In the fields of computer vision and image analysis, the scale-invariant feature operator (or SFOP) is an algorithm to detect local features in images. The algorithm was published by Förstner et al. in 2009. == Algorithm == The scale-invariant feature operator (SFOP) is based on two theoretical concepts: spiral model feature operator Desired properties of keypoint detectors: Invariance and repeatability for object recognition Accuracy to support camera calibration Interpretability: Especially corners and circles, should be part of the detected keypoints (see figure). As few control parameters as possible with clear semantics Complementarity to known detectors scale-invariant corner/circle detector. == Theory == === Maximize the weight === Maximize the weight w {\displaystyle w} = 1/variance of a point p {\displaystyle p} w ( p , α , τ , σ ) = ( N ( σ ) − 2 ) λ m i n ( M ( p , α , τ , σ ) ) Ω ( p , α , τ , σ ) {\displaystyle w(\mathbf {p} ,\alpha ,\tau ,\sigma )=\left(N(\sigma )-2\right){\frac {\lambda _{min}(M(\mathbf {p} ,\alpha ,\tau ,\sigma ))}{\Omega (\mathbf {p} ,\alpha ,\tau ,\sigma )}}} comprising: 1. the image model Ω ( p , α , τ , σ ) = ∑ n = 1 N ( σ ) [ ( q n − p ) T R α ∇ T g ( q n ) ] 2 G σ ( q n − p ) = N ( σ ) t r { R α ∇ τ ∇ τ T R α T ∗ p p T G σ ( p ) } {\displaystyle {\begin{aligned}\Omega (\mathbf {p} ,\alpha ,\tau ,\sigma )&=\sum _{n=1}^{N(\sigma )}[(\mathbf {q} _{n}-\mathbf {p} )^{T}\mathbf {R} _{\alpha }\mathbf {\nabla } _{T}g(\mathbf {q} _{n})]^{2}G_{\sigma }(\mathbf {q} _{n}-\mathbf {p} )\\&=N(\sigma )\mathbf {tr} \left\{R_{\alpha }\mathbf {\nabla } _{\tau }\mathbf {\nabla } _{\tau }^{T}R_{\alpha }^{T}\mathbf {p} \mathbf {p} ^{T}G_{\sigma }(\mathbf {p} )\right\}\end{aligned}}} 2. the smaller eigenvalue of the structure tensor M ( p , α , τ , σ ) ⏟ structure tensor = G σ ( p ) ⏟ weighted summation ∗ ( R σ ∇ τ ∇ τ T R σ T ) ⏟ squared rotated gradients {\displaystyle \underbrace {M(\mathbf {p} ,\alpha ,\tau ,\sigma )} _{\text{structure tensor}}=\underbrace {G_{\sigma }(\mathbf {p} )} _{\text{weighted summation}}\underbrace {(R_{\sigma }\nabla _{\tau }\nabla _{\tau }^{T}R_{\sigma }^{T})} _{\text{squared rotated gradients}}} === Reduce the search space === Reduce the 5-dimensional search space by linking the differentiation scale τ {\displaystyle \tau } to the integration scale τ = σ / 3 {\displaystyle \tau =\sigma /3} solving for the optimal α ^ {\displaystyle {\hat {\alpha }}} using the model Ω ( α ) = a − b cos ( 2 α − 2 α 0 ) {\displaystyle \Omega (\alpha )=a-b\cos(2\alpha -2\alpha _{0})} and determining the parameters from three angles, e. g. Ω ( 0 ∘ ) , Ω ( 60 ∘ ) , Ω ( 120 ∘ ) → a , b , α 0 → α ^ {\displaystyle \Omega (0^{\circ }),\Omega (60^{\circ }),\Omega (120^{\circ })\quad \rightarrow \quad a,b,\alpha _{0}\quad \rightarrow \quad {\hat {\alpha }}} pre-selection possible: α = 0 ∘ → junctions , α = 90 ∘ → circular features {\displaystyle \alpha =0^{\circ }\,\rightarrow \,{\mbox{junctions}},\quad \alpha =90^{\circ }\,\rightarrow \,{\mbox{circular features}}} === Filter potential keypoints === non-maxima suppression over scale, space and angle thresholding the isotropy λ 2 ( M ) {\displaystyle \lambda _{2(M)}} :eigenvalues characterize the shape of the keypoint, smallest eigenvalue has to be larger than threshold T λ {\displaystyle T_{\lambda }} derived from noise variance V ( n ) {\displaystyle V(n)} and significance level S {\displaystyle S} : T λ ( V ( n ) , τ , σ , S ) = N ( σ ) 16 π τ 4 V ( n ) χ 2 , S 2 {\displaystyle T_{\lambda }(V(n),\tau ,\sigma ,S)={\frac {N(\sigma )}{16\pi \tau ^{4}}}V(n)\chi _{2,S}^{2}} == Algorithm == == Results == === Interpretability of SFOP keypoints ===
WhatsApp Messenger, commonly known simply as WhatsApp, is an American social media, instant messaging (IM), and Voice over IP (VoIP) service accessible via desktop and mobile app. Owned by Meta Platforms, the service allows users to send text messages, voice messages, and video messages, make voice and video calls, and share images, documents, user locations, and other content. The service requires a cellular mobile telephone number to register. WhatsApp was launched in May 2009. In January 2018, WhatsApp released a standalone business app called WhatsApp Business which can communicate with the standard WhatsApp client. As of May 2025, the service had 3 billion monthly active users, making it the most