AI Grammar Tester

AI Grammar Tester — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

NER model

NER is one of several formulas for accessing live subtitles in television broadcasts and events that are produced using speech recognition. The three letters stand for number, edit error and recognition error. It has been promoted as an alternative to Word error rate (Word Error Rate) which is a more objective measure. The overall score is calculated as follows: Firstly, the number of edit and recognition errors is deducted from the total number of words in the live subtitles. This number is then divided by the total number of words in the live subtitles and finally multiplied by one hundred. N E R v a l u e = N − E − R N ∗ 100 {\displaystyle NERvalue={\frac {N-E-R}{N}}100} . The acronyms stand for the following: N (number) = total number of words in the live subtitles E (Edit error) = edit error R (Recognition error) = recognition error This measurement process has been used for public television broadcasts in European countries like Italy and Switzerland. One major drawback with NER is that it requires a human assessor to rate errors as either: 1 Minor edition or recognition errors 2 Normal edition or recognition errors 3 Serious errors which are then weighted in the assessment process. This is both subjective, time consuming and costly. Also, NER fails to account for words left out subtitles which is something that does not take account of the D/deaf audience who want verbatim subtitles. As a result, NER cannot accurately reflect the audience's experience of subtitles. Another problem is the inconsistency of human evaluation of subtitles, particularly with live subtitles, where there are differing opinions of the importance of subtitle errors. By way of contrast, Word error rate is an objective measure of subtitle errors, since it measures the textual discrepancy between the subtitles and the speech.
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EditDV

EditDV was a video editing software released by Radius, Inc. in late 1997 as an evolution of their earlier Radius Edit product. EditDV was one of the first products providing professional-quality editing of the then new DV format at a relatively affordable cost ($999 including Radius FireWire capture card) and was named "The Best Video Tool of 1998". Originally EditDV was available for Macintosh only but in February 2000 EditDV 2.0 for Windows was released. With version 3.0 EditDV's name was changed to CineStream. == Features == Originally bundled with a FireWire card, EditDV 1.5 got updated into a less expensive software only package for use with the newer PowerMac G3 that came with a FireWire interface. Later, a scaled down version named EditDV 1.6.1 Unplugged was released as a freeware version next to EditDV 2.0. Unlike many other applications at the time which transcoded video to M-JPEG for editing, EditDV provided lossless native editing of the DV format. Only transitions (such as dissolves or wipes), effects (such as rotating or scaling the video, adjusting the audio level, or adding titles) and filters (such as changing the brightness or color balance) needed to be rendered. This also had the disadvantage to not work with analogue video capture. EditDV was built on top of QuickTime and supported QuickTime filters as well as its own built-in effects and transitions. Effects could be animated using keyframes. EditDV 2.0 worked natively with Quicktime MOV format. For Microsoft Windows users, where the standard was AVI, this required the use of a provided external conversion tool afterwards when AVI was wanted. The user interface had a Project window for organising clips into bins, a Sequence window with a multi-track timeline for arranging clips into a program using three-point editing, and Source and Program monitor windows. A finished program could either be exported as a QuickTime movie or written back to DV tape using the "print to video" command. Version 3.0, then renamed CineStream, shifted towards web designers who wanted to add video streaming interactivity to a website. The new feature called EventStream allowed setting clickable hot spots to link to another location, either to another page with a URL or to another video. This feature distinguished CineStream from the rest of the competition. == Products == The EditDV product family included a number of related products, all sharing a similar name: EditDV Video editing software (Mac and Windows) SoftDV A QuickTime software codec for playing DV media, included as part of EditDV (Mac and Windows) MotoDV PCI-based FireWire interface with DV capture software (Mac and Windows) PhotoDV Software to capture high-quality stills from a DV tape using MotoDV hardware (Mac and Windows) RotoDV Software for rotoscoping (painting over video), released in Sept 1999 (Macintosh only) == Name changes and eventual demise == In 1999, the company Radius Inc. changed its name to Digital Origin. In 2000, Digital Origin Inc (and EditDV) was bought by Media 100. In early 2001, Media 100 released an updated version of EditDV under the new name CineStream 3.0. Later that year (October 2001) Media 100 was bought by Autodesk's Discreet Division. CineStream for Macintosh required classic Mac OS. It was never ported to Mac OS X and faced increasing competition on that platform from Apple's own Final Cut Pro application. Development of EditDV/Cinestream was officially discontinued in 2002.
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VGACAD

