The Open Syllabus Project (OSP) is an online open-source platform that catalogs and analyzes millions of college syllabi. Founded by researchers from the American Assembly at Columbia University, the OSP has amassed the most extensive collection of searchable syllabi. Since its beta launch in 2016, the OSP has collected over 7 million course syllabi from over 80 countries, primarily by scraping publicly accessible university websites. The project is directed by Joe Karaganis. == History == The OSP was formed by a group of data scientists, sociologists, and digital-humanities researchers at the American Assembly, a public-policy institute based at Columbia University. The OSP was partly funded by the Sloan Foundation and the Arcadia Fund. Joe Karaganis, former vice-president of the American Assembly, serves as the project director of the OSP. The project builds on prior attempts to archive syllabi, such as H-Net, MIT OpenCourseWare, and historian Dan Cohen's defunct Syllabus Finder website (Cohen now sits on the OSP's advisory board). The OSP became a non-profit and independent of the American Assembly in November 2019. In January 2016, the OSP launched a beta version of their "Syllabus Explorer," which they had collected data for since 2013. The Syllabus Explorer allows users to browse and search texts from over one million college course syllabi. The OSP launched a more comprehensive version 2.0 of the Syllabus Explorer in July 2019. The newer version includes an interactive visualization that displays texts as dots on a knowledge map. As of 2022, the OSP has collected over 7 million course syllabi. The Syllabus Explorer represents the "largest collection of searchable syllabi ever amassed." == Methodology == The OSP has collected syllabi data from over 80 countries dating to 2000. The syllabi stem from over 4,000 worldwide institutions. Most of the OSP's data originates from the United States. Canada, Australia, and the U.K also have large datasets. The OSP primarily collects syllabi by scraping publicly accessible university websites. The OSP also allows syllabi submissions from faculty, students, and administrators. The OSP developers use machine learning and natural language processing to extract metadata from such syllabi. Since only metadata is collected, no individual syllabus or personal identifying information is found in the OSP database. The OSP classifies the syllabi into 62 subject fields – corresponding to the U.S. Department of Education's Classification of Instructional Programs (CIP). Additionally, the OSP assigns each text a "teaching score" from 0–100. This score represents the text's percentile rank among citations in the total citation count and is a numerical indicator of the relative frequency of which a particular work is taught. The OSP also has data on which texts are most likely to be assigned together. The developers behind the OSP admit that the database is incomplete and likely contains "a fair number of errors." Karaganis estimates that 80–100 million syllabi exist in the United States alone. The OSP is unable to access syllabi behind private course-management software like Blackboard. == Notable findings == === Anthropology === Using data from the OSP, anthropologist Laurence Ralph uncovered that black anthropologists are "woefully under-represented in (if not erased from) most anthropology syllabi." Black authors wrote less than 1 percent of the top 1,000 assigned works. === Economics === The database indicates Greg Mankiw is the most frequently cited author for college economics courses. === English literature === The OSP found that Mary Shelley's Frankenstein was the most widely taught novel in college courses. Additionally, the majority of novels published after 1945 taught in English classes were historical fiction. === Female writers === The most read female writer on college campuses is Kate L. Turabian for her A Manual for Writers of Research Papers, Theses, and Dissertations . Turabian is followed by Diana Hacker, Toni Morrison, Jane Austen, and Virginia Woolf. === Film === The most assigned film according to the OSP is the 1929 Soviet documentary film, Man with a Movie Camera. English filmmaker Alfred Hitchcock is the most assigned director in college courses. === History === Historians George Brown Tindall and David Emory Shi's America: A Narrative History is the number one assigned textbook for history, followed by Anne Moody's memoir, Coming of Age in Mississippi. === Philosophy === The most assigned texts in the field of philosophy include Aristotle's Nicomachean Ethics, John Stuart Mill's Utilitarianism, and Plato's Republic. Plato's Republic was also the second most assigned text in universities in the English-speaking world (only behind Strunk and White's Elements of Style). === Physics === David Halliday's et al. Fundamentals of Physics is the number one ranked physics textbook in the OSP's database. === Political science === Data from the OSP indicates that the dominant political science texts are written almost exclusively by white men and scholars based in the West. In the top 200 most-frequently assigned works, 15 are authored by at least one woman. === Public administration === American president Woodrow Wilson's article "The Study of Administration" was the most frequently assigned text in public affairs and administration syllabi. == Reception == According to William Germano et al., the OSP is a "fascinating resource but is also prone to misrepresenting or at least distracting us from the most important business of a syllabus: communicating with students." Historian William Caferro remarks that the OSP is a "tacit experience of sharing, but a useful one." English professor Bart Beaty writes that, "Despite the many reservations about the completeness of its data, the OSP provides a rare opportunity for scholars to move beyond the anecdotal in discussions of canon-formation in teaching." Media theorist Elizabeth Losh opines that "big data approaches", like the OSP, may "raise troubling questions for instructors about informed consent, pedagogical privacy, and quantified metrics."