used messenger app. The name of the app is meant to sound like "what's up". The service was created by WhatsApp Inc. of Mountain View, California, which was acquired by Facebook in February 2014 for approximately US$19.3 billion. It became the world's most popular messaging application in 2015, with 900 million users, and had more than 2 billion active users worldwide in February 2020. WhatsApp Business had approximately 200 million monthly users in 2023. By 2016, it had become the primary means of Internet communication in regions including the Americas, the Indian subcontinent, and large parts of Europe and Africa. == History == === 2009–2014 === WhatsApp was founded by Brian Acton and Jan Koum, former employees of Yahoo. Koum incorporated WhatsApp Inc. in California on February 24, 2009. A month earlier, Koum had purchased an iPhone, and he and Acton decided to create an app for the App Store. The idea started off as an app that would display statuses in a phone's Contacts menu, showing if a person was at work or on a call. Their discussions often took place at the home of Koum's Russian friend Alex Fishman in West San Jose. They realized that to take the idea further, they would need an iPhone developer. Fishman visited RentACoder.com, found Russian developer Igor Solomennikov, and introduced him to Koum. Koum named the app WhatsApp to sound like "what's up" and it was published on the Apple App Store and BlackBerry App World in May and June 2009 respectively. However, when early versions of WhatsApp kept crashing, Koum considered giving up and looking for a new job. Acton encouraged him to wait for a "few more months". In June 2009, when the app had been downloaded by only a handful of Fishman's Russian-speaking friends, Apple launched push technology, allowing users to be pinged even when not using the app. Koum updated WhatsApp so that everyone in the user's network would be notified when a user's status changed. This new facility, to Koum's surprise, was used by users to ping "each other with jokey custom statuses like, 'I woke up late' or 'I'm on my way.'" Fishman said, "At some point it sort of became instant messaging". WhatsApp 2.0, released for iPhone in August 2009, featured a purpose-designed messaging component; the number of active users suddenly increased to 250,000. Although Acton was working on another startup idea, he decided to join the company. In October 2009, Acton persuaded five former friends at Yahoo! to invest $250,000 in seed funding, and Acton became a co-founder and was given a stake. He officially joined WhatsApp on November 1. Koum then hired a friend in Los Angeles, Chris Peiffer, to develop a BlackBerry version, which arrived two months later. Subsequently, WhatsApp for Symbian OS was added in May 2010, and for Android OS in August 2010. In 2010 Google made multiple acquisition offers for WhatsApp, which were all declined. To cover the cost of sending verification texts to users, WhatsApp was changed from a free service to a paid one. In December 2009, the ability to send photos was added to the iOS version. By early 2011, WhatsApp was one of the top 20 apps in the U.S. Apple App Store. In April 2011, Sequoia Capital invested about $8 million for more than 15% of the company, after months of negotiation by Sequoia partner Jim Goetz. By February 2013, WhatsApp had about 200 million active users and 50 staff members. Sequoia invested another $50 million at a $1.5 billion valuation. Some time in 2013 WhatsApp acquired Santa Clara–based startup SkyMobius, the developers of Vtok, a video and voice calling app. As of December 2013, the service had 400 million monthly active users. That year, the company had $148 million in expenses and a net loss of $138 million. === 2014–2015 === On February 19, 2014, one year after the venture capital financing round at a $1.5 billion valuation, Facebook, Inc. (now Meta Platforms) agreed to acquire the company for US$19 billion, its largest acquisition to date. At the time, it was the largest acquisition of a venture-capital-backed company in history. Sequoia Capital received an approximate 5,000% return on its initial investment. Facebook paid $4 billion in cash, $12 billion in Facebook shares, and an additional $3 billion in restricted stock units granted to WhatsApp's founders Koum and Acton. Employee stock was scheduled to vest over