VGACAD was the parent of a suite of shareware graphic utilities made for the MS-DOS operating system used in the IBM PC and clones. It was popular for editing and capturing images using BSAVE (graphics image format) and provided an early graphic editing suite compatible with multiple graphic cards and resolutions, used on the IBM PC. == Usage == Written by Lawrence Gozum in 1987, it was the genesis of multiple versions and improvements over 10 years. Ran with his brother, Marvin initially helped with design ideas, strategic focus, technical support calls, and managing the early shareware business. The growth of the VGACAD suite grew quickly to preoccupy most of their time. Lawrence then focused more of his efforts on software and formed Applied Insights, to manage VGACAD and its offspring, VidFun, and Ai Picture Explorer. At its peak, its users ranged from individuals, Federal government offices, museums and major newspapers. == Features == VGACAD was a misnomer, and meant VGA-Computer Assisted Drawing, rather than computer-aided design, as CAD is commonly referred to today. Its longevity was due to its color accuracy, speed, small size, and that its suite of small utilities often worked stand-alone. One called VGACAP, for 'capture', dumped video memory into a file that could later be converted to popular graphic image formats, later made commonplace when Microsoft Windows programmed the print screen key to dump graphics into the clipboard. However, VGACAP ran insulated apart from early versions of Windows, and thus could capture screens were applications prohibited such function.
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Screenpal

ScreenPal (formerly known as Screencast-O-Matic) is cross-platform screen capture and screen recording software originally developed in 2006. == History == The company was founded by AJ Gregory in 2006 as Screencast-O-Matic. The software includes features for screen recording, screenshot capture, video editing, image editing, and a video and image hosting service. It is available for Windows and Mac operating systems, and has mobile apps for iOS and Android. The company launched a video editor in 2015. It began offering free video and image hosting in 2019, with premium hosting options for subscribers. In 2023, it was rebranded as ScreenPal.
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Certified social engineering prevention specialist

Certified Social Engineering Prevention Specialist (CSEPS) is a social engineering security-awareness training and professional certification program originally developed by Kevin Mitnick and Alexis Kasperavičius. == Course structure == The original CSEPS program was structured as a multi-module corporate security-awareness course designed to teach employees, managers, and IT personnel how social engineers manipulate human behavior to bypass technical security systems. The curriculum combined case studies, psychological analysis, attack demonstrations, pretexting exercises, and operational security scenarios. The course materials described social engineering as the exploitation of "the human factor" in information security and argued that traditional technical defenses alone were insufficient to protect organizations from deception-based attacks. The training program was divided into instructional modules covering topics such as: social engineering methodology and threat analysis intelligence gathering and reconnaissance dumpster diving pretexting elicitation technique telephone-system exploitation and caller-ID spoofing psychological influence techniques industrial espionage identity theft organizational vulnerabilities security policy development and employee awareness training The course also analyzed historical and contemporary case studies involving information theft, corporate espionage, fraudulent wire transfers, and telephone-based impersonation attacks. Training exercises required participants to analyze how attackers established credibility, manipulated trust, overcame objections, and exploited organizational procedures. According to The Wall Street Journal, CSEPS was delivered as a two-day "boot camp" course costing approximately US$1,500 per attendee. Clients reportedly included the United States Air Force and the United States Marine Corps. The certification examination included multiple-choice and written-response sections dealing with social-engineering defense scenarios and mitigation strategies. == History == In 2003, Mitnick and Kasperavičius partnered with the Florida-based IT training company Intense School Inc. to offer CSEPS classes throughout the United States. In 2020, Mitnick partnered with security-awareness training company KnowBe4, and elements of the original CSEPS material became incorporated into KnowBe4's social-engineering awareness training offerings.
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Screenpal

