Phase correlation

Phase correlation is an approach to estimate the relative translative offset between two similar images (digital image correlation) or other data sets. It is commonly used in image registration and relies on a frequency-domain representation of the data, usually calculated by fast Fourier transforms. The term is applied particularly to a subset of cross-correlation techniques that isolate the phase information from the Fourier-space representation of the cross-correlogram. == Example == The following image demonstrates the usage of phase correlation to determine relative translative movement between two images corrupted by independent Gaussian noise. The image was translated by (20,23) pixels. Accordingly, one can clearly see a peak in the phase-correlation representation at approximately (20,23). == Method == Given two input images g a {\displaystyle \ g_{a}} and g b {\displaystyle \ g_{b}} : Apply a window function (e.g., a Hamming window) on both images to reduce edge effects (this may be optional depending on the image characteristics). Then, calculate the discrete 2D Fourier transform of both images. G a = F { g a } , G b = F { g b } {\displaystyle \ \mathbf {G} _{a}={\mathcal {F}}\{g_{a}\},\;\mathbf {G} _{b}={\mathcal {F}}\{g_{b}\}} Calculate the cross-power spectrum by taking the complex conjugate of the second result, multiplying the Fourier transforms together elementwise, and normalizing this product elementwise. R = G a ∘ G b ∗ | G a ∘ G b ∗ | {\displaystyle \ R={\frac {\mathbf {G} _{a}\circ \mathbf {G} _{b}^{}}{|\mathbf {G} _{a}\circ \mathbf {G} _{b}^{}|}}} Where ∘ {\displaystyle \circ } is the Hadamard product (entry-wise product) and the absolute values are taken entry-wise as well. Written out entry-wise for element index ( j , k ) {\displaystyle (j,k)} : R j k = G a , j k ⋅ G b , j k ∗ | G a , j k ⋅ G b , j k ∗ | {\displaystyle \ R_{jk}={\frac {G_{a,jk}\cdot G_{b,jk}^{}}{|G_{a,jk}\cdot G_{b,jk}^{}|}}} Obtain the normalized cross-correlation by applying the inverse Fourier transform. r = F − 1 { R } {\displaystyle \ r={\mathcal {F}}^{-1}\{R\}} Determine the location of the peak in r {\displaystyle \ r} . ( Δ x , Δ y ) = arg ⁡ max ( x , y ) { r } {\displaystyle \ (\Delta x,\Delta y)=\arg \max _{(x,y)}\{r\}} === Subpixel registration === Commonly, interpolation methods are used to estimate the peak location in the cross-correlogram to non-integer values, despite the fact that the data are discrete, and this procedure is often termed 'subpixel registration'. A large variety of subpixel interpolation methods are given in the technical literature. Common peak interpolation methods such as parabolic interpolation have been used, and the OpenCV computer vision package uses a centroid-based method, though these generally have inferior accuracy compared to more sophisticated methods. Because the Fourier representation of the data has already been computed, it is especially convenient to use the Fourier shift theorem with real-valued (sub-integer) shifts for this purpose, which essentially interpolates using the sinusoidal basis functions of the Fourier transform. An especially popular FT-based estimator is given by Foroosh et al. In this method, the subpixel peak location is approximated by a simple formula involving peak pixel value and the values of its nearest neighbors, where r ( 0 , 0 ) {\displaystyle r_{(0,0)}} is the peak value and r ( 1 , 0 ) {\displaystyle r_{(1,0)}} is the nearest neighbor in the x direction (assuming, as in most approaches, that the integer shift has already been found and the comparand images differ only by a subpixel shift). Δ x = r ( 1 , 0 ) r ( 1 , 0 ) ± r ( 0 , 0 ) {\displaystyle \ \Delta x={\frac {r_{(1,0)}}{r_{(1,0)}\pm r_{(0,0)}}}} The Foroosh et al. method is quite fast compared to most methods, though it is not always the most accurate. Some methods shift the peak in Fourier space and apply non-linear optimization to maximize the correlogram peak, but these