four years subsequent to closing. Days after the announcement, WhatsApp users experienced a loss of service, leading to anger across social media. The acquisition was influenced by the data provided by Onavo, Facebook's research app for monitoring competitors and trending usage of social activities on mobile phones, as well as startups that were performing "unusually well". The acquisition caused many users to try, or move to, other message services. Telegram claimed that it acquired 8 million new users, and Line, 2 million. At a keynote presentation at the Mobile World Congress in Barcelona in February 2014, Facebook CEO Mark Zuckerberg said that Facebook's acquisition of WhatsApp was closely related to the Internet.org vision. A TechCrunch article said about Zuckerberg's vision:The idea, he said, is to develop a group of basic internet services that would be free of charge to use – "a 911 for the internet". These could be a social networking service like Facebook, a messaging service, maybe search and other things like weather. Providing a bundle of these free of charge to users will work like a gateway drug of sorts – users who may be able to afford data services and phones these days just don't see the point of why they would pay for those data services. This would give them some context for why they are important, and that will lead them to pay for more services like this – or so the hope goes. Three days after announcing the Facebook purchase, Koum said they were working to introduce voice calls. He also said that new mobile phones would be sold in Germany with the WhatsApp brand, and that their ultimate goal was to be on all smartphones. In August 2014, WhatsApp was the most popular messaging app in the world, with more than 600 million users. By early January 2015, WhatsApp had 700 million monthly users and over 30 billion messages every day. In April 2015, Forbes predicted that between 2012 and 2018, the telecommunications industry would lose $386 billion because of "over-the-top" services like WhatsApp and Skype. That month, WhatsApp had over 800 million users. By September 2015, it had grown to 900 million; and by February 2016, one billion. On November 30, 2015, the Android WhatsApp client made links to Telegram unclickable and not copyable. Multiple sources confirmed that it was intentional, not a bug, and that it had been implemented when the Android source code that recognized Telegram URLs had been identified. (The word "telegram" appeared in WhatsApp's code.) Some considered it an anti-competitive measure; WhatsApp offered no explanation. === 2016–2019 === On January 18, 2016, WhatsApp's co-founder Jan Koum announced that it would no longer charge users a $1 annual subscription fee, in an effort to remove a barrier faced by users without payment cards. He also said that the app would not display any third-party ads, and that it would have new features such as the ability to communicate with businesses. On May 18, 2017, the European Commission announced that it was fining Facebook €110 million for "providing misleading information about WhatsApp takeover" in 2014. The Commission said that in 2014 when Facebook acquired the messaging app, it "falsely claimed it was technically impossible to automatically combine user information from Facebook and WhatsApp." However, in the summer of 2016, WhatsApp had begun sharing user information with its parent company, allowing information such as phone numbers to be used for targeted Facebook advertisements. Facebook acknowledged the breach, but said the errors in their 2014 filings were "not intentional". In September 2017, WhatsApp's co-founder Brian Acton left the company to start a nonprofit group, later revealed as the Signal Foundation, which developed the WhatsApp competitor Signal. He explained his reasons for leaving in an interview with Forbes a year later. WhatsApp also
Asymmetric follow
An asymmetric follow social network is one which allows many people to follow an individual or account without having to follow them back. It is also known as asynchronous follow or sometimes asymmetric friendship. Asymmetric follow is a common pattern on Twitter, where someone may have thousands of followers, but themselves follow few (or no) accounts. In September 2010 Facebook started experimenting with a similar feature, which Facebook calls "Subscribe To."