ScreenPal (formerly known as Screencast-O-Matic) is cross-platform screen capture and screen recording software originally developed in 2006. == History == The company was founded by AJ Gregory in 2006 as Screencast-O-Matic. The software includes features for screen recording, screenshot capture, video editing, image editing, and a video and image hosting service. It is available for Windows and Mac operating systems, and has mobile apps for iOS and Android. The company launched a video editor in 2015. It began offering free video and image hosting in 2019, with premium hosting options for subscribers. In 2023, it was rebranded as ScreenPal.
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Edits (app)

Edits is an American photo and short form video editing software service owned by Meta Platforms. It allows users to create videos and edit them by using features like green screens, and AI animation, and also provides real-time statistics to Instagram creators to track their accounts. Accounts directly from Instagram can be imported, and videos can be exported vice-versa. It is available solely on iOS and Android. On Apple, it supports over 32 different languages, including French, Spanish, and Chinese. It has been noted by critics as a direct competitor for apps like CapCut, owned by Chinese brand ByteDance. The Instagram head, Adam Mosseri, also acknowledged these similarities. Launched on April 22 for both iOS and Android. It received over 5M+ users on Apple and Android combined in its first 4 days since its launch. == History == On January 19, 2025, following the ban of all ByteDance Apps from the Google Play Store, and App Store, Instagram head Adam Mosseri announced on Threads that they would be launching the app in February for iOS, followed by an Android counterpart. He said the app is working with select people to test its features. In a separate post, he emphasized that the app is "more for creators than casual video makers". == Features == Edits contains many similar features to other competition of video editors like KineMaster, Inshot, and CapCut. When creating a video, users have the option to export in resolution of HD, 4K, and 2K, along with having HDR and SDR support. Like many traditional video editing software, it includes a timeline, and basic undo-redo buttons. On the bottom bar, 7 tabs for editing exist, namely the Split, Volume, Adjust, Speed, Delete, Filters, Green Screen, Voice FX, Extract Audio, Mirror, Slip, Replace and Duplicate bars. Basic features, like splitting, and adjusting speed and volume of clips are present, along with more advanced Green Screens, and AI features. Being a mobile video editor app, Edits also has drag-and-drop features to ease customer usage. Users have the ability to record videos directly within the app. This feature allows users to create content without needing extra software or devices. They can choose from several focal lengths, which affect how close or wide the shot appears. The app also supports different frame rates. Users have the ability to record videos directly within the app. This feature allows users to create content without needing extra software or devices. Once users are done filming your clips, they can simply transfer them into a project to start editing immediately. Upcoming features for the app include Keyframes, AI-powered modification, Collaboration, and Enhanced creativity. == Reception == Since its release, it received over 5 million downloads in 4 days. Critically, the app received great rankings from many. From users, the app received an average of 4.45 stars over Google Play Store and App Store in the first few days, with Google Play Store receiving the least stars. As in reviews, it was received mixed by the public. Many people praised the smoothness and intuivity of the app. "The app is more than just a basic editor, offering a full suite of creative tools, including a dedicated tab for inspiration and trending audio, as well as a tab for managing drafts," said a blogger. Some users were disappointed with the range of editing tools, some users have noted that it could benefit from more transition options between clips. Some even reported crashing between clips.
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JasPer

JasPer is a computer software project to create a reference implementation of the codec specified in the JPEG-2000 Part-1 standard (i.e. ISO/IEC 15444-1) - started in 1997 at Image Power Inc. and at the University of British Columbia. It consists of a C library and some sample applications useful for testing the codec. The copyright owner began licensing the code to the public under an MIT License-style license in 2004 in response to requests from the open-source community. As of 2011 JasPer operated as a component of many software projects, both free and proprietary, including (but not limited to) netpbm (as of release 10.12), ImageMagick and KDE (as of version 3.2). As of 22 June 2010 the GEGL graphics library supported JasPer in its latest Git versions. In a series of objective JPEG-2000-compression quality tests conducted in 2004, "JasPer was the best codec, closely followed by IrfanView and Kakadu". However, Jasper remains one of the slowest implementations of the JPEG-2000 codec, as it was designed for reference, not performance. == Etymology == The name "JasPer" has simultaneous connotations with Canada's Jasper National Park, with the semi-precious gemstone, jasper, and with "JP" as an abbreviation of the JPEG-2000 standard.
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Israeli cybersecurity industry

