The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization. It allows for the efficient computation of gradients through random variables, enabling the optimization of parametric probability models using stochastic gradient descent, and the variance reduction of estimators. It was developed in the 1980s in operations research, under the name of "pathwise gradients", or "stochastic gradients". Its use in variational inference was proposed in 2013. == Mathematics == Let z {\displaystyle z} be a random variable with distribution q ϕ ( z ) {\displaystyle q_{\phi }(z)} , where ϕ {\displaystyle \phi } is a vector containing the parameters of the distribution. === REINFORCE estimator === Consider an objective function of the form: L ( ϕ ) = E z ∼ q ϕ ( z ) [ f ( z ) ] {\displaystyle L(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[f(z)]} Without the reparameterization trick, estimating the gradient ∇ ϕ L ( ϕ ) {\displaystyle \nabla _{\phi }L(\phi )} can be challenging, because the parameter appears in the random variable itself. In more detail, we have to statistically estimate: ∇ ϕ L ( ϕ ) = ∇ ϕ ∫ d z q ϕ ( z ) f ( z ) {\displaystyle \nabla _{\phi }L(\phi )=\nabla _{\phi }\int dz\;q_{\phi }(z)f(z)} The REINFORCE estimator, widely used in reinforcement learning and especially policy gradient, uses the following equality: ∇ ϕ L ( ϕ ) = ∫ d z q ϕ ( z ) ∇ ϕ ( ln q ϕ ( z ) ) f ( z ) = E z ∼ q ϕ ( z ) [ ∇ ϕ ( ln q ϕ ( z ) ) f ( z ) ] {\displaystyle \nabla _{\phi }L(\phi )=\int dz\;q_{\phi }(z)\nabla _{\phi }(\ln q_{\phi }(z))f(z)=\mathbb {E} _{z\sim q_{\phi }(z)}[\nabla _{\phi }(\ln q_{\phi }(z))f(z)]} This allows the gradient to be estimated: ∇ ϕ L ( ϕ ) ≈ 1 N ∑ i = 1 N ∇ ϕ ( ln q ϕ ( z i ) ) f ( z i ) {\displaystyle \nabla _{\phi }L(\phi )\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }(\ln q_{\phi }(z_{i}))f(z_{i})} The REINFORCE estimator has high variance, and many methods were developed to reduce its variance. === Reparameterization estimator === The reparameterization trick expresses z {\displaystyle z} as: z = g ϕ ( ϵ ) , ϵ ∼ p ( ϵ ) {\displaystyle z=g_{\phi }(\epsilon ),\quad \epsilon \sim p(\epsilon )} Here, g ϕ {\displaystyle g_{\phi }} is a deterministic function parameterized by ϕ {\displaystyle \phi } , and ϵ {\displaystyle \epsilon } is a noise variable drawn from a fixed distribution p ( ϵ ) {\displaystyle p(\epsilon )} . This gives: L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ f ( g ϕ ( ϵ ) ) ] {\displaystyle L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[f(g_{\phi }(\epsilon ))]} Now, the gradient can be estimated as: ∇ ϕ L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ ∇ ϕ f ( g ϕ ( ϵ ) ) ] ≈ 1 N ∑ i = 1 N ∇ ϕ f ( g ϕ ( ϵ i ) ) {\displaystyle \nabla _{\phi }L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[\nabla _{\phi }f(g_{\phi }(\epsilon ))]\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }f(g_{\phi }(\epsilon _{i}))} == Examples == For some common distributions, the reparameterization trick takes specific forms: Normal distribution: For z ∼ N ( μ , σ 2 ) {\displaystyle z\sim {\mathcal {N}}(\mu ,\sigma ^{2})} , we can use: z = μ + σ ϵ , ϵ ∼ N ( 0 , 1 ) {\displaystyle z=\mu +\sigma \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,1)} Exponential distribution: For z ∼ Exp ( λ ) {\displaystyle z\sim {\text{Exp}}(\lambda )} , we can use: z = − 1 λ log ( ϵ ) , ϵ ∼ Uniform ( 0 , 1 ) {\displaystyle z=-{\frac {1}{\lambda }}\log(\epsilon ),\quad \epsilon \sim {\text{Uniform}}(0,1)} Discrete distribution can be reparameterized by the Gumbel distribution (Gumbel-softmax trick or "concrete distribution") and diffusion models. In general, any distribution that is differentiable with respect to its parameters can be reparameterized by inverting the multivariable CDF function, then apply the implicit method. See for an exposition and application to the Gamma, Beta, Dirichlet, and von Mises distributions. == Applications == === Variational autoencoder === In Variational