CSS box model
In web development, the CSS box model refers to how HTML elements are modeled in browser engines and how the dimensions of those HTML elements are derived from CSS properties. It is a fundamental concept for the composition of HTML webpages. The guidelines of the box model are described by web standards World Wide Web Consortium (W3C) specifically the CSS Working Group. For much of the late-1990s and early 2000s there had been non-standard compliant implementations of the box model in mainstream browsers. With the advent of CSS2 in 1998, which introduced the box-sizing property, the problem had mostly been resolved. == Specifics == The Cascading Style Sheets (CSS) specification describes how elements of web pages are displayed by graphical browsers. Section 4 of the CSS1 specification defines a "formatting model" that gives block-level elements—such as p and blockquote—a width and height, and three levels of boxes surrounding it: padding, borders, and margins. While the specification never uses the term "box model" explicitly, the term has become widely used by web developers and web browser vendors. All HTML elements can be considered "boxes", this includes div tag, p tag, or a tag. Each of those boxes has five modifiable dimensions: the height and width describe dimensions of the actual content of the box (text, images, ...) the padding describes the space between this content and the border of the box the border is any kind of line (solid, dotted, dashed...) surrounding the box, if present the margin is the space around the border According to the CSS1 specification, released by W3C in 1996 and revised in 1999, when a width or height is explicitly specified for any block-level element, it should determine only the width or height of the visible element, with the padding, borders, and margins applied afterward. Before CSS3, this box model was known as W3C box model, in CSS3, it is known as the content-box. The total width of a box is therefore margin-left + border-left + padding-left + width + padding-right + border-right + margin-right. Similarly, the total height of a box equals margin-top + border-top + padding-top + height + padding-bottom + border-bottom + margin-bottom. For example, the following CSS code would specify the box dimensions of each block belonging to 'my-class'. Moreover, each such box will have total height 140px and width 240px. CSS3 introduced the Internet Explorer box model to the standard, known referred to as border-box. == History == Before HTML 4 and CSS, very few HTML elements supported both border and padding, so the definition of the width and height of an element was not very contentious. However, it varied depending on the element. The HTML width attribute of a table defined the width of the table including its border. On the other hand, the HTML width attribute of an image defined the width of the image itself (inside any border). The only element to support padding in those early days was the table cell. Width for the cell was defined as "the suggested width for a cell content in pixels excluding the cell padding." In 1996, CSS introduced margin, border and padding for many more elements. It adopted a definition width in relation to content, border, margin and padding similar to that for a table cell. This has since become known as the W3C box model. At the time, very few browser vendors implemented the W3C box model to the letter. The two major browsers at the time, Netscape 4.0 and Internet Explorer 4.0 both defined width and height as the distance from border to border. This has been referred to as the traditional or the Internet Explorer box model. Internet Explorer in "quirks mode" includes the content, padding and borders within a specified width or height; this results in a narrower or shorter rendering of a box than would result following the standard behavior. The Internet Explorer box model behavior was often considered a bug, because of the way in which earlier versions of Internet Explorer handle the box model or sizing of elements in a web page, which differs from the standard way recommended by the W3C for the Cascading Style Sheets language. As of Internet Explorer 6, the browser supports an alternative rendering mode (called the "standards-compliant mode") which solves this discrepancy. However, for backward compatibility reasons, all versions still behave in the usual, non-standard way by default (see quirks mode). Internet Explorer for Mac is not affected by this non-standard behavior. === Workarounds === Internet Explorer versions 6 and onward are not affected by the bug if the page contains certain HTML document type declarations. These versions maintain the buggy behavior when in quirks mode for reasons of backward compatibility. For example, quirks mode is triggered: When the document type declaration is absent or incomplete; When an HTML 3 or earlier document is encountered; When an HTML 4.0 Transitional or Frameset document type declaration is used and a system identifier (URI) is not present; When an SGML comment or other unrecognized content