The Israeli cybersecurity industry is a rapidly growing sector within Israel's technology and innovation ecosystem. Israel is internationally recognized as a powerhouse in the cybersecurity domain, with numerous cybersecurity startups, established companies, research institutions, and government initiatives. Tel Aviv itself is being ranked 7th in annual list of best global tech ecosystems, as reported by the Jerusalem Post. == History == The roots of Israel's cybersecurity industry can be traced back to the country's strong focus on national security and intelligence. The establishment of elite military units such as Unit 8200, the Israeli Intelligence Corps unit responsible for signals intelligence and code decryption, played a significant role in the development of cybersecurity expertise in the country. Many former members of Unit 8200 have gone on to establish successful cybersecurity companies or join existing organizations, bringing their unique skill sets and experience to the private sector. == Market overview == As of 2024, Israel housed more than 450 cybersecurity startups and companies. In 2023, the value of exits by Israeli tech companies reached $7.5 billion. Israel's cybersecurity industry is characterized by a high concentration of startups develop new technologies in areas such as network security, endpoint protection, data security, cloud security, and threat intelligence. In recent years, the sector has attracted significant investment from both local and international venture capital firms, as well as major technology companies such as Microsoft, Google, and IBM. Several Israeli cybersecurity companies have gained global recognition and success, with some being acquired by major corporations or conducting successful initial public offerings (IPOs). === Key Israeli cybersecurity companies === Some key Israeli cybersecurity companies include: Check Point Software Technologies CyberArk Cato Networks Radware Wiz === Financial activity === Israel’s cybersecurity sector has seen significant financial activity. As of 2023, mergers and acquisitions in the cybersecurity sector totaled $2.8 billion. In the first quarter of 2024, the sector secured $846 million in private funding. == Background == The military experience helped much. Israel's mandatory military service, combined with the expertise developed within elite units such as Unit 8200, has fostered a strong talent pool with practical experience in cybersecurity. Israel's thriving startup ecosystem, often referred to as the "Startup Nation," has fostered an environment of innovation and collaboration that has contributed to the growth of the cybersecurity industry. Israeli cybersecurity companies often collaborate with international partners, both in the private and public sectors, to share knowledge and develop joint solutions. === Government Initiatives and Support === The government also supported well through various initiatives, such as the Israel National Cyber Directorate (INCD), which works to strengthen cybersecurity defenses and promote the development of the sector. === Academic institutions === Israeli universities and research centers are involved in cybersecurity research and education, contributing to the development of new technologies and training the next generation of cybersecurity professionals. Academic Tech transfer offices in Israel also facilitate the commercialization of cybersecurity technologies. Some academic institutions with cybersecurity laboratories include: Tel Aviv University Technion Ben-Gurion University
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Non-native speech database

A non-native speech database is a speech database of non-native pronunciations of English. Such databases are used in the development of: multilingual automatic speech recognition systems, text to speech systems, pronunciation trainers, and second language learning systems. == List == The actual table with information about the different databases is shown in Table 2. === Legend === In the table of non-native databases some abbreviations for language names are used. They are listed in Table 1. Table 2 gives the following information about each corpus: The name of the corpus, the institution where the corpus can be obtained, or at least further information should be available, the language which was actually spoken by the speakers, the number of speakers, the native language of the speakers, the total amount of non-native utterances the corpus contains, the duration in hours of the non-native part, the date of the first public reference to this corpus, some free text highlighting special aspects of this database and a reference to another publication. The reference in the last field is in most cases to the paper which is especially devoted to describe this corpus by the original collectors. In some cases it was not possible to identify such a paper. In these cases a paper is referenced which is using this corpus is. Some entries are left blank and others are marked with unknown. The difference here is that blank entries refer to attributes where the value is just not known. Unknown entries, however, indicate that no information about this attribute is available in the database itself. As an example, in the Jupiter weather database no information about the origin of the speakers is given. Therefore this data would be less useful for verifying accent detection or similar issues. Where possible, the name is a standard name of the corpus, for some of the smaller corpora, however, there was no established name and hence an identifier had to be created. In such cases, a combination of the institution and the collector of the database is used. In the case where the databases contain native and non-native speech, only attributes of the non-native part of the corpus are listed. Most of the corpora are collections of read speech. If the corpus instead consists either partly or completely of spontaneous utterances, this is mentioned in the Specials column.
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Articulatory speech recognition