Autoencoders (VAEs), the VAE objective function, known as the Evidence Lower Bound (ELBO), is given by: ELBO ( ϕ , θ ) = E z ∼ q ϕ ( z | x ) [ log p θ ( x | z ) ] − D KL ( q ϕ ( z | x ) | | p ( z ) ) {\displaystyle {\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{z\sim q_{\phi }(z|x)}[\log p_{\theta }(x|z)]-D_{\text{KL}}(q_{\phi }(z|x)||p(z))} where q ϕ ( z | x ) {\displaystyle q_{\phi }(z|x)} is the encoder (recognition model), p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} is the decoder (generative model), and p ( z ) {\displaystyle p(z)} is the prior distribution over latent variables. The gradient of ELBO with respect to θ {\displaystyle \theta } is simply E z ∼ q ϕ ( z | x ) [ ∇ θ log p θ ( x | z ) ] ≈ 1 L ∑ l = 1 L ∇ θ log p θ ( x | z l ) {\displaystyle \mathbb {E} _{z\sim q_{\phi }(z|x)}[\nabla _{\theta }\log p_{\theta }(x|z)]\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\theta }\log p_{\theta }(x|z_{l})} but the gradient with respect to ϕ {\displaystyle \phi } requires the trick. Express the sampling operation z ∼ q ϕ ( z | x ) {\displaystyle z\sim q_{\phi }(z|x)} as: z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ , ϵ ∼ N ( 0 , I ) {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,I)} where μ ϕ ( x ) {\displaystyle \mu _{\phi }(x)} and σ ϕ ( x ) {\displaystyle \sigma _{\phi }(x)} are the outputs of the encoder network, and ⊙ {\displaystyle \odot } denotes element-wise multiplication. Then we have ∇ ϕ ELBO ( ϕ , θ ) = E ϵ ∼ N ( 0 , I ) [ ∇ ϕ log p θ ( x | z ) + ∇ ϕ log q ϕ ( z | x ) − ∇ ϕ log p ( z ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{\epsilon \sim {\mathcal {N}}(0,I)}[\nabla _{\phi }\log p_{\theta }(x|z)+\nabla _{\phi }\log q_{\phi }(z|x)-\nabla _{\phi }\log p(z)]} where z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon } . This allows us to estimate the gradient using Monte Carlo sampling: ∇ ϕ ELBO ( ϕ , θ ) ≈ 1 L ∑ l = 1 L [ ∇ ϕ log p θ ( x | z l ) + ∇ ϕ log q ϕ ( z l | x ) − ∇ ϕ log p ( z l ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )\approx {\frac {1}{L}}\sum _{l=1}^{L}[\nabla _{\phi }\log p_{\theta }(x|z_{l})+\nabla _{\phi }\log q_{\phi }(z_{l}|x)-\nabla _{\phi }\log p(z_{l})]} where z l = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ l {\displaystyle z_{l}=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon _{l}} and ϵ l ∼ N ( 0 , I ) {\displaystyle \epsilon _{l}\sim {\mathcal {N}}(0,I)} for l = 1 , … , L {\displaystyle l=1,\ldots ,L} . This formulation enables backpropagation through the sampling process, allowing for end-to-end training of the VAE model using stochastic gradient descent or its variants. === Variational inference === More generally, the trick allows using stochastic gradient descent for variational inference. Let the variational objective (ELBO) be of the form: ELBO ( ϕ ) = E z ∼ q ϕ ( z ) [ log p ( x , z ) − log q ϕ ( z ) ] {\displaystyle {\text{ELBO}}(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[\log p(x,z)-\log q_{\phi }(z)]} Using the reparameterization trick, we can estimate the gradient of this objective with respect to ϕ {\displaystyle \phi } : ∇ ϕ ELBO ( ϕ ) ≈ 1 L ∑ l = 1 L ∇ ϕ [ log p ( x , g ϕ ( ϵ l ) ) − log q ϕ ( g ϕ ( ϵ l ) ) ] , ϵ l ∼ p ( ϵ ) {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi )\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\phi }[\log p(x,g_{\phi }(\epsilon _{l}))-\log q_{\phi }(g_{\phi }(\epsilon _{l}))],\quad \epsilon _{l}\sim p(\epsilon )} === Dropout === The reparameterization trick has been applied to reduce the variance in dropout, a regularization technique in neural networks. The original dropout can be reparameterized with Bernoulli distributions: y = ( W ⊙ ϵ ) x , ϵ i j ∼ Bernoulli ( α i j ) {\displaystyle y=(W\odot \epsilon )x,\quad \epsilon _{ij}\sim {\text{Bernoulli}}(\alpha _{ij})} where W {\displaystyle W} is the weight matrix, x {\displaystyle x} is the input, and α i j {\displaystyle \alpha _{ij}} are the (fixed) dropout rates. More generally, other