Image moment
In image processing, computer vision and related fields, an image moment is a certain particular weighted average (moment) of the image pixels' intensities, or a function of such moments, usually chosen to have some attractive property or interpretation. Image moments are useful to describe objects after segmentation. Simple properties of the image which are found via image moments include area (or total intensity), its centroid, and information about its orientation. == Raw moments == For a 2D continuous function f(x,y) the moment (sometimes called "raw moment") of order (p + q) is defined as M p q = ∫ − ∞ ∞ ∫ − ∞ ∞ x p y q f ( x , y ) d x d y {\displaystyle M_{pq}=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }x^{p}y^{q}f(x,y)\,dx\,dy} for p,q = 0,1,2,... Adapting this to scalar (grayscale) image with pixel intensities I(x,y), raw image moments Mij are calculated by M i j = ∑ x ∑ y x i y j I ( x , y ) {\displaystyle M_{ij}=\sum _{x}\sum _{y}x^{i}y^{j}I(x,y)\,\!} In some cases, this may be calculated by considering the image as a probability density function, i.e., by dividing the above by ∑ x ∑ y I ( x , y ) {\displaystyle \sum _{x}\sum _{y}I(x,y)\,\!} A uniqueness theorem states that if f(x,y) is piecewise continuous and has nonzero values only in a finite part of the xy plane, moments of all orders exist, and the moment sequence (Mpq) is uniquely determined by f(x,y). Conversely, (Mpq) uniquely determines f(x,y). In practice, the image is summarized with functions of a few lower order moments. === Examples === Simple image properties derived via raw moments include: Area (for binary images) or sum of grey level (for greytone images): M 00 {\displaystyle M_{00}} Centroid: { x ¯ , y ¯ } = { M 10 M 00 , M 01 M 00 } {\displaystyle \{{\bar {x}},\ {\bar {y}}\}=\left\{{\frac {M_{10}}{M_{00}}},{\frac {M_{01}}{M_{00}}}\right\}} == Central moments == Central moments are defined as μ p q = ∫ − ∞ ∞ ∫ − ∞ ∞ ( x − x ¯ ) p ( y − y ¯ ) q f ( x , y ) d x d y {\displaystyle \mu _{pq}=\int \limits _{-\infty }^{\infty }\int \limits _{-\infty }^{\infty }(x-{\bar {x}})^{p}(y-{\bar {y}})^{q}f(x,y)\,dx\,dy} where x ¯ = M 10 M 00 {\displaystyle {\bar {x}}={\frac {M_{10}}{M_{00}}}} and y ¯ = M 01 M 00 {\displaystyle {\bar {y}}={\frac {M_{01}}{M_{00}}}} are the components of the centroid. If ƒ(x, y) is a digital image, then the previous equation becomes μ p q = ∑ x ∑ y ( x − x ¯ ) p ( y − y ¯ ) q f ( x , y ) {\displaystyle \mu _{pq}=\sum _{x}\sum _{y}(x-{\bar {x}})^{p}(y-{\bar {y}})^{q}f(x,y)} The central moments of order up to 3 are: μ 00 = M 00 , μ 01 = 0 , μ 10 = 0 , μ 11 = M 11 − x ¯ M 01 = M 11 − y ¯ M 10 , μ 20 = M 20 − x ¯ M 10 , μ 02 = M 02 − y ¯ M 01 , μ 21 = M 21 − 2 x ¯ M 11 − y ¯ M 20 + 2 x ¯ 2 M 01 , μ 12 = M 12 − 2 y ¯ M 11 − x ¯ M 02 + 2 y ¯ 2 M 10 , μ 30 = M 30 − 3 x ¯ M 20 + 2 x ¯ 2 M 10 , μ 03 = M 03 − 3 y ¯ M 02 + 2 y ¯ 2 M 01 . {\displaystyle {\begin{aligned}\mu _{00}&=M_{00},&\mu _{01}&=0,\\\mu _{10}&=0,&\mu _{11}&=M_{11}-{\bar {x}}M_{01}=M_{11}-{\bar {y}}M_{10},\\\mu _{20}&=M_{20}-{\bar {x}}M_{10},&\mu _{02}&=M_{02}-{\bar {y}}M_{01},\\\mu _{21}&=M_{21}-2{\bar {x}}M_{11}-{\bar {y}}M_{20}+2{\bar {x}}^{2}M_{01},&\mu _{12}&=M_{12}-2{\bar {y}}M_{11}-{\bar {x}}M_{02}+2{\bar {y}}^{2}M_{10},\\\mu _{30}&=M_{30}-3{\bar {x}}M_{20}+2{\bar {x}}^{2}M_{10},&\mu _{03}&=M_{03}-3{\bar {y}}M_{02}+2{\bar {y}}^{2}M_{01}.