Letter frequency is the number of times letters of the alphabet appear on average in written language. Letter frequency analysis dates back to the Arab mathematician Al-Kindi (c. AD 801–873), who formally developed the method to break ciphers. Letter frequency analysis gained importance in Europe with the development of movable type in AD 1450, wherein one must estimate the amount of type required for each letterform. Linguists use letter frequency analysis as a rudimentary technique for language identification, where it is particularly effective as an indication of whether an unknown writing system is alphabetic, syllabic, or logographic. The use of letter frequencies and frequency analysis plays a fundamental role in cryptograms and several word puzzle games, including hangman, Scrabble, Wordle and the television game show Wheel of Fortune. One of the earliest descriptions in classical literature of applying the knowledge of English letter frequency to solving a cryptogram is found in Edgar Allan Poe's famous story "The Gold-Bug", where the method is successfully applied to decipher a message giving the location of a treasure hidden by Captain Kidd. Herbert S. Zim, in his classic introductory cryptography text Codes and Secret Writing, gives the English letter frequency sequence as "ETAON RISHD LFCMU GYPWB VKJXZQ", the most common letter pairs as "TH HE AN RE ER IN ON AT ND ST ES EN OF TE ED OR TI HI AS TO", and the most common doubled letters as "LL EE SS OO TT FF RR NN PP CC". Different ways of counting can produce somewhat different orders. Letter frequencies also have a strong effect on the design of some keyboard layouts. The most frequent letters are placed on the home row of the Blickensderfer typewriter, the Dvorak keyboard layout, Colemak and other optimized layouts, while the commonly used QWERTY layout places common letters apart from each other to prevent typewriter jamming. == Background == The frequency of letters in text has been studied for use in cryptanalysis, and frequency analysis in particular, dating back to the Arab mathematician al-Kindi (c. AD 801–873 ), who formally developed the method (the ciphers breakable by this technique go back at least to the Caesar cipher used by Julius Caesar, so this method could have been explored in classical times). Letter frequency analysis gained additional importance in Europe with the development of movable type in AD 1450, wherein one must estimate the amount of type required for each letterform, as evidenced by the variations in letter compartment size in typographer's type cases. No exact letter frequency distribution underlies a given language, since all writers write slightly differently. However, most languages have a characteristic distribution which is strongly apparent in longer texts. Even language changes as extreme as from Old English to modern English (regarded as mutually unintelligible) show strong trends in related letter frequencies: over a small sample of Biblical passages, from most frequent to least frequent, enaid sorhm tgþlwu æcfy ðbpxz of Old English compares to eotha sinrd luymw fgcbp kvjqxz of modern English, with the most extreme differences concerning letterforms not shared. Linotype machines for the English language assumed the letter order, from most to least common, to be etaoin shrdlu cmfwyp vbgkqj xz based on the experience and custom of manual compositors. The equivalent for the French language was elaoin sdrétu cmfhyp vbgwqj xz. Arranging the alphabet in Morse into groups of letters that require equal amounts of time to transmit, and then sorting these groups in increasing order, yields e it san hurdm wgvlfbk opxcz jyq. Letter frequency was used by other telegraph systems, such as the Murray Code. Similar ideas are used in modern data-compression techniques such as Huffman coding. Letter frequencies, like word frequencies, tend to vary, both by writer and by subject. For instance, ⟨d⟩ occurs with greater frequency in fiction, as most fiction is written in past tense and thus most verbs will end in the inflectional suffix -ed / -d. One cannot write an essay about x-rays without using ⟨x⟩ frequently, and the essay will have an idiosyncratic letter frequency if the essay is about, say, Queen Zelda of Zanzibar requesting X-rays from Qatar to examine hypoxia in zebras. Different authors have habits which can be reflected in their use of letters. Hemingway's writing style, for example, is visibly different from Faulkner's. Letter, bigram, trigram, word frequencies, word length, and sentence length can be calculated for specific authors and used to prove or disprove authorship of texts, even for authors whose styles are not so divergent. Accurate average letter frequencies can only be gleaned by analyzing a large amount of representative text. With the availability of modern computing and collections of large text corpora, such calculations are easily made. Examples can be drawn from a variety of sources (press reporting, religious texts, scientific texts and general fiction) and there are differences especially for general fiction with the position of ⟨h⟩ and ⟨i⟩, with ⟨h⟩ becoming more common. Different dialects of a language will also affect a letter's frequency. For example, an author in the United States would produce something in which ⟨z⟩ is more common than an author in the United Kingdom writing on the same topic: words like "analyze", "apologize", and "recognize" contain the letter in American English, whereas the same words are spelled "analyse", "apologise", and "recognise" in British English. This would highly affect the frequency of the letter ⟨z⟩, as it is rarely used by British writers in the English language. The "top twelve" letters constitute about 80% of the total usage. The "top eight" letters constitute about 65% of the total usage. Letter frequency as a function of rank can be fitted well by several rank functions, with the two-parameter Cocho/Beta rank function being the best. Another rank function with no adjustable free parameter also fits the letter frequency distribution reasonably well (the same function has been used to fit the amino acid frequency in protein sequences.) A spy using the VIC cipher or some other cipher based on a straddling checkerboard typically uses a mnemonic such as "a sin to err" (dropping the second "r") or "at one sir" to remember the top eight characters. == Relative frequencies of letters in the English language == There are three ways to count letter frequency that result in very different charts for common letters. The first method, used in the chart below, is to count letter frequency in lemmas of a dictionary. The lemma is the word in its canonical form. The second method is to include all word variants when