appears before the document type declaration Internet Explorer 6 also uses quirks mode if there is an XML declaration prior to the document type declaration. Various workarounds have been devised to force Internet Explorer versions 5 and earlier to display Web pages using the W3C box model. These workarounds generally exploit unrelated bugs in Internet Explorer's CSS selector processing in order to hide certain rules from the browser. The best known of these workarounds is the "box model hack" developed by Tantek Çelik, a former Microsoft employee who developed this idea while working on Internet Explorer for the Macintosh. It involves specifying a width declaration for Internet Explorer for Windows, and then overriding it with another width declaration for CSS-compliant browsers. This second declaration is hidden from Internet Explorer for Windows by exploiting other bugs in the way that it parses CSS rules. The implementation of these CSS “hacks” has been further complicated by the public release of Internet Explorer 7, which has had some issues fixed, but not others, causing undesired results in pages using these hacks. Box model hacks have proven unreliable because they rely on bugs in browsers' CSS support that may be fixed in later versions. For this reason, some Web developers have instead recommended either avoiding specifying both width and padding for the same element or using conditional comment and/or CSS filters to work around the box model bug in older versions of Internet Explorer. == Support for Internet Explorer's box model == Web designer Doug Bowman has said that the original Internet Explorer box model represents a better, more logical approach. Peter-Paul Koch gives the example of a physical box, whose dimensions always refer to the box itself, including potential padding, but never its content. He says that this box model is more useful for graphic designers, who create designs based on the visible width of boxes rather than the width of their content. Bernie Zimmermann says that the Internet Explorer box model is closer to the definition of cell dimensions and padding used in the HTML table model. The W3C has included a "box-sizing" property in CSS3. When box-sizing: border-box; is specified for an element, any padding or border of the element is drawn inside the specified width and height, "as commonly implemented by legacy HTML user agents". Internet Explorer 8, WebKit browsers such as Apple Safari 5.1+ and Google Chrome, Gecko-based browsers such as Mozilla Firefox 29.0 and later, Opera 7.0 and later, and Konqueror 3.3.2 and later support the CSS3 box-sizing property. Gecko browsers previous than 29.0 support the same functionality using the browser-specific -moz-box-sizing property. border-box is the default box model used in Bootstrap framework.
Mean opinion score
Mean opinion score (MOS) is a measure used in the domain of Quality of Experience and telecommunications engineering, representing overall quality of a stimulus or system. It is the arithmetic mean over all individual "values on a predefined scale that a subject assigns to his opinion of the performance of a system quality". Such ratings are usually gathered in a subjective quality evaluation test, but they can also be algorithmically estimated. MOS is a commonly used measure for video, audio, and audiovisual quality evaluation, but not restricted to those modalities. ITU-T has defined several ways of referring to a MOS in Recommendation ITU-T P.800.1, depending on whether the score was obtained from audiovisual, conversational, listening, talking, or video quality tests. == Rating scales and mathematical definition == The MOS is expressed as a single rational number, typically in the range 1–5, where 1 is lowest perceived quality, and 5 is the highest perceived quality. Other MOS ranges are also possible, depending on the rating scale that has been used in the underlying test. The Absolute Category Rating scale is very commonly used, which maps ratings between Bad and Excellent to numbers between 1 and 5, as seen in below table. Other standardized quality rating scales exist in ITU-T Recommendations (such as ITU-T P.800 or ITU-T P.910). For example, one could use a continuous scale ranging between 1–100. Which scale is used depends on the purpose of the test. In certain contexts there are no statistically significant differences between ratings for the same stimuli when they are obtained using different scales. The MOS is calculated as the arithmetic mean over single ratings performed by human subjects for a given stimulus in a subjective quality evaluation test. Thus: M O S = ∑ n = 1 N R n N {\displaystyle MOS={\frac {\sum _{n=1}^{N}{R_{n}}}{N}}} Where R {\displaystyle R} are the individual ratings for a given stimulus by N {\displaystyle N} subjects. == Properties of the MOS == The MOS is subject to certain mathematical properties and biases. In general, there is an ongoing debate on the usefulness of the MOS to quantify Quality of Experience in a single scalar value. When the MOS is acquired using a categorical rating scales, it