\end{aligned}}} It can be shown that: μ p q = ∑ m p ∑ n q ( p m ) ( q n ) ( − x ¯ ) ( p − m ) ( − y ¯ ) ( q − n ) M m n {\displaystyle \mu _{pq}=\sum _{m}^{p}\sum _{n}^{q}{p \choose m}{q \choose n}(-{\bar {x}})^{(p-m)}(-{\bar {y}})^{(q-n)}M_{mn}} Central moments are translational invariant. === Examples === Information about image orientation can be derived by first using the second order central moments to construct a covariance matrix. μ 20 ′ = μ 20 / μ 00 = M 20 / M 00 − x ¯ 2 μ 02 ′ = μ 02 / μ 00 = M 02 / M 00 − y ¯ 2 μ 11 ′ = μ 11 / μ 00 = M 11 / M 00 − x ¯ y ¯ {\displaystyle {\begin{aligned}\mu '_{20}&=\mu _{20}/\mu _{00}=M_{20}/M_{00}-{\bar {x}}^{2}\\\mu '_{02}&=\mu _{02}/\mu _{00}=M_{02}/M_{00}-{\bar {y}}^{2}\\\mu '_{11}&=\mu _{11}/\mu _{00}=M_{11}/M_{00}-{\bar {x}}{\bar {y}}\end{aligned}}} The covariance matrix of the image I ( x , y ) {\displaystyle I(x,y)} is now cov [ I ( x , y ) ] = [ μ 20 ′ μ 11 ′ μ 11 ′ μ 02 ′ ] . {\displaystyle \operatorname {cov} [I(x,y)]={\begin{bmatrix}\mu '_{20}&\mu '_{11}\\\mu '_{11}&\mu '_{02}\end{bmatrix}}.} The eigenvectors of this matrix correspond to the major and minor axes of the image intensity, so the orientation can thus be extracted from the angle of the eigenvector associated with the largest eigenvalue towards the axis closest to this eigenvector. It can be shown that this angle Θ is given by the following formula: Θ = 1 2 arctan ( 2 μ 11 ′ μ 20 ′ − μ 02 ′ ) {\displaystyle \Theta ={\frac {1}{2}}\arctan \left({\frac {2\mu '_{11}}{\mu '_{20}-\mu '_{02}}}\right)} The above formula holds as long as: μ 20 ′ − μ 02 ′ ≠ 0 {\displaystyle \mu '_{20}-\mu '_{02}\neq 0} The eigenvalues of the covariance matrix can easily be shown to be λ i = μ 20 ′ + μ 02 ′ 2 ± 4 μ ′ 11 2 + ( μ ′ 20 − μ ′ 02 ) 2 2 , {\displaystyle \lambda _{i}={\frac {\mu '_{20}+\mu '_{02}}{2}}\pm {\frac {\sqrt {4{\mu '}_{11}^{2}+({\mu '}_{20}-{\mu '}_{02})^{2}}}{2}},} and are proportional to the squared length of the eigenvector axes. The relative difference in magnitude of the eigenvalues are thus an indication of the eccentricity of the image, or how elongated it is. The eccentricity is 1 − λ 2 λ 1 . {\displaystyle {\sqrt {1-{\frac {\lambda _{2}}{\lambda _{1}}}}}.} == Moment invariants == Moments are well-known for their application in image analysis, since they can be used to derive invariants with respect to specific transformation classes. The term invariant moments is often abused in this context. However, while moment invariants are invariants that are formed from moments, the only moments that are invariants themselves are the central moments. Note that the invariants detailed below are exactly invariant only in the continuous domain. In a discrete domain, neither scaling nor rotation are well defined: a discrete image transformed in such a way is generally an approximation, and the transformation is not reversible. These invariants therefore are only approximately invariant when describing a shape in a discrete image. === Translation invariants === The central moments μi j of any order are, by construction, invariant with respect to translations. === Scale invariants === Invariants ηi j with respect to both translation and scale can be constructed from central moments by dividing through a properly scaled zero-th central moment: η i j = μ i j μ 00 ( 1 + i + j 2 ) {\displaystyle \eta _{ij}={\frac {\mu _{ij}}{\mu _{00}^{\left(1+{\frac {i+j}{2}}\right)}}}\,\!