some time in 2019/2020 to join the Czech Institute of Informatics, Robotics and Cybernetics. Mikolov has argued that humanity might be at a greater existential risk if an artificial general intelligence is not developed.

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  Is an AI Coding Assistant Worth It in 2026?

  Curious about the best AI coding assistant? An AI coding assistant is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI coding assistant slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  The Best Free AI Photo Editor for Beginners

  Comparing the best AI photo editor? An AI photo editor is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI photo editor slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  Color balance

  In photography and image processing, color balance is the global adjustment of the intensities of the colors (typically red, green, and blue primary colors). An important goal of this adjustment is to render specific colors – particularly neutral colors like white or grey – correctly. Hence, the general method is sometimes called gray balance, neutral balance, or white balance. Color balance changes the overall mixture of colors in an image and is used for color correction. Generalized versions of color balance are used to correct colors other than neutrals or to deliberately change them for effect. White balance is one of the most common kinds of balancing, and is when colors are adjusted to make a white object (such as a piece of paper or a wall) appear white and not a shade of any other colour. Image data acquired by sensors – either film or electronic image sensors – must be transformed from the acquired values to new values that are appropriate for color reproduction or display. Several aspects of the acquisition and display process make such color correction essential – including that the acquisition sensors do not match the sensors in the human eye, that the properties of the display medium must be accounted for, and that the ambient viewing conditions of the acquisition differ from the display viewing conditions. The color balance operations in popular image editing applications usually operate directly on the red, green, and blue channel pixel values, without respect to any color sensing or reproduction model. In film photography, color balance is typically achieved by using color correction filters over the lights or on the camera lens. == Generalized color balance == Sometimes the adjustment to keep neutrals neutral is called white balance, and the phrase color balance refers to the adjustment that in addition makes other colors in a displayed image appear to have the same general appearance as the colors in an original scene. It is particularly important that neutral (gray, neutral, white) colors in a scene appear neutral in the reproduction. === Psychological color balance === Humans relate to flesh tones more critically than other colors. Trees, grass and sky can all be off without concern, but if human flesh tones are 'off' then the human subject can look sick or dead. To address this critical color balance issue, the tri-color primaries themselves are formulated to not balance as a true neutral color. The purpose of this color primary imbalance is to more faithfully reproduce the flesh tones through the entire brightness range. == Illuminant estimation and adaptation == Most digital cameras have means to select color correction based on the type of scene lighting, using either manual lighting selection, automatic white balance, or custom white balance. The algorithms for these processes perform generalized chromatic adaptation. Many methods exist for color balancing. Setting a button on a camera is a way for the user to indicate to the processor the nature of the scene lighting. Another option on some cameras is a button which one may press when the camera is pointed at a gray card or other neutral colored object. This captures an image of the ambient light, which enables a digital camera to set the correct color balance for that light. There is a large literature on how one might estimate the ambient lighting from the camera data and then use this information to transform the image data. A variety of algorithms have been proposed, and the quality of these has been debated. A few examples and examination of the references therein will lead the reader to many others. Examples are Retinex, an artificial neural network or a Bayesian method. == Chromatic colors == Color balancing an image affects not only the neutrals, but other colors as well. An image that is not color balanced is said to have a color cast, as everything in the image appears to have been shifted towards one color. Color balancing may be thought in terms of removing this color cast. Color balance is also related to color constancy. Algorithms and techniques used