tend to be very slow since they must apply an inverse Fourier transform or its equivalent in the objective function. It is also possible to infer the peak location from phase characteristics in Fourier space without the inverse transformation, as noted by Stone. These methods usually use a linear least squares (LLS) fit of the phase angles to a planar model. The long latency of the phase angle computation in these methods is a disadvantage, but the speed can sometimes be comparable to the Foroosh et al. method depending on the image size. They often compare favorably in speed to the multiple iterations of extremely slow objective functions in iterative non-linear methods. Since all subpixel shift computation methods are fundamentally interpolative, the performance of a particular method depends on how well the underlying data conform to the assumptions in the interpolator. This fact also may limit the usefulness of high numerical accuracy in an algorithm, since the uncertainty due to interpolation method choice may be larger than any numerical or approximation error in the particular method. Subpixel methods are also particularly sensitive to noise in the images, and the utility of a particular algorithm is distinguished not only by its speed and accuracy but its resilience to the particular types of noise in the application. == Rationale == The method is based on the Fourier shift theorem. Let the two images g a {\displaystyle \ g_{a}} and g b {\displaystyle \ g_{b}} be circularly-shifted versions of each other: g b ( x , y ) = d e f g a ( ( x − Δ x ) mod M , ( y − Δ y ) mod N ) {\displaystyle \ g_{b}(x,y)\ {\stackrel {\mathrm {def} }{=}}\ g_{a}((x-\Delta x){\bmod {M}},(y-\Delta y){\bmod {N}})} (where the images are M × N {\displaystyle \ M\times N} in size). Then, the discrete Fourier transforms of the images will be shifted relatively in phase: G b ( u , v ) = G a ( u , v ) e − 2 π i ( u Δ x M + v Δ y N ) {\displaystyle \mathbf {G} _{b}(u,v)=\mathbf {G} _{a}(u,v)e^{-2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}} One can then calculate the normalized cross-power spectrum to factor out the phase difference: R ( u , v ) = G a G b ∗ | G a G b ∗ | = G a G a ∗ e 2 π i ( u Δ x M + v Δ y N ) | G a G a ∗ e 2 π i ( u Δ x M + v Δ y N ) | = G a G a ∗ e 2 π i ( u Δ x M + v Δ y N ) | G a G a ∗ | = e 2 π i ( u Δ x M + v Δ y N ) {\displaystyle {\begin{aligned}R(u,v)&={\frac {\mathbf {G} _{a}\mathbf {G} _{b}^{}}{|\mathbf {G} _{a}\mathbf {G} _{b}^{}|}}\\&={\frac {\mathbf {G} _{a}\mathbf {G} _{a}^{}e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}}{|\mathbf {G} _{a}\mathbf {G} _{a}^{}e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}|}}\\&={\frac {\mathbf {G} _{a}\mathbf {G} _{a}^{}e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}}{|\mathbf {G} _{a}\mathbf {G} _{a}^{}|}}\\&=e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}\end{aligned}}} since the magnitude of an imaginary exponential always is one, and the phase of G a G a ∗ {\displaystyle \ \mathbf {G} _{a}\mathbf {G} _{a}^{}} always is zero. The inverse Fourier transform of a complex exponential is a Dirac delta function, i.e. a single peak: r ( x , y ) = δ ( x + Δ x , y + Δ y ) {\displaystyle \ r(x,y)=\delta (x+\Delta x,y+\Delta y)} This result could have been obtained by calculating the cross correlation directly. The advantage of this method is that the discrete Fourier transform and its inverse can be performed using the fast Fourier transform, which is much faster than correlation for large images. === Benefits === Unlike many spatial-domain algorithms, the phase correlation method is resilient to noise, occlusions, and other defects typical of medical or satellite images. The method can be extended to determine rotation and scaling differences between two images by first converting the images to log-polar coordinates. Due to properties of the Fourier transform, the rotation and scaling parameters can be determined in a manner invariant to