distributions can be used than the Bernoulli distribution, such as the gaussian noise: y i = μ i + σ i ⊙ ϵ i , ϵ i ∼ N ( 0 , I ) {\displaystyle y_{i}=\mu _{i}+\sigma _{i}\odot \epsilon _{i},\quad \epsilon _{i}\sim {\mathcal {N}}(0,I)} where μ i = m i ⊤ x {\displaystyle \mu _{i}=\mathbf {m} _{i}^{\top }x} and σ i 2 = v i ⊤ x 2 {\displaystyle \sigma _{i}^{2}=\mathbf {v} _{i}^{\top }x^{2}} , with m i {\displaystyle \mathbf {m} _{i}} and v i {\displaystyle \mathbf {v} _{i}} being the mean and variance of the i {\displaystyle i} -th output neuron. The reparameterization trick can be applied to all such cases, resulting in the variational dropout method.
Macromedia FreeHand
Macromedia FreeHand (formerly Aldus FreeHand) is a discontinued computer application for creating two-dimensional vector graphics oriented primarily to professional illustration, desktop publishing and content creation for the Web. FreeHand was similar in scope, intended market, and functionality to Adobe Illustrator, CorelDRAW and Xara Designer Pro. Because of FreeHand's dedicated page layout and text control features, it also compares to Adobe InDesign and QuarkXPress. Professions using FreeHand include graphic design, illustration, cartography, fashion and textile design, product design, architects, scientific research, and multimedia production. FreeHand was created by Altsys Corporation in 1988 and licensed to Aldus Corporation, which released versions 1 through 4. In 1994, Aldus merged with Adobe Systems and because of the overlapping market with Adobe Illustrator, FreeHand was returned to Altsys by order of the Federal Trade Commission. Altsys was later bought by Macromedia, which released FreeHand versions 5 through 11 (FreeHand MX). In 2005, Adobe Systems acquired Macromedia and its product line which included FreeHand MX, under whose ownership it presently resides. Since 2003, FreeHand development has been discontinued; in the Adobe Systems catalog, FreeHand has been replaced by Adobe Illustrator. FreeHand MX continues to run under Windows 11 and under Mac OS X 10.6 (Snow Leopard) within Rosetta, a PowerPC code emulator, and requires a registration patch supplied by Adobe. FreeHand 10 runs without problems on Mac OS X Snow Leopard with Rosetta enabled, and does not require a registration patch. Later versions of macOS can use a Mac OS X Snow Leopard Server virtual machine to emulate the required PowerPC support. == History == === Altsys and Aldus FreeHand === In 1984, James R. Von Ehr founded Altsys Corporation to develop graphics applications for personal computers. Based in Plano, Texas, the company initially produced font editing and conversion software; Fontastic Plus, Metamorphosis, and the Art Importer. Their premier PostScript font-design package, Fontographer, was released in 1986 and was the first such program on the market. With the PostScript background having been established by Fontographer, Altsys also developed FreeHand (originally called Masterpiece) as a Macintosh Postscript-based illustration program that used Bézier curves for drawing and was similar to Adobe Illustrator. FreeHand was announced as "... a Macintosh graphics program described as having all the features of Adobe's Illustrator plus drawing tools such as those in Mac Paint and Mac Draft and special effects similar to those in Cricket Draw." Seattle's Aldus Corporation acquired a licensing agreement with Altsys Corporation to release FreeHand along with their flagship product, Pagemaker, and Aldus FreeHand 1.0 was released in 1988. FreeHand's product name used intercaps; the F and H were capitalized. The partnership between the two companies continued with Altsys developing FreeHand and with Aldus controlling marketing and sales. After 1988, a competitive exchange between Aldus FreeHand and Adobe Illustrator ensued on the Macintosh platform with each software advancing new tools, achieving better speed, and matching significant features. Windows PC development also allowed