to attain color constancy are frequently used for color balancing, as well. Color constancy is, in turn, related to chromatic adaptation. Conceptually, color balancing consists of two steps: first, determining the illuminant under which an image was captured; and second, scaling the components (e.g., R, G, and B) of the image or otherwise transforming the components so they conform to the viewing illuminant. Viggiano found that white balancing in the camera's native RGB color model tended to produce less color inconstancy (i.e., less distortion of the colors) than in monitor RGB for over 4000 hypothetical sets of camera sensitivities. This difference typically amounted to a factor of more than two in favor of camera RGB. This means that it is advantageous to get color balance right at the time an image is captured, rather than edit later on a monitor. If one must color balance later, balancing the raw image data will tend to produce less distortion of chromatic colors than balancing in monitor RGB. == Mathematics of color balance == Color balancing is sometimes performed on a three-component image (e.g., RGB) using a 3x3 matrix. This type of transformation is appropriate if the image was captured using the wrong white balance setting on a digital camera, or through a color filter. Changing the color balance of an image can improve classifier results on a trained ML model. === Scaling monitor R, G, and B === In principle, one wants to scale all relative luminances in an image so that objects which are believed to be neutral appear so. If, say, a surface with R = 240 {\displaystyle R=240} was believed to be a white object, and if 255 is the count which corresponds to white, one could multiply all red values by 255/240. Doing analogously for green and blue would result, at least in theory, in a color balanced image. In this type of transformation the 3x3 matrix is a diagonal matrix. [ R G B ] = [ 255 / R w ′ 0 0 0 255 / G w ′ 0 0 0 255 / B w ′ ] [ R ′ G ′ B ′ ] {\displaystyle \left[{\begin{array}{c}R\\G\\B\end{array}}\right]=\left[{\begin{array}{ccc}255/R'_{w}&0&0\\0&255/G'_{w}&0\\0&0&255/B'_{w}\end{array}}\right]\left[{\begin{array}{c}R'\\G'\\B'\end{array}}\right]} where R {\displaystyle R} , G {\displaystyle G} , and B {\displaystyle B} are the color balanced red, green, and blue components of a pixel in the image; R ′ {\displaystyle R'} , G ′ {\displaystyle G'} , and B ′ {\displaystyle B'} are the red, green, and blue components of the image before color balancing, and R w ′ {\displaystyle R'_{w}} , G w ′ {\displaystyle G'_{w}} , and B w ′ {\displaystyle B'_{w}} are the red, green, and blue components of a pixel which is believed to be a white surface in the image before color balancing. This is a simple scaling of the red, green, and blue channels, and is why color balance tools in Photoshop have a white eyedropper tool. It has been demonstrated that performing the white balancing in the phosphor set assumed by sRGB tends to produce large errors in chromatic colors, even though it can render the neutral surfaces perfectly neutral. === Scaling X, Y, Z === If the image may be transformed into CIE XYZ tristimulus values, the color balancing may be performed there. This has been termed a "wrong von Kries" transformation. Although it has been demonstrated to offer usually poorer results than balancing in monitor RGB, it is mentioned here as a bridge to other things. Mathematically, one computes: [ X Y Z ] = [ X w / X w ′ 0 0 0 Y w / Y w ′ 0 0 0 Z w / Z w ′ ] [ X ′ Y ′ Z ′ ] {\displaystyle \left[{\begin{array}{c}X\\Y\\Z\end{array}}\right]=\left[{\begin{array}{ccc}X_{w}/X'_{w}&0&0\\0&Y_{w}/Y'_{w}&0\\0&0&Z_{w}/Z'_{w}\end{array}}\right]\left[{\begin{array}{c}X'\\Y'\\Z'\end{array}}\right]} where X {\displaystyle X} , Y {\displaystyle Y} , and Z {\displaystyle Z} are the color-balanced tristimulus values; X w {\displaystyle X_{w}} , Y w {\displaystyle Y_{w}} , and Z w {\displaystyle Z_{w}} are the tristimulus values of the viewing illuminant (the white point to which the image is being transformed to conform to); X w ′ {\displaystyle X'_{w}} , Y w ′ {\displaystyle Y'_{w}} , and Z w ′ {\displaystyle Z'_{w}} are the tristimulus values of an object believed to be white in the un-color-balanced image, and X ′ {\displaystyle X'} , Y ′ {\displaystyle Y'} , and Z ′ {\displaystyle Z'} are the tristimulus values of a pixel in the un-color-balanced image. If the tristimulus values of the monitor primaries are in a matrix P {\displaystyle \mathbf {P} } so that: [ X Y Z ] = P [ L R L G L B ] {\displaystyle \left[{\begin{array}{c}X\\Y\\Z\end{array}}\right]=\mathbf {P} \left[{\begin{array}{c}L_{R}\\L_{G}\\L_{B}\end{array}}\right]} where L R {\displaystyle L_{R}} , L G {\displaystyle L_{G}} , and L B {\displaystyle L_{B}} are the un-gamma corrected monitor RGB, one may use: [ L R L G L B ] = P − 1 [ X w / X w ′ 0 0