translation. === Limitations === In practice, it is more likely that g b {\displaystyle \ g_{b}} will be a simple linear shift of g a {\displaystyle \ g_{a}} , rather than a circular shift as required by the explanation above. In such cases, r {\displaystyle \ r} will not be a simple delta function, which will reduce the performance of the method. In such cases, a window function (such as a Gaussian or Tukey window) should be employed during the Fourier transform to reduce edge effects, or the images should be zero padded so that the edge effects can be ignored. If the images consist of a flat background, with all detail situated away from the edges, then a linear shift will be equivalent to a circular shift, and the above derivation will hold exactly. The peak can be sharpened by using edge or vector correlation. For periodic images (such as a chessboard or picket fence), phase correlation may yield ambiguous results with several peaks in the resulting output. == Applications == Phase correlation is the preferred m

Cepstral mean and variance normalization

Cepstral mean and variance normalization (CMVN) is a computationally efficient normalization technique for robust speech recognition. The performance of CMVN is known to degrade for short utterances. This is due to insufficient data for parameter estimation and loss of discriminable information as all utterances are forced to have zero mean and unit variance. CMVN minimizes distortion by noise contamination for robust feature extraction by linearly transforming the cepstral coefficients to have the same segmental statistics. Cepstral Normalization has been effective in the CMU Sphinx for maintaining a high level of recognition accuracy over a wide variety of acoustical environments. == Cepstral Normalization Techniques == There are multiple algorithms that achieve Cepstral Normalization in different ways. === Fixed codeword-dependent cepstral normalization (FCDCN) === FCDCN was developed to provide a form of compensation that provides greater recognition accuracy than SDCN but in a more computationally-efficient manner than the CDCN algorithm. The FCDCN algorithm applies an additive correction that depends on the instantaneous SNR of the input (like SDCN), but that can also vary from codeword to codeword (like CDCN). === Multiple Fixed Codeword-dependent Cepstral Normalization (MFCDCN) === MFCDCN is a simple extension of FCDCN algorithm that does not need environment specific training. In MFCDCN, compensation vectors are pre-computed in parallel for a set of target environments, using the FCDCN algorithm. === Incremental Multiple Fixed Codeword-dependent Cepstral Normalization (IMFCDCN) === While environment selection for the compensation vectors of MFCDCN is generally performed on an utterance-by-utterance basis, IMFCFCN improves on it by allowing the classification process to make use of cepstral vectors from previous utterances in a given session. == Cepstral Noise Subtraction == Automatic speech recognition (ASR) describes the steps of transcribing speech utterances represented as acoustic wave forms to written words. As is, CMVN has been used in different applications as this technique has proven to provide better speech recognitions results in different environments. CMVN has the capabilities to reduce differences between test and training data produced by channel distortions and colorizations . CMVN has also been found to be able to reduce differences in feature representation between speakers can also partly reduce the influence of background noise.

Control communications

In telecommunications, control communications is the branch of technology devoted to the design, development, and application of communications facilities used specifically for control purposes, such as for controlling (a) industrial processes, (b) movement of resources, (c) electric power generation, distribution, and utilization, (d) communications networks, and (e) transportation systems.