Illustrator 2 (aka, Illustrator 88 on the Mac) and FreeHand 3 to release Windows versions to the graphics market. FreeHand 1.0 sold for $495 in 1988. It included the standard drawing tools and features as other draw programs including special effects in fills and screens, text manipulation tools, and full support for CMYK color printing. It was also possible to create and insert PostScript routines anywhere within the program. FreeHand performed in preview mode instead of keyline mode but performance was slower. FreeHand 2.0 sold for $495 in 1989. Besides improving on the features of FreeHand 1.0, FreeHand 2 added faster operation, Pantone colors, stroked text, flexible fill patterns and automatically import graphic assets from other programs. It added accurate control over a color monitor screen display, limited only by its resolution. FreeHand 3.0 sold for $595 in 1991. New features included resizable color, style, and layer panels including an Attributes menu. Also tighter precision of both the existing tools and aligning of objects. FH3 created compound Paths. Text could be converted to paths, applied to an ellipse, or made vertical. Carried over from version 1.0, FreeHand 3 suffered by having text entered into a dialog box instead of directly to the page. In October 1991, a 3.1 upgrade made FreeHand work with System 7 but additionally, it supported pressure-sensitive drawing which offered varying line widths with a users stroke. It improved element manipulation and added more import/export options. FreeHand 4.0 sold for $595 in 1994. Altsys ported FreeHand 3.0 to the NeXT system creating a new program named Virtuoso. Virtuoso continued its development at Altsys and version 2.0 of Virtuoso was feature-equivalent to FreeHand 4 (with the addition of NeXT-specific features such as Services and Display PostScript) and file compatible, with Virtuoso 2 able to open FreeHand 4 files and vice versa. A prominent feature of this version was the ability to type directly into the page and wrap inside or outside any shape. It also included drag-and-drop color imaging, a larger pasteboard, and a user interface that featured floating, rollup panels. The colors palette included a color mixer for adding new colors to the swatch list. Speed increases were made. In the same year of FreeHand 4 release, Adobe Systems announced merger plans with Aldus Corporation for $525 million. Fear about the end of competition between these two leading applications was reported in the media and expressed by customers (Illustrator versus FreeHand and Adobe Photoshop versus Aldus PhotoStyler.) Because of this overlapping of the market, Altsys stepped in by suing Aldus, saying that the merger deal was "a prima facie violation of a non-compete clause within the FreeHand licensing agreement." Altsys CEO Jim Von Ehr explained, "No one loves FreeHand more than we do. We will do whatever it takes to see it survive." The Federal Trade Commission issued a complaint against Adobe Systems on October 18, 1994, ordering a divestiture of FreeHand to "remedy the lessening of competition resulting from the acquisition as alleged in the Commission's complaint," and further, the FTC ordering, "That for a period of ten (10) years from the date on which this order becomes final, respondents shall not, without the prior approval of the Commission, directly or indirectly, through subsidiaries, partnerships, or otherwise .. Acquire any Professional Illustration Software or acquire or enter into any exclusive license to Professional Illustration Software;" (referring to FreeHand.) FreeHand was returned to Altsys with all licensing and marketing rights as well as Aldus FreeHand's customer list. === Macromedia Freehand === By late 1994, Altsys still retained all rights to FreeHand. Despite brief plans to keep it in-house to sell it along with Fontographer and Virtuoso, Altsys reached an agreement with the multimedia software company, Macromedia, to be acquired. This mutual agreement provided