} where i + j ≥ 2. Note that translational invariance directly follows by only using central moments. === Rotation invariants === As shown in the work of Hu, invariants with respect to translation, scale, and rotation can be constructed: I 1 = η 20 + η 02 {\displaystyle I_{1}=\eta _{20}+\eta _{02}} I 2 = ( η 20 − η 02 ) 2 + 4 η 11 2 {\displaystyle I_{2}=(\eta _{20}-\eta _{02})^{2}+4\eta _{11}^{2}} I 3 = ( η 30 − 3 η 12 ) 2 + ( 3 η 21 − η 03 ) 2 {\displaystyle I_{3}=(\eta _{30}-3\eta _{12})^{2}+(3\eta _{21}-\eta _{03})^{2}} I 4 = ( η 30 + η 12 ) 2 + ( η 21 + η 03 ) 2 {\displaystyle I_{4}=(\eta _{30}+\eta _{12})^{2}+(\eta _{21}+\eta _{03})^{2}} I 5 = ( η 30 − 3 η 12 ) ( η 30 + η 12 ) [ ( η 30 + η 12 ) 2 − 3 ( η 21 + η 03 ) 2 ] + ( 3 η 21 − η 03 ) ( η 21 + η 03 ) [ 3 ( η 30 + η 12 ) 2 − ( η 21 + η 03 ) 2 ] {\displaystyle I_{5}=(\eta _{30}-3\eta _{12})(\eta _{30}+\eta _{12})[(\eta _{30}+\eta _{12})^{2}-3(\eta _{21}+\eta _{03})^{2}]+(3\eta _{21}-\eta _{03})(\eta _{21}+\eta _{03})[3(\eta _{30}+\eta _{12})^{2}-(\eta _{21}+\eta _{03})^{2}]} I 6 = ( η 20 − η 02 ) [ ( η 30 + η 12 ) 2 − ( η 21 + η 03 ) 2 ] + 4 η 11 ( η 30 + η 12 ) ( η 21 + η 03 ) {\displaystyle I_{6}=(\eta _{20}-\eta _{02})[(\eta _{30}+\eta _{12})^{2}-(\eta _{21}+\eta _{03})^{2}]+4\eta _{11}(\eta _{30}+\eta _{12})(\eta _{21}+\eta _{03})} I 7 = ( 3 η 21 − η 03 ) ( η 30 + η 12 ) [ ( η 30 + η 12 ) 2 − 3 ( η 21 + η 03 ) 2 ] − ( η 30 − 3 η 12 ) ( η 21 + η 03 ) [ 3 ( η 30 + η 12 ) 2 − ( η 21 + η 03 ) 2 ] . {\displaystyle I_{7}=(3\eta _{21}-\eta _{03})(\eta _{30}+\eta _{12})[(\eta _{30}+\eta _{12})^{2}-3(\eta _{21}+\eta _{03})^{2}]-(\eta _{30}-3\eta _{12})(\eta _{21}+\eta _{03})[3(\eta _{30}+\eta _{12})^{2}-(\eta _{21}+\eta _{03})^{2}].} These are well-known as Hu moment invariants. The first one, I1, is analogous to the moment of inertia around the image's centroid, where the pixels' intensities are analogous to physical density. The first six, I1 ... I6, are reflection symmetric, i.e. they are unchanged if the image is changed to a mirror image. The last one, I7, is reflection antisymmetric (changes sign under reflection), which enables it to distinguish mirror images of otherwise identical im
JotterPad
JotterPad is a text editor app for Android, developed by Two App Studio. It is proprietary software that uses the freemium pricing strategy. == Features == Jotterpad supports the markdown and fountain markup languages. Among its features are themes, synchronisation with Google Drive and Dropbox, dictionary and thesaurus, and snapshots. JotterPad uses a freemium pricing model, which means that a restricted version of the app is offered for free, while access to additional functionality requires payment. About half of the features are available in the free version. The synchronisation feature was originally limited to one account, and in Jotterpad 12 the option to synchronise using multiple accounts was added as a monthly subscription service.
Josh (app)