ISO/IEC JTC 1/SC 6

ISO/IEC JTC 1/SC 6 Telecommunications and information exchange between systems is a standardization subcommittee of the Joint Technical Committee ISO/IEC JTC 1. It is part of the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC), which develops and facilitates standards within the field of telecommunications and information exchange between systems. ISO/IEC JTC 1/SC 6 was established in 1964, following the creation of a Special Working Group under ISO/TC 97 on Data Link Control Procedures and Modem Interfaces. The international secretariat of ISO/IEC JTC 1/SC 6 is the Korean Agency for Technology and Standards (KATS), located in South Korea. == Scope == The scope of ISO/IEC JTC 1/SC 6 is “Standardization in the field of telecommunications dealing with the exchange of information between open systems including system functions, procedures, parameters as well as the conditions for their use. The standardization encompasses protocols and services of lower layers, including physical, data link, network, and transport as well as those of upper layers including but not limited to Directory and ASN.1.” Future Network has recently been added as an important work scope. A considerable part of the work is done in effective cooperation with ITU-T and other standardization bodies including IEEE 802 and Ecma International. == Structure == ISO/IEC JTC 1/SC 6 has three active working groups (WGs), each of which carries out specific tasks in standards development within the field of telecommunications and information exchange between systems. The focus of each working group is described in the group’s terms of reference. Working groups can be established if new working areas arise, or disbanded if the group’s working area is no longer relevant to standardization needs. Active working groups of ISO/IEC JTC 1/SC 6 are: == Collaborations == ISO/IEC JTC 1/SC 6 works in close collaboration with a number of other organizations or subcommittees, both internal and external to ISO or IEC. Organizations internal to ISO or IEC that collaborate with or are in liaison with ISO/IEC JTC 1/SC 6 include: ISO/IEC JTC 1/WG 7, Sensor networks ISO/IEC JTC 1/SC 17, Cards and personal identification ISO/IEC JTC 1/SC 25, Interconnection of information technology equipment ISO/IEC JTC 1/SC 27, IT security techniques ISO/IEC JTC 1/SC 29, Coding of audio, picture, multimedia and hypermedia information ISO/IEC JTC 1/SC 31, Automatic identification and data capture techniques ISO/IEC JTC 1/SC 38, Distributed application platforms & services (DAPS) ISO/TC 68, Financial services ISO/TC 122, Packaging ISO/TC 184/SC 5, Interoperability, integration, and architectures for enterprise systems and automation applications ISO/TC 215, Health Informatics IEC/SC 46A, Coaxial cables IEC/SC 46C, Wires and symmetric cables IEC/TC 48, Electrical connectors and mechanical structures for electrical and electronic equipment IEC/SC 48B, Electrical connectors IEC/TC 65, Industrial-process measurement, control and automation IEC/SC 65C, Industrial networks IEC/TC 86, Fibre optics IEC/SC 86C, Fibre optic systems and active devices IEC/TC 93, Design automation Some organizations external to ISO or IEC that collaborate with or are in liaison to ISO/IEC JTC 1/SC 6 include: European Conference of Postal and Telecommunications Administrations (CEPT) European Organization for Nuclear Research (CERN) European Commission (EC) European Telecommunications Standards Institute (ETSI) Ecma International International Civil Aviation Organization (ICAO) IEEE 802 LMSC (LAN/MAN Standards Committee) Internet Society (ISOC) International Telecommunications Satellite Organization (ITSO) ITU-T Organization for the Advancement of Structured Information Standards (OASIS) NFC Forum MFA Forum United Nations Conference on Trade and Development (UNCTAD) United Nations Economic Commission for Europe (UNECE) Universal Postal Union (UPU) World Meteorological Organization (WMO) CEN/TC 247/WG 4 == Member countries == Countries pay a fee to ISO to be members of subcommittees. The 19 "P" (participating) members of ISO/IEC JTC 1/SC 6 are: Austria, Belgium, Canada, China, Czech Republic, Finland, Germany, Greece, Jamaica, Japan, Kazakhstan, Republic of Korea, Netherlands, Russian Federation, Spain, Switzerland, Tunisia, United Kingdom, and United States. The 31 "O" (observing) members of ISO/IEC JTC 1/SC 6 are: Argentina, Bosnia and Herzegovina, Colombia, Cuba, Cyprus, France, Ghana, Hong Kong, Hungary, Iceland, India, Indonesia, Islamic Republic of Iran, Ireland, Italy, Kenya, Luxembourg, Malaysia, Malta, New Zealand, Norway, Philippines, Poland, Romania, Saudi Arabia, Serbia, Singapore, Slovenia, Thailand, Turkey, and Ukraine. == Published standards == There are 365 published standards under the direct responsibility of ISO/IEC JTC 1/SC 6. Published standards by ISO/IEC JTC 1/SC 6 include:

Acquisition of DirecTV by AT&T

AT&T Inc. announced an agreement with the DirecTV Group on May 18, 2014, to acquire the company for $48.5 billion in a joint cash-stock transaction and assumed debts of $18.6 billion for a total offer of $67.1 billion. Due to stalling growth in the wireless sector, AT&T began diversifying into mass media to expand its consumer offerings. After regulatory agencies approved the purchase on July 24, 2015, AT&T briefly became the largest Pay-TV provider. DirecTV was brought under AT&T's communication segment and DirecTV Now was launched on November 30, 2016, as an alternative to cord-cutting. In the years following the purchase, DirecTV lost millions of subscribers across its satellite and streaming services and by 2019, calls grew for AT&T to divest itself off the business. Initially, AT&T rejected these calls and defended the acquisition, but by February 2021, it reached a deal with TPG Inc. to transfer ownership of DirecTV. Under the terms of the agreement, AT&T would retain a 70% majority stake in DirecTV but would no longer oversee its daily operations. The deal was finalized by August 2, 2021, with AT&T receiving $7.1 billion. By July 3, 2025, AT&T sold its majority stake to TPG, ending any ties of involvement. == Background and Development == === AT&T's history === The company to bear the name "AT&T" was founded on March 3, 1885, as American Telephone and Telegraph Company (or AT&T Corporation) by Theodore Newton Vail as a long-distance subsidiary of the Bell Telephone Company. By December 1899, the Bell Telephone's assets were transferred to AT&T, with the latter gaining control of the Bell System, a regional network of local telecom companies. Theodore Vail became AT&T's President in 1907 and under his leadership, AT&T gained a monopoly over the telephone sector in the United States. This near century dominance earned AT&T the nickname of "Ma Bell." In 1974, the U.S. Department of Justice sued AT&T on accounts of antitrust violations. AT&T challenged the lawsuit, but in 1982, it reached a settlement with the DOJ to break apart its Bell System monopoly into seven regional companies. On January 1, 1984, the Bell System came to an end and led to a reshaped telecom industry. One of these regional companies, Southwestern Bell, emerged as the smallest, but after the passage of the 1996 Telecom Act, deregulated telecom rules allowed SBC to become a major telecom company. AT&T briefly became the largest cable and broadband company by the end of the 20th Century, but later deconsolidated to exit those industries. In 2005, SBC acquired its former parent, AT&T, and took on its branding as AT&T Inc, while retaining its previous business history. The newly reincorporated AT&T acquired BellSouth in 2006 and reconstituted much of its former Bell System. === DirecTV's history === == Acquisition Timeline == == Managing DirecTV == == Divestment and Spinoff ==

Bayesian programming

Bayesian programming is a formalism and a methodology for having a technique to specify probabilistic models and solve problems when less than the necessary information is available. Edwin T. Jaynes proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete and uncertain information. In his founding book Probability Theory: The Logic of Science he developed this theory and proposed what he called "the robot," which was not a physical device, but an inference engine to automate probabilistic reasoning—a kind of Prolog for probability instead of logic. Bayesian programming is a formal and concrete implementation of this "robot". Bayesian programming may also be seen as an algebraic formalism to specify graphical models such as, for instance, Bayesian networks, dynamic Bayesian networks, Kalman filters or hidden Markov models. Indeed, Bayesian programming is more general than Bayesian networks and has a power of expression equivalent to probabilistic factor graphs. == Formalism == A Bayesian program is a means of specifying a family of probability distributions. The constituent elements of a Bayesian program are presented below: Program { Description { Specification ( π ) { Variables Decomposition Forms Identification (based on δ ) Question {\displaystyle {\text{Program}}{\begin{cases}{\text{Description}}{\begin{cases}{\text{Specification}}(\pi ){\begin{cases}{\text{Variables}}\\{\text{Decomposition}}\\{\text{Forms}}\\\end{cases}}\\{\text{Identification (based on }}\delta )\end{cases}}\\{\text{Question}}\end{cases}}} A program is constructed from a description and a question. A description is constructed using some