FreeHand and Fontographer a new home with ample resources for marketing, sales, and competition against the newly merged Adobe-Aldus company. Altsys would remain in Richardson, Texas, but would be renamed as the Digital Arts Group of Macromedia and was responsible for the continued development of FreeHand. Macromedia received FreeHand's 200,000 customers and expanded its traditional product line of multimedia graphics software to illustration and design graphics software. CEO James Von Ehr became a Macromedia vice-president until 1997 when he left to start another venture. FreeHand 5.0 sold for $595 in 1995. This version featured a more customizable and expanded workspace, multiple views, stronger design and editing tools, a report generator, spell check, paragraph styles, multicolor gradient fills up to 64 colors, speed improvements, and it accepted Illustrator plugins. In September 1995, a 5.5 upgrade added Photoshop plug-in support, PDF import capabilities, the Extract feature, inline graphics to text, improved auto-expanding text containers, the Crop feature, and the Create PICT Image feature. A FreeHand 5.5 upgrade was part of the FreeHand Graphics Studio (a suite that included Fontographer, Macromedia xRes image editing application, and Extreme 3D animation and modeling application). FreeHand 6.0 in 1996. This version only existed in beta. Some Freehand 7 prerelease versions were released under the Freehand 6 tag. FreeHand 7.0 sold for $399 in 1996, or $449 as part of the FreeHand Graphics Studio (see above.) Features included a redesigned user interface that allowed recombining Inspectors, Panel Tabs, Dockable Panels, Smart Cursors,
Army Chief Information Officer/G-6
In September 2020, the Army realigned the previously consolidated CIO/G-6 function into two separate roles, Office of the Chief Information Officer and Deputy Chief of Staff, G-6, that report to the secretary of the Army and chief of staff of the Army, respectively. The realignment came after several months of planning and coordination. Lt. Gen. John Morrison was nominated to the Senate for promotion and assignment as the G-6 and confirmed, assuming that position in August 2020. Subsequently, the Secretary of the Army, Ryan McCarthy appointed Dr. Raj G. Iyer as the first civilian Chief Information Officer, a career Senior Executive Service position in November 2020. == G-6 == Advise chief of staff of the Army and the Chief Information Officer on planning, fielding, and execution of C4IT worldwide Army operations Develop and execute the plan for the Unified Network Implement Army information assurance Supervise C4IT, Signal support, Information security, Force structure and equipping activities in support of warfighting operations Oversee management of the Signal forces == Planned realignment == On June 11, 2020, the Army announced that the two roles of CIO and Deputy Chief of Staff, G-6 (DCS, G-6) would be realigned no later than August 31, 2020, with separate individuals responsible for each position. With the realignment: CIO core functions will be policy, governance, and oversight. Focus areas include: Information Environment, Cybersecurity, Enterprise Architecture, and Data Policy/Oversight/Governance, Enterprise Architecture, Enterprise Cloud Management and IT Spend/Category Management. DCS, G-6 core functions will be planning, strategy, and implementation. Focus areas include: Information Environment/Network, Planning and Integration, Theater Synchronization, Architecture Integration, Enterprise Information Environment (EIE) Mission Area Portfolio Management and Mission Decision Packet Management. In order to support multi-domain operations, the Army will have to connect Enterprise networks and tactical networks. —LTG Morrison, DCS, G-6 DCS G-6 released the Army Unified Network Plan under the Army Digital Transformation Strategy, to help the Army to establish a Multi-Domain Operations capable force by 2028. The Unified Network will enable Army