Josh (stylized as JOSH) was a video-sharing social networking service but it has since evolved into a live call and chat application owned by VerSe Innovation – an Indian technology company based in Bangalore, India. Josh was an Indian short video app that was launched in immediately after the Indian Government banned TikTok and other Chinese apps in June 2020. The founders of the platform have promoted the app as the “Instagram for Bharat” referring to their focus on the Indian audience that speaks its own regional and state languages. Josh was among the top 10 most downloaded apps social and entertainment apps in India of 2021 and had 150 million monthly active users as per April 2022. The word 'Josh' translates to fervour or passion. The app was launched under the aegis of the Atmanirbhar Bharat campaign and to compete with the duopoly of Google and Facebook in India. Josh's parent company VerSe Innovations Pvt. Ltd. owns another startup Dailyhunt, which a content and news aggregator application. Both Dailyhunt and Josh are a part of the VerSe's focus on the "next billion" regional language users of India. Founders Virendra Gupta and Umang Bedi conceptualised Josh as a short-video platform that made content creation accessible to vernacular language users, essentially the non-English speaking audience in India. == Features == Josh is currently available in 12 Indian languages and allows users to upload, share, remix bite-sized videos of up to 120 seconds. There are various categories across the video section including viral, trending, glamour, dance, devotion, yoga and cooking among others. Similar to Instagram and TikTok, it has a video feed which is curated for individuals on the basis of their app behaviour. The app hosts many daily, weekly and monthly social media challenges. == Funding == In December 2020, within 3 months of its launch, Josh's parent app VerSe Innovation raised more than $100 million from investors including Alphabet Inc's Google and Microsoft. In February 2021, VerSe Innovation raised $100 million in Series H funding from Qatar Investment Authority, the sovereign wealth fund of the State of Qatar, and Glade Brook Capital Partners. In August 2021, VerSe raised over $450 million in its Series I financing round with a valuation of $1 billion. Investors included Canada Pension Plan Investment Board (CPPIB), Siguler Guff, Baillie Gifford, Carlyle Asia Partners Growth II affiliates, and others. The startup announced its plan to expand overseas and broaden its ecommerce play for both Dailyhunt and Josh. In April 2022, VerSe announced that it has raised $805 million in funding from investors at a valuation of nearly $5 billion. ByteDance Offloads Stake In Josh Parent VerSe, Exits At 56% Discount == Partnerships == In February 2021, Saregama and Josh signed a music licensing deal, wherein Josh expanded its musical library with 1.3 lakh songs from Saregama in 25 different languages. To improve their user experience, Josh partnered with computer vision company D-ID in August 2021. The company helped Josh introduce photo-to-video features, live portrait technology, animate their photos etc. In order to solidify their efforts in enhancing Josh, VerSe acquired Indian social networking platform GolBol in October 2021. The move came as an effort by the startup to strengthen their discovery initiatives on the platform and classify content at scale and understand the core behaviour of Indian regional audiences. Josh has also announced its plans to include live commerce as a potential revenue stream through its partnership with multiple large e-commerce players. == Notable campaigns == Say No To Dowry – In association with Josh, the Kerala Police partook in the #SayNo2Dowry online social media campaign that was started to highlight and stop the social evil in the state. Salute India – Josh entered the Guinness World Records by creating the largest online video album of people saluting (29,529). It organised an online campaign #SaluteIndia on the app during the 75th Independence Day of India during 10–15 August 2021.