specification ( π {\displaystyle \pi } ) as given by the programmer and an identification or learning process for the parameters not completely specified by the specification, using a data set ( δ {\displaystyle \delta } ). A specification is constructed from a set of pertinent variables, a decomposition and a set of forms. Forms are either parametric forms or questions to other Bayesian programs. A question specifies which probability distribution has to be computed. === Description === The purpose of a description is to specify an effective method of computing a joint probability distribution on a set of variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} given a set of experimental data δ {\displaystyle \delta } and some specification π {\displaystyle \pi } . This joint distribution is denoted as: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} . To specify preliminary knowledge π {\displaystyle \pi } , the programmer must undertake the following: Define the set of relevant variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} on which the joint distribution is defined. Decompose the joint distribution (break it into relevant independent or conditional probabilities). Define the forms of each of the distributions (e.g., for each variable, one of the list of probability distributions). ==== Decomposition ==== Given a partition of { X 1 , X 2 , … , X N } {\displaystyle \left\{X_{1},X_{2},\ldots ,X_{N}\right\}} containing K {\displaystyle K} subsets, K {\displaystyle K} variables are defined L 1 , ⋯ , L K {\displaystyle L_{1},\cdots ,L_{K}} , each corresponding to one of these subsets. Each variable L k {\displaystyle L_{k}} is obtained as the conjunction of the variables { X k 1 , X k 2 , ⋯ } {\displaystyle \left\{X_{k_{1}},X_{k_{2}},\cdots \right\}} belonging to the k t h {\displaystyle k^{th}} subset. Recursive application of Bayes' theorem leads to: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∧ ⋯ ∧ L K ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ L 1 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ L K − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\wedge \cdots \wedge L_{K}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid L_{1}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid L_{K-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)\end{aligned}}} Conditional independence hypotheses then allow further simplifications. A conditional independence hypothesis for variable L k {\displaystyle L_{k}} is defined by choosing some variable X n {\displaystyle X_{n}} among the variables appearing in the conjunction L k − 1 ∧ ⋯ ∧ L 2 ∧ L 1 {\displaystyle L_{k-1}\wedge \cdots \wedge L_{2}\wedge L_{1}} , labelling R k {\displaystyle R_{k}} as the conjunction of these chosen variables and setting: P ( L k ∣ L k − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) = P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid L_{k-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)=P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} We then obtain: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ R 2 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ R K ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid R_{2}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid R_{K}\wedge \delta \wedge \pi \right)\end{aligned}}} Such a simplification of the joint distribution as a product of simpler distributions is called a decomposition, derived using the chain rule. This ensures that each variable appears at the most once on the left of a conditioning bar, which is the necessary and sufficient condition to write mathematically valid decompositions. ==== Forms ==== Each distribution P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} appearing in the product is then associated with either a parametric form (i.e., a function f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} ) or a question to another Bayesian program P ( L k ∣ R k ∧ δ ∧ π ) = P ( L ∣ R ∧ δ ^ ∧ π ^ ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)=P\left(L\mid R\wedge {\widehat {\delta }}\wedge {\widehat {\pi }}\right)} . When it is a form f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} , in general, μ {\displaystyle \mu } is a vector of parameters that may depend on R k {\displaystyle R_{k}} or δ {\displaystyle \delta } or both. Learning takes place when some of these parameters are computed using the data set δ {\displaystyle \delta } . An important feature of Bayesian programming is this capacity to use questions to other Bayesian programs as components of the definition of a new Bayesian program. P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} is obtained by some inferences done by another Bayesian program defined by