is based on – similar to Likert scales – an ordinal scale. In this case, the ranking of the scale items is known, but their interval is not. Therefore, it is mathematically incorrect to calculate a mean over individual ratings in order to obtain the central tendency; the median should be used instead. However, in practice and in the definition of MOS, it is considered acceptable to calculate the arithmetic mean. It has been shown that for categorical rating scales (such as ACR), the individual items are not perceived equidistant by subjects. For example, there may be a larger "gap" between Good and Fair than there is between Good and Excellent. The perceived distance may also depend on the language into which the scale is translated. However, there exist studies that could not prove a significant impact of scale translation on the obtained results. Several other biases are present in the way MOS ratings are typically acquired. In addition to the above-mentioned issues with scales that are perceived non-linearly, there is a so-called "range-equalization bias": subjects, over the course of a subjective experiment, tend to give scores that span the entire rating scale. This makes it impossible to compare two different subjective tests if the range of presented quality differs. In other words, the MOS is never an absolute measure of quality, but only relative to the test in which it has been acquired. For the above reasons – and due to several other contextual factors influencing the perceived quality in a subjective test – a MOS value should only be reported if the context in which the values have been collected in is known and reported as well. MOS values gathered from different contexts and test designs therefore should not be directly compared. Recommendation ITU-T P.800.2 prescribes how MOS values should be reported. Specifically, P.800.2 says:it is not meaningful to directly compare MOS values produced from separate experiments, unless those experiments were explicitly designed to be compared, and even then the data should be statistically analysed to ensure that such a comparison is valid. == MOS for speech and audio quality estimation == MOS historically originates from subjective measurements where listeners would sit in a "quiet room" and score a telephone call quality as they perceived it. This kind of test methodology had been in use in the telephony industry for decades and was standardized in Recommendation ITU-T P.800. It specifies that "the talker should be seated in a quiet room with volume between 30 and 120 m³ and a reverberation time less than 500 ms (preferably in the range 200–300 ms). The room noise level must be below 30 dBA with no dominant peaks in the spectrum." Requirements for other modalities were similarly specified in later ITU-T Recommendations. == MOS estimation using quality models == Obtaining MOS ratings may be time-consuming and expensive as it requires the recruitment of human assessors. For various use cases such as codec development or service quality monitoring purposes – where quality should be estimated repeatedly and automatically – MOS scores can also be predicted by objective quality models, which typically have been developed and trained using human MOS ratings. A question that arises from using such models is whether the MOS differences produced are noticeable to the users. For example, when rating images on a five point MOS scale, an image with a MOS equal to 5 is expected to be noticeably better in quality than one with a MOS equal to 1. Contrary to that, it is not evident whether an image with a MOS equal to 3.8 is noticeably better in quality than one with a MOS equal to 3.6. Research conducted on determining the smallest MOS difference that is perceptible to users for digital photographs showed that a MOS difference of approximately 0.46 is required in order for 75% of the users to be able to detect the higher quality image. Nevertheless, image quality expectation, and hence MOS, changes over time with the change of user expectations. As a result, minimum noticeable MOS differences determined using analytical methods such as in may change over time.
ACLU Mobile Justice
ACLU Mobile Justice was a video live streaming application developed for smartphones by various state chapters of the American Civil Liberties Union. It was intended to allow instant, secure video recording and transmission of interactions with, and perceived abuses by, law enforcement officers. Since its release by the ACLU of California for California residents, other versions of the app have been released for 16 other states and the District of Columbia by their ACLU chapters. It was discontinued in February 2025.
Signal-to-crosstalk ratio
The signal-to-crosstalk ratio at a specified point in a circuit is the ratio of the power of the wanted signal to the power of the unwanted signal from another channel. The signals are adjusted in each channel so that they are of equal power at the zero transmission level point in their respective channels. The signal-to-crosstalk ratio is usually expressed in dB.