Image texture
An image texture is the small-scale structure perceived on an image, based on the spatial arrangement of color or intensities. It can be quantified by a set of metrics calculated in image processing. Image texture metrics give us information about the whole image or selected regions. Image textures can be artificially created or found in natural scenes captured in an image. Image textures are one way that can be used to help in segmentation or classification of images. For more accurate segmentation the most useful features are spatial frequency and an average grey level. To analyze an image texture in computer graphics, there are two ways to approach the issue: structured approach and statistical approach. == Structured approach == A structured approach sees an image texture as a set of primitive texels in some regular or repeated pattern. This works well when analyzing artificial textures. To obtain a structured description a characterization of the spatial relationship of the texels is gathered by using Voronoi tessellation of the texels. == Statistical approach == A statistical approach sees an image texture as a quantitative measure of the arrangement of intensities in a region. In general this approach is easier to compute and is more widely used, since natural textures are made of patterns of irregular subelements. === Edge detection === The use of edge detection is to determine the number of edge pixels in a specified region, helps determine a characteristic of texture complexity. After edges have been found the direction of the edges can also be applied as a characteristic of texture and can be useful in determining patterns in the texture. These directions can be represented as an average or in a histogram. Consider a region with N pixels. the gradient-based edge detector is applied to this region by producing two outputs for each pixel p: the gradient magnitude Mag(p) and the gradient direction Dir(p). The edgeness per unit area can be defined by F e d g e n e s s = | { p | M a g ( p ) > T } | N {\displaystyle F_{edgeness}={\frac {|\{p|Mag(p)>T\}|}{N}}} for some threshold T. To include orientation with edgeness histograms for both gradient magnitude and gradient direction can be used. Hmag(R) denotes the normalized histogram of gradient magnitudes of region R, and Hdir(R) denotes the normalized histogram of gradient orientations of region R. Both are normalized according to the size NR Then F m a g , d i r = ( H m a g ( R ) , H d i r ( R ) ) {\displaystyle F_{mag,dir}=(H_{mag}(R),H_{dir}(R))} is a quantitative texture description of region R. === Co-occurrence matrices === The co-occurrence matrix captures numerical features of a texture using spatial relations of similar gray tones. Numerical features computed from the co-occurrence matrix can be used to represent, compare, and classify textures. The following are a subset of standard features derivable from a normalized co-occurrence matrix: A n g u l a r 2 n d M o m e n t = ∑ i ∑ j p [ i , j ] 2 C o n t r a s t = ∑ i = 1 N g ∑ j = 1 N g n 2 p [ i , j ] , where | i − j | = n C o r r e l a t i o n = ∑ i = 1 N g ∑ j = 