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  Roni Rosenfeld (Hebrew: רוני רוזנפלד) is an Israeli-American computer scientist and computational epidemiologist, currently serving as the head of the Machine Learning Department at Carnegie Mellon University. He is an international expert in machine learning, infectious disease forecasting, statistical language modeling and artificial intelligence. == Education == Rosenfeld received his B.Sc. in mathematics and physics from Tel Aviv University in 1985. He received his Ph.D. in computer science from Carnegie Mellon University in 1994. While a graduate student, he developed and open-sourced a statistical language-modeling toolkit to allow anyone to create statistical language models from their own corpora and experiment with and extend the toolkit's capabilities. The toolkit has been used by more than 100 NLP laboratories in more than 20 countries. Rosenfeld's Ph.D. thesis, A Maximum Entropy Approach to Adaptive Statistical Language Modeling, was advised by Raj Reddy and Xuedong Huang and won the 2001 Computer, Speech and Language award for "Most Influential Paper in the Last 5 Years." == Career == Shortly after receiving his Ph.D., Rosenfeld joined the faculty of the Carnegie Mellon School of Computer Science as an assistant professor. He was promoted to the rank of associate professor in 1999 and received tenure in 2001. In 2005 he was promoted to professor of language technologies, machine learning computer science and computational biology in the School of Computer Science at Carnegie Mellon University. Rosenfeld also holds adjunct appointments at the University of Pittsburgh School of Medicine, department of computational and systems biology. From 2002 to 2003, Rosenfeld was a visiting professor at the University of Hong Kong. Rosenfeld is the director of Carnegie Mellon's Machine Learning for Social Good (ML4SG) program. He has held educational leadership positions in a variety of programs, including the M.S. in computational finance (1997–1999), graduate computational and statistical learning (2001–2003), M.S. in machine learning (2017) and undergraduate minor in machine learning. Rosenfeld was appointed Head of Carnegie Mellon's Machine Learning Department in 2018. == Research == Rosenfeld's research interests include epidemiological forecasting, information and communication technologies for development (ICT4D), and machine learning for social good. === Epidemiological forecasting === Rosenfeld is a world expert in epidemiological forecasting. He founded and directs the Delphi research group, which has won most of the epidemiological forecasting challenges organized by the U.S. CDC and other U.S. government agencies. In December 2016, the CDC named his group the "Most Accurate Forecaster" for 2015–2016, and in October 2017, the Delphi group's two systems took the top two spots in the 2016-2017 flu forecasting challenge. The CDC recognized Rosenfeld's Delphi group at Carnegie Mellon University as having contributed the most accurate national-, regional-, and state-level influenza-like illness forecasts and national-level hospitalization forecasts to the site. In 2019, the CDC recognized forecasts provided by the Delphi group at Carnegie Mellon as having been the most accurate for five seasons in a row, and named the Delphi group an Influenza Forecasting Center of Excellence, a five-year designation that includes $3 million in research funding. Rosenfeld describes his forecasting research goal as "to make epidemiological forecasting as universally accepted and useful as weather forecasting is today." His recent work in the area has focused on selecting high value epidemiological forecasting targets (e.g. Influenza and Dengue); creating baseline forecasting methods for them; establishing metrics for measuring and tracking forecasting accuracy; estimating the limits of forecastability for each target; and identifying new sources of data that could be helpful to the forecasting goal. == Honors and awards == 2017 Joel and Ruth Spira Teaching Award 2017 CDC Influenza Forecasting Challenge "Most Accurate Forecaster" 1992 Allen Newell Medal for Research Excellence

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