Articulatory speech recognition means the recovery of speech (in forms of phonemes, syllables or words) from acoustic signals with the help of articulatory modeling or an extra input of articulatory movement data. Speech recognition (or automatic speech recognition, acoustic speech recognition) means the recovery of speech from acoustics (sound wave) only. Articulatory information is extremely helpful when the acoustic input is in low quality, perhaps because of noise or missing data. Measurable information from the articulatory system (e.g. tongue, jaw movements) can supplement acoustic signals to improve phone recognition accuracy by 2%. However, attempts to estimate articulatory data from acoustic signals alone have not significantly enhanced recognition performance.
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Office automation

Office automation refers to the varied computer machinery and software used to digitally create, collect, store, manipulate, and relay office information needed for accomplishing basic tasks. Raw data storage, electronic transfer, and the management of electronic business information comprise the basic activities of an office automation system. Office automation helps in optimizing or automating existing office procedures. The backbone of office automation is a local area network, which allows users to transfer data, mail and voice across the network. All office functions, including dictation, typing, filing, copying, fax, telex, microfilm and records management, telephone and telephone switchboard operations, fall into this category. Office automation was a popular term in the 1970s and 1980s as the desktop computer exploded onto the scene. Advantages of office automation include that it can get many tasks accomplished faster, it eliminates the need for a large staff, less storage is required to store data, and multiple people can update data simultaneously in the event of changes in schedule. == Outline == Businesses can easily purchase and stock their wares with the aid of technology. Many of the manual tasks that used to be done by hand can now be done through hand held devices and UPC and SKU coding. In the retail setting, automation also increases choice. Customers can easily process their payments through automated credit card machines and no longer have to wait in line for an employee to process and manually type in the credit card numbers. Office payrolls have been automated, which means no one has to manually cut checks, and those checks that are cut can be printed through computer programs. Direct deposit can be automatically set up and this further reduces the manual process, and most employees who participate in direct deposit often find their paychecks come earlier than if they'd have to wait for their checks to be written and then cleared by the bank. Other ways automation has reduced employee manpower on tasks is automated voice direction. Through the use of prompts, automated phone menus and directed calls, the need for employees to be dedicated to answer the phones has been reduced, and in some cases, eliminated.
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Art Recognition