formations, as part of the Joint Force, to operate in highly contested and congested operational environments with the speed and global range to achieve decision dominance and maintain overmatch. The plan shapes, synchronizes, integrates and governs Unified Network efforts and aligns the personnel, organizational structure and capabilities required to enable MDO at all echelons. == Chief signal officers and their successors == Chief signal officers (1860–1964) Maj. Albert J. Myer 1860–1863 Lt. Col. William J. L. Nicodemus 1863–1864 Col. Benjamin F. Fisher 1864–1866 Col. Albert J. Myer 1866–1880 (promoted to brigadier general 16 June 1880) Brig. Gen. William B. Hazen 1880–1887 Brig. Gen. Adolphus W. Greely 1887–1906 Brig. Gen. James Allen 1906–1913 Brig. Gen. George P. Scriven 1913–1917 Brig. Gen. George O. Squier 1917–1923 (promoted to major general 6 October 1917) Maj. Gen. Charles McK. Saltzman 1924–1928 Maj. Gen. George Sabin Gibbs 1928–1931 Maj. Gen. Irving J. Carr 1931–1934 Maj. Gen. James B. Allison 1935–1937 Maj. Gen. Joseph O. Mauborgne 1937–1941 Maj. Gen. Dawson Olmstead 1941–1943 Maj. Gen. Harry C. Ingles 1943–1947 Maj. Gen. Spencer B. Akin 1947–1951 Maj. Gen. George I. Back 1951–1955 Lt. Gen. James D. O’Connell 1955–1959 Maj. Gen. Ralph T. Nelson 1959–1962 Maj. Gen. Earle F. Cook 1962–1963 Maj. Gen. David Parker Gibbs 1963–1964 Chiefs of communications-electronics (1964–1967) Maj. Gen. David Parker Gibbs 1964–1966 Maj. Gen. Walter E. Lotz, Jr. 1966–1967 Assistant chiefs of staff for communications-electronics (1967–1974) Maj. Gen. Walter E. Lotz, Jr. 1967–1968 Maj. Gen. George E. Pickett 1968–1972 Lt. Gen. Thomas Rienzi 1972–1974 Directors of telecommunications and command and control (1974–1978) (a directorate of ODCSOPS) Lt. Gen. Thomas Rienzi 1974–1977 Lt. Gen. Charles R. Myer 1977–1978 Assistant chiefs of staff for automation and communications (1978–1981) Lt. Gen. Charles R. Myer 1978–1979 Maj. Gen. Clay T. Buckingham 1979–1981 Assistant deputy chiefs of staff for operations and plans (command, control, communications, and computers) (1981–1984) Maj. Gen. Clay T. Buckingham 1981–1982 Maj. Gen. James M. Rockwell 1982–1984 Assistant chiefs of staff for information management (1984–1987) Lt. Gen. David K. Doyle 1984–1986 Lt. Gen. Thurman D. Rodgers 1986–1987 Directors of information systems for command, control, communications, and computers Lt. Gen. Thurman D. Rodgers 1987–1988 Lt. Gen. Bruce R. Harris 1988–1990 Lt. Gen. Jerome B. Hilmes 1990–1992 Lt. Gen. Peter A. Kind 1992–1994 Lt. Gen. Otto J. Guenther 1995–1997 Lt. Gen. William H. Campbell Chief Information Officer, Military Deputy to the Army Acquisition Executive, and Director of Information Systems for Command, Control, Communications and Computers Lt. Gen. William H. Campbell 1997–2000
Color reproduction
Color reproduction is an aspect of color science concerned with producing light spectra that evoke a desired color, either through additive (light emitting) or subtractive (surface color) models. It converts physical correlates of color perception (CIE 1931 XYZ color space tristimulus values and related quantities) into light spectra that can be experienced by observers. In this way, it is the opposite of colorimetry. It is concerned with the faithful reproduction of a color in one medium, with a color in another, so it is a central concept in color management and relies heavily on color calibration. For example, food packaging must be able to faithfully reproduce the colors of the foods therein in order to appeal to a customer. This involves proper color calibration of at least four devices: Lighting, which must have a high color rendering index and not give a color cast to the object. Camera, which measures the reflected spectrum of the object and converts to a trichromatic color space (e.g. RGB). Screen, which reproduces color so a designer can proof the captured image and make color corrections as necessary. Printer, which reproduces the final color on paper.