1 N g ( i j ) p [ i , j ] − μ x μ y σ x σ y E n t r o p y = − ∑ i ∑ j p [ i , j ] l n ( p [ i , j ] ) {\displaystyle {\begin{aligned}Angular{\text{ }}2nd{\text{ }}Moment&=\sum _{i}\sum _{j}p[i,j]^{2}\\Contrast&=\sum _{i=1}^{Ng}\sum _{j=1}^{Ng}n^{2}p[i,j]{\text{, where }}|i-j|=n\\Correlation&={\frac {\sum _{i=1}^{Ng}\sum _{j=1}^{Ng}(ij)p[i,j]-\mu _{x}\mu _{y}}{\sigma _{x}\sigma _{y}}}\\Entropy&=-\sum _{i}\sum _{j}p[i,j]ln(p[i,j])\\\end{aligned}}} where p [ i , j ] {\displaystyle p[i,j]} is the [ i , j ] {\displaystyle [i,j]} th entry in a gray-tone spatial dependence matrix, and Ng is the number of distinct gray-levels in the quantized image. One negative aspect of the co-occurrence matrix is that the extracted features do not necessarily correspond to visual perception. It is used in dentistry for the objective evaluation of lesions [DOI: 10.1155/2020/8831161], treatment efficacy [DOI: 10.3390/ma13163614; DOI: 10.11607/jomi.5686; DOI: 10.3390/ma13173854; DOI: 10.3390/ma13132935] and bone reconstruction during healing [DOI: 10.5114/aoms.2013.33557; DOI: 10.1259/dmfr/22185098; EID: 2-s2.0-81455161223; DOI: 10.3390/ma13163649]. === Laws texture energy measures === Another approach is to use local masks to detect various types of texture features. Laws originally used four vectors representing texture features to create sixteen 2D masks from the outer products of the pairs of vectors. The four vectors and relevant features were as follows: L5 = [ +1 +4 6 +4 +1 ] (Level) E5 = [ -1 -2 0 +2 +1 ] (Edge) S5 = [ -1 0 2 0 -1 ] (Spot) R5 = [ +1 -4 6 -4 +1 ] (Ripple) To these 4, a fifth is sometimes added: W5 = [ -1 +2 0 -2 +1 ] (Wave) From Laws' 4 vectors, 16 5x5 "energy maps" are then filtered down to 9 in order to remove certain symmetric pairs. For instance, L5E5 measures vertical edge content and E5L5 measures horizontal edge content. The average of these two measures is the "edginess" of the content. The resulting 9 maps used by Laws are as follows: L5E5/E5L5 L5R5/R5L5 E5S5/S5E5 S5S5 R5R5 L5S5/S5L5 E5E5 E5R5/R5E5 S5R5/R5S5 Running each of these nine maps over an image to create a new image of the value of the origin ([2,2]) results in 9 "energy maps," or conceptually an image with each pixel associated with a vector of 9 texture attributes. === Autocorrelation and power spectrum === The autocorrelation function of an image can be used to detect repetitive patterns of textures. == Texture segmentation == The use of image texture can be used as a description for regions into segments. There are two main types of segmentation based on image texture, region based and boundary based. Though image texture is not a perfect measure for segmentation it is used along with other measures, such as color, that helps solve segmenting in image. === Region based === Attempts to group or cluster pixels based on texture properties. === Boundary based === Attempts to group or cluster pixels based on edges between pixels that come from different texture properties.
Flexidraw
Flexidraw is a 1985 graphics computer program published by Inkwell Systems. == Gameplay == Flexidraw is a graphics program that allows users to produce drawings using a light pen and print them. == Reception == Roy Wagner reviewed the product for Computer Gaming World, and stated that "Of the many graphics programs available Flexidraw is certainly the best supported by it's [sic] parent company."