Art Recognition is a Swiss technology company headquartered in Adliswil, within the Zurich metropolitan area, Switzerland. Art Recognition specializes in the application of artificial intelligence (AI) for art authentication and the detection of art forgeries. == Overview == Art Recognition was established in 2019 by Dr. Carina Popovici and Christiane Hoppe-Oehl. Art Recognition employs a combination of machine learning techniques, computer vision algorithms, and deep neural networks to assess the authenticity of artworks. The company's technology undergoes a process of data collection, dataset preparation, and training. === Academic partnerships and grants === Art Recognition has established a relationship with Innosuisse, a Swiss innovation agency, to expand its research and development initiatives. It has also formed a strategic collaboration with Nils Büttner, an art historian and professor at the State Academy of Fine Arts Stuttgart (ABK Stuttgart). === Notable developments === In May 2024, Art Recognition played a key role in identifying counterfeit artworks, including alleged Monets and Renoirs, being sold on eBay. Germann Auction in November 2024 became the first auction house to successfully conduct a sale of artwork authenticated entirely by artificial intelligence. As of January 2025, Art Recognition has appointed art crime expert and Pulitzer Prize finalist Noah Charney as an advisor. === Recognition and debates === The company was featured on the front page of The Wall Street Journal for its involvement in the authentication case of the Flaget Madonna, believed to have been partly painted by Raphael. A broadcast by the Swiss public television SRF covered how the algorithm can be used to detect art forgeries with high accuracy. The technology developed by Art Recognition has been recognized for its role in providing a technology-based art authentication solution, compared to traditional methods. == Controversial cases == Art Recognition's AI algorithm has been applied to several high-profile and controversial artworks, sparking significant interest and debate in the art world. Samson and Delilah at the National Gallery in London: The National Gallery's "Samson and Delilah", traditionally attributed to the artist Rubens, has also been examined using Art Recognition's AI, which has assessed the painting as non-authentic. De Brecy Tondo Madonna. A research team from Bradford University and the University of Nottingham initially attributed the painting to Raphael, employing an AI face recognition software, while the AI developed at Art Recognition returned a negative result. The Bradford group's AI was trained on 49 images, whereas Art Recognition employed a larger dataset of over 100 images. Lucian Freud Painting Controversy: Featured in The New Yorker, a painting attributed to Lucian Freud became a subject of dispute. Art Recognition's AI analysis played a big role in examining the painting's authenticity. Titian at Kunsthaus Zürich: A painting attributed to Titian, housed at Kunsthaus Zürich, has been a topic of debate among art experts. The application of Art Recognition's technology offered a new perspective. Following this debate, Kunsthaus Zürich has announced plans to initiate a comprehensive project aimed at resolving the authenticity questions surrounding the painting. Art Recognition has contributed to the authentication debate surrounding The Polish Rider, a painting traditionally attributed to Rembrandt but subject to scholarly debate.
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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.
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Signal transfer function

The signal transfer function (SiTF) is a measure of the signal output versus the signal input of a system such as an infrared system or sensor. There are many general applications of the SiTF. Specifically, in the field of image analysis, it gives a measure of the noise of an imaging system, and thus yields one assessment of its performance. == SiTF evaluation == In evaluating the SiTF curve, the signal input and signal output are measured differentially; meaning, the differential of the input signal and differential of the output signal are calculated and plotted against each other. An operator, using computer software, defines an arbitrary area, with a given set of data points, within the signal and background regions of the output image of the infrared sensor, i.e. of the unit under test (UUT), (see "Half Moon" image below). The average signal and background are calculated by averaging the data of each arbitrarily defined region. A second order polynomial curve is fitted to the data of each line. Then, the polynomial is subtracted from the average signal and background data to yield the new signal and background. The difference of the new signal and background data is taken to yield the net signal. Finally, the net signal is plotted versus the signal input. The signal input of the UUT is within its own spectral response. (e.g. color-correlated temperature, pixel intensity, etc.). The slope of the linear portion of this curve is then found using the method of least squares. == SiTF curve == The net signal is calculated from the average signal and background, as in signal to noise ratio (imaging)#Calculations. The SiTF curve is then given by the signal output data, (net signal data), plotted against the signal input data (see graph of SiTF to the right). All the data points in the linear region of the SiTF curve can be used in the method of least squares to find a linear approximation. Given n {\displaystyle n\,} data points ( x i , y i ) {\displaystyle (x_{i}\,,y_{i}\,)} a best fit line parameterized as y = m x + b {\displaystyle y=mx+b\,} is given by: m = ∑ x i y i n − ∑ x i n ∑ y i n ∑ x i 2 n − ( ∑ x i n ) 2 b = ∑ y i n − m ∑ x i n {\displaystyle m={\frac {{\frac {\sum x_{i}y_{i}}{n}}-{\frac {\sum x_{i}}{n}}{\frac {\sum y_{i}}{n}}}{{\frac {\sum x_{i}^{2}}{n}}-({\frac {\sum x_{i}}{n}})^{2}}}\qquad \qquad b={\frac {\sum y_{i}}{n}}-m{\frac {\sum x_{i}}{n}}}
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