the specifications π ^ {\displaystyle {\widehat {\pi }}} and the data δ ^ {\displaystyle {\widehat {\delta }}} . This is similar to calling a subroutine in classical programming and provides an easy way to build hierarchical models. === Question === Given a description (i.e., P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} ), a question is obtained by partitioning { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} into three sets: the searched variables, the known variables and the free variables. The 3 variables S e a r c h e d {\displaystyle Searched} , K n o w n {\displaystyle Known} and F r e e {\displaystyle Free} are defined as the conjunction of the variables belonging to these sets. A question is defined as the set of distributions: P ( S e a r c h e d ∣ Known ∧ δ ∧ π ) {\displaystyle P\left(Searched\mid {\text{Known}}\wedge \delta \wedge \pi \right)} made of many "instantiated questions" as the cardinal of K n o w n {\displaystyle Known} , each instantiated question being the distribution: P ( Searched ∣ Known ∧ δ ∧ π ) {\displaystyle P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)} === Inference === Given the joint distribution P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} , it is always possible to compute any possible question using the following general inference: P ( Searched ∣ Known ∧ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∣ Known ∧ δ ∧ π ) ] = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] P ( Known ∣ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] ∑ Free ∧ Searched [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] = 1 Z × ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] {\displaystyle {\begin{aligned}&P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)\\={}&\sum _{\text{Free}}\left[P\left({\text{Searched}}\wedge {\text{Free}}\mid {\text{Known}}\wedge \delta \wedge \

Digital Cinema Initiatives

Digital Cinema Initiatives, LLC (DCI) is a consortium of major motion picture studios, formed to establish specifications for a common systems architecture for digital cinema systems. The organization was formed in March 2002 by Metro-Goldwyn-Mayer, Paramount Pictures, Sony Pictures, 20th Century Studios, Universal Studios, Walt Disney Studios and Warner Bros. Entertainment The primary purpose of DCI is to establish and document specifications for an open architecture for digital cinema that ensures a uniform and high level of technical performance, reliability and quality. By establishing a common set of content requirements, distributors, studios, exhibitors, d-cinema manufacturers and vendors can be assured of interoperability and compatibility. Because of the relationship of DCI to many of Hollywood's key studios, conformance to DCI's specifications is considered a requirement by software developers or equipment manufacturers targeting the digital cinema market. == Specification == On July 20, 2005, DCI released Version 1.0 of its "Digital Cinema System Specification", commonly referred to as the "DCI Specification". The document describes overall system requirements and specifications for digital cinema. Between March 28, 2006, and March 21, 2007, DCI issued 148 errata to Version 1.0. DCI released Version 1.1 of the DCI Specification on April 12, 2007, incorporating the previous 148 errata into the DCI Specification. On April 15, 2007, at the annual NAB Digital Cinema Summit, DCI announced the new version, as well as some future plans. They released the "Stereoscopic Digital Cinema Addendum" to begin to establish 3-D technical specifications in response to the popularity of 3-D stereoscopic films. It was also announced "which studios would take over the leadership roles in DCI after the current leadership term expires at the end of September." Subsequently, between August 27, 2007, and February 1, 2008, DCI issued 100 errata to Version 1.1. So, DCI released Version 1.2 of the DCI Specification on March 7, 2008, again incorporating the previous 100 errata into the specification document. An additional 96 errata were issued by August 30, 2012, so a revised Version 1.2 incorporating those additional errata was approved on October 10, 2012. DCI approved DCI Specification Version 1.3 on June 27, 2018, integrating the 45 errata issued to the previous version into a new document. On July 20, 2020, fifteen years to the day after Version 1.0, DCI issued a new DCI Specification Version 1.4 that assimilated 29 errata issued since Version 1.3. On October 13, 2021, DCI approved a new DCI Specification Version 1.4.1 that integrated the 23 errata that had been issued to DCI Specification Version 1.4. For the convenience of users, DCI also created an online HTML version of DCI Specification, Version 