Space partitioning
In geometry, space partitioning is the process of dividing an entire space (usually a Euclidean space) into two or more disjoint subsets (see also partition of a set). In other words, space partitioning divides a space into non-overlapping regions. Any point in the space can then be identified to lie in exactly one of the regions. == Overview == Space-partitioning systems are often hierarchical, meaning that a space (or a region of space) is divided into several regions, and then the same space-partitioning system is recursively applied to each of the regions thus created. The regions can be organized into a tree, called a space-partitioning tree. Most space-partitioning systems use planes (or, in higher dimensions, hyperplanes) to divide space: points on one side of the plane form one region, and points on the other side form another. Points exactly on the plane are usually arbitrarily assigned to one or the other side. Recursively partitioning space using planes in this way produces a BSP tree, one of the most common forms of space partitioning. == Uses == === In computer graphics === Space partitioning is particularly important in computer graphics, especially heavily used in ray tracing, where it is frequently used to organize the objects in a virtual scene. A typical scene may contain millions of polygons. Performing a ray/polygon intersection test with each would be a very computationally expensive task. Storing objects in a space-partitioning data structure (k-d tree or BSP tree for example) makes it easy and fast to perform certain kinds of geometry queries—for example in determining whether a ray intersects an object, space partitioning can reduce the number of intersection test to just a few per primary ray, yielding a logarithmic time complexity with respect to the number of polygons. Space partitioning is also often used in scanline algorithms to eliminate the polygons out of the camera's viewing frustum, limiting the number of polygons processed by the pipeline. There is also a usage in collision detection: determining whether two objects are close to each other can be much faster using space partitioning. === In integrated circuit design === In integrated circuit design, an important step is design rule check. This step ensures that the completed design is manufacturable. The check involves rules that specify widths and spacings and other geometry patterns. A modern design can have billions of polygons that represent wires and transistors. Efficient checking relies heavily on geometry query. For example, a rule may specify that any polygon must be at least n nanometers from any other polygon. This is converted into a geometry query by enlarging a polygon by n/2 at all sides and query to find all intersecting polygons. === In probability and statistical learning theory === The number of components in a space partition plays a central role in some results in probability theory. See Growth function for more details. === In geography and GIS === There are many studies and applications where Geographical Spatial Reality is partitioned by hydrological criteria, administrative criteria, mathematical criteria or many others. In the context of cartography and GIS - Geographic Information System, is common to identify cells of the partition by standard codes. For example the for HUC code identifying hydrographical basins and sub-basins, ISO 3166-2 codes identifying countries and its subdivisions, or arbitrary DGGs - discrete global grids identifying quadrants or locations. == Data structures == Common space-partitioning systems include: BSP trees Quadtrees Octrees k-d trees Bins == Number of components == Suppose the n-dimensional Euclidean space is partitioned by r {\displaystyle r} hyperplanes that are ( n − 1 ) {\displaystyle (n-1)} -dimensional. What is the number of components in the partition? The largest number of components is attained when the hyperplanes are in general position, i.e, no two are parallel and no three have the same intersection. Denote this maximum number of components by C o m p ( n , r ) {\displaystyle Comp(n,r)} . Then, the following recurrence relation holds: C o m p ( n , r ) = C o m p ( n , r − 1 ) + C o m p ( n − 1 , r − 1 ) {\displaystyle Comp(n,r)=Comp(n,r-1)+Comp(n-1,r-1)} C o m p ( 0 , r ) = 1 {\displaystyle Comp(0,r)=1} - when there are no dimensions, there is a single point. C o m p ( n , 0 ) = 1 {\displaystyle Comp(n,0)=1} - when there are no hyperplanes, all the space is a single component. And its solution is: C o m p ( n , r ) = ∑ k = 0 n ( r k ) {\displaystyle Comp(n,r)=\sum _{k=0}^{n}{r \choose k}} if r ≥ n {\displaystyle r\geq n} C o m p ( n , r ) = 2 r {\displaystyle Comp(n,r)=2^{r}} if r ≤ n {\displaystyle r\leq n} (consider e.g. r {\displaystyle r} perpendicular hyperplanes; each additional hyperplane divides each existing component to 2). which is upper-bounded as: C o m p ( n , r ) ≤ r n + 1 {\displaystyle Comp(n,r)\leq r^{n}+1}