ShowDocument
ShowDocument is an online web application that allows multiple users to conduct web meetings, upload, share and review documents from remote locations. The service was developed by the HBR Labs company, established in 2007. == Features == Users can collaborate on and review documents in real time, with annotations and text being visible to all users and accessible for co-editing. The idea of every user being able to annotate can cause conflicts within the sessions, and so main navigation options are under the "presenter"'s control - which can be given to a different user as well. An earlier version of the application, by contrast, had allowed all users to navigate and edit at once, causing the system to drop all incomplete edits. It is possible to draw and write on a virtual whiteboard, and to stream a YouTube video to a group in full synchronization. A feature also exists for co-browsing of Google Maps. Entering an open session in the application can be done with a given code number, or by receiving a link through an Email message. Different file formats can be uploaded and saved either online or offline, such as PDF. A PDF file's text cannot be edited - text is edited through the separate text editor. Although the platform contains a text chat, it is not intended to replace instant messaging software, as there are no extensive messaging features. The application has a paid and free version, with the free version having a few limitations: audio and video options are disabled, number of participants is limited and sessions are time-limited. == Development == ShowDocument was first developed in 2007. On September 8, 2009, HBR labs released a new update which included features such as secure online document storage and mobile device support.
Ericom Connect
Ericom Connect is a remote access/application publishing solution produced by Ericom Software that provides secure, centrally managed access to physical or hosted desktops and applications running on Microsoft Windows and Linux systems. == Product overview == Ericom Connect is desktop virtualization and application virtualization software that allows users to run applications remotely, without installing them on the local computer or device. The software is noted for its scalability, ease of deployment, and compatibility with any type of infrastructure, cloud or physical. Ericom Connect uses AccessPad (native client for desktops), AccessToGo (native client for mobile), or AccessNow, one of the first HTML5 RDP solutions to support clientless access to Windows desktops and applications from any device with an HTML5-compatible browser, including Macintosh computers, mobile devices, and Google Chromebooks. Other notable features include performance monitoring, built-in real-time analytics & BI, support for two-factor authentication (using RSA SecurID), multi-tenancy and multi-datacenter support via a single unified web interface, and a “Launch Simulation” feature that allows users to visualize and simulate actual step-by-step user processes directly from within the administration console. In addition to scalability, by distributing configurations, logs, etc., across multiple servers there is no single point of failure, as can be the case if all configuration information is stored on one server. == History == Ericom Connect was introduced in 2015. Ericom Connect is a successor to Ericom PowerTerm Web Connect. PowerTerm Web Connect used an architecture similar to what was then current with Citrix and VMWare, relying on a centralized SQL server, a connection broker, image management for different hypervisors, and a variety of clients. Ericom Connect uses a new grid architecture that provides more scalability, reliability, and flexibility than before.
Deblurring
Deblurring is the process of removing blurring artifacts from images. Deblurring recovers a sharp image S from a blurred image B, where S is convolved with K (the blur kernel) to generate B. Mathematically, this can be represented as B = S ∗ K {\displaystyle B=SK} (where represents convolution). While this process is sometimes known as unblurring, deblurring is the correct technical word. The blur K is typically modeled as point spread function and is convolved with a hypothetical sharp image S to get B, where both the S (which is to be recovered) and the point spread function K are unknown. This is an example of an inverse problem. In almost all cases, there is insufficient information in the blurred image to uniquely determine a plausible original image, making it an ill-posed problem. In addition the blurred image contains additional noise which complicates the task of determining the original image. This is generally solved by the use of a regularization term to attempt to eliminate implausible solutions. This problem is analogous to echo removal in the signal processing domain. Nevertheless, when coherent beam is used for imaging, the point spread function can be modeled mathematically. By proper deconvolution of the point spread function K and the blurred image B, the blurred image B can be deblurred (unblur) and the sharp image S can be recovered.