1.4.1. Due to the HTML conversion process, the footnotes in the DCSS now appear as endnotes. The PDF version contains pagination and page numbers whereas the HTML version does not. DCI Specification Version 1.4.2, dated June 15, 2022, includes revisions and refinements respecting Object-Based Audio Essence (OBAE), also known as Immersive Audio Bitstream (IAB). Version 1.4.2 also implements post-show log record collection utilizing SMPTE 430-17 SMS-OMB Communications Protocol Specification. Additionally, Version 1.4.2 incorporated two prior addenda: the Digital Cinema Object-Based Audio Addendum, dated October 1, 2018 and the Stereoscopic Digital Cinema Addendum, Version 1.0, dated July 11, 2007. Users using Version 1.4.2 no longer need to refer to the separate addenda. Previous DCSS versions are archived on the DCI web site. Based on many SMPTE and ISO standards, such as JPEG 2000-compressed image and "broadcast wave" PCM/WAV sound, the DCI Specification explains the route to create an entire Digital Cinema Package (DCP) from a raw collection of files known as the Digital Cinema Distribution Master (DCDM), as well as the specifics of its content protection, encryption, and forensic marking. The DCI Specification also establishes standards for the decoder requirements and the presentation environment itself, such as ambient light levels, pixel aspect and shape, image luminance, white point chromaticity, and those tolerances to be kept. Even though it specifies what kind of information is required, the DCI Specification does not include specific information about how data within a distribution package is to be formatted. Formatting of this information is defined by the Society of Motion Picture and Television Engineers (SMPTE) digital cinema standards and related documents. == Image and audio capability overview == === 2D image === 2048×1080 (2K) at 24 frame/s or 48 frame/s, or 4096×2160 (4K) at 24 frame/s In 2K, for Scope (2.39:1) presentation 2048×858 pixels of the imager is used In 2K, for Flat (1.85:1) presentation 1998×1080 pixels of the imager is used In 4K, for Scope (2.39:1) presentation 4096×1716 pixels of the imager is used In 4K, for Flat (1.85:1) presentation 3996×2160 pixels of the imager is used 12 bits per color component (36 bits per pixel) via dual HD-SDI (encrypted) 10 bits only permitted for 2K at 48 frame/s CIE XYZ color space, gamma-corrected TIFF 6.0 container format (one file per frame) JPEG 2000 compression From 0 to 5 or from 1 to 6 wavelet decomposition levels for 2K or 4K resolutions, respectively Compression rate of 4.71 bits/pixel (2K @ 24 frame/s), 2.35 bits/pixel (2K @ 48 frame/s), 1.17 bits/pixel (4K @ 24 frame/s) 250 Mbit/s maximum image bit rate === Stereoscopic 3D image === 2048×1080 (2K) at 48 frame/s - 24 frame/s per eye (4096×2160 4K not supported) In 2K, for Scope (2.39:1) presentation 2048×858 pixels of the imager is used In 2K, for Flat (1.85:1) presentation 1998×1080 pixels of the imager is used Optionally, in the HD-SDI link only: 12 bit color, YCxCz 4:2:2 (i.e. chroma subsampling in XYZ space), each eye in separate stream === Audio === 24 bits per sample, 48 kHz or 96 kHz Up to 16 channels WAV container, uncompressed PCM DCI has additionally published a document outlining recommended practice for High Frame Rate digital cinema. This document discloses the following proposed frame rates: 60, 96, and 120 frames per second for 2D at 2K resolution; 48 and 60 for stereoscopic 3D at 2K resolution; 48 and 60 for 2D at 4K resolution. The maximum compressed bit rate for support of all proposed frame rates should be 500 Mbit/s. == Related information == The idea for DCI was originally mooted in late 1999 by Tom McGrath, then COO of Paramount Pictures, who applied to the U.S. Department of Justice for anti-trust waivers to allow the joint cooperation of all seven major motion picture studios. Universal Pictures made one of the first feature-length DCPs created to DCI specifications, using their film Serenity. Although it was not distributed theatrically, it had one public screening on November 7, 2005, at the USC Entertainment Technology Center's Digital Cinema Laboratory in the Pacific Theatre, Hollywood. Inside Man (2006) was Universal's first DCP commercial release, and, in addition to 35mm film distribution, was delivered via hard drive to 20 theatres in the United States along with two trailers. The Academy Film Archive houses the Digital Cinema Initiatives, LLC Collection, which includes film and digital elements from DCI's Standard Evaluation Material (StEM), a 12-minute production shot on 35mm and 65mm film, created for vendors and standards organizations to test and evaluate image compression and digital projection technologies.