counting, such as "abstracts", "abstracted" and "abstracting" and not just the lemma of "abstract". This second method results in letters like ⟨s⟩ appearing much more frequently, such as when counting letters from lists of the most used English words on the Internet. ⟨s⟩ is especially common in inflected words (non-lemma forms) because it is added to form plurals and third person singular present tense verbs. A final method is to count letters based on their frequency of use in actual texts, resulting in certain letter combinations like ⟨th⟩ becoming more common due to the frequent use of common words like "the", "then", "both", "this", etc. Absolute usage frequency measures like this are used when creating keyboard layouts or letter frequencies in old fashioned printing presses. An analysis of entries in the Concise Oxford dictionary, ignoring frequency of word use, gives an order of "EARIOTNSLCUDPMHGBFYWKVXZJQ". The letter-frequency table above is taken from Pavel Mička's website, which cites Robert Lewand's Cryptological Mathematics. According to Lewand, arranged from most to least common in appearance, the letters are: etaoinshrdlcumwfgypbvkjxqz. Lewand's ordering differs slightly from others, such as Cornell University Math Explorer's Project, which produced a table after measuring 40,000 words. In English, the space character occurs almost twice as frequently as the top letter (⟨e⟩) and the non-alphabetic characters (digits, punctuation, etc.) collectively occupy the fourth position (having already included the space) between ⟨t⟩ and ⟨a⟩. == Relative frequencies of the first letters of a word in the English language == The frequency of the first letters of words or names is helpful in pre-assigning space in physical files and indexes. Given 26 filing cabinet drawers, rather than a 1:1 assignment of one drawer to one letter of the alphabet, it is often useful to use a more equal-frequency-letter code by assigning several low-frequency letters to the same drawer (often one drawer is labeled VWXYZ), and to split up the most-frequent initial letters (⟨s, a, c⟩) into several drawers (often 6 drawers Aa-An, Ao-Az, Ca-Cj, Ck-Cz, Sa-Si, Sj-Sz). The same system is used in some mult
Test data
Test data are sets of inputs or information used to verify the correctness, performance, and reliability of software systems. Test data encompass various types, such as positive and negative scenarios, edge cases, and realistic user scenarios, and aims to exercise different aspects of the software to uncover bugs and validate its behavior. Test data is also used in regression testing to verify that new code changes or enhancements do not introduce unintended side effects or break existing functionalities. == Background == Test data may be used to verify that a given set of inputs to a function produces an expected result. Alternatively, data can be used to challenge the program's ability to handle unusual, extreme, exceptional, or unexpected inputs. Test data can be produced in a focused or systematic manner, as is typically the case in domain testing, or through less focused approaches, such as high-volume randomized automated tests. Test data can be generated by the tester or by a program or function that assists the tester. It can be recorded for reuse or used only once. Test data may be created manually, using data generation tools (often based on randomness), or retrieved from an existing production environment. The data set may consist of synthetic (fake) data, but ideally, it should include representative (real) data. == Limitations == Due to privacy regulations such as GDPR, PCI, and the HIPAA, the use of privacy-sensitive personal data for testing is restricted. However, anonymized (and preferably subsetted) production data may be used as representative data for testing and development. Programmers may also choose to generate synthetic data as an alternative to using real or anonymized data. While synthetic data can offer significant advantages, such as enhanced privacy and flexibility, it also comes with limitations. For instance, generating synthetic data that accurately reflects real-world complexity can be challenging. There is also a risk of synthetic data not fully capturing the nuances of real data, potentially leading to gaps in test coverage. == Domain testing == Domain testing is a set of techniques focusing on test data. This includes identifying critical inputs, values at the boundaries between equivalence classes, and combinations of inputs that drive the system toward specific outputs. Domain testing helps ensure that various scenarios are effectively tested, including edge cases and unusual conditions.
Spectral shape analysis
Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under isometries, it is well suited for the analysis or retrieval of non-rigid shapes, i.e. bendable objects such as humans, animals, plants, etc. == Laplace == The Laplace–Beltrami operator is involved in many important differential equations, such as the heat equation and the wave equation. It can be defined on a Riemannian manifold as the divergence of the gradient of a real-valued function f: Δ f := div grad f . {\displaystyle \Delta f:=\operatorname {div} \operatorname {grad} f.} Its spectral components can be computed by solving the Helmholtz equation (or Laplacian eigenvalue problem): Δ φ i + λ i φ i = 0. {\displaystyle \Delta \varphi _{i}+\lambda _{i}\varphi _{i}=0.} The solutions are the eigenfunctions φ i {\displaystyle \varphi _{i}} (modes) and corresponding eigenvalues λ i {\displaystyle \lambda _{i}} , representing a diverging sequence of positive real numbers. The first eigenvalue is zero for closed domains or when using the Neumann boundary condition. For some shapes, the spectrum can be computed analytically (e.g. rectangle, flat torus, cylinder, disk or sphere). For the sphere, for example, the eigenfunctions are the spherical harmonics. The most important properties of the eigenvalues and eigenfunctions are that they are isometry invariants. In other words, if the shape is not stretched (e.g. a sheet of paper bent into the third dimension), the spectral values will not change. Bendable objects, like animals, plants and humans, can move into different body postures with only minimal stretching at the joints. The resulting shapes are called near-isometric and can be compared using spectral shape analysis. == Discretizations == Geometric shapes are often represented as 2D curved surfaces, 2D surface meshes (usually triangle meshes) or 3D solid objects (e.g. using voxels or tetrahedra meshes). The Helmholtz equation can be solved for all these cases. If a boundary exists, e.g. a square, or the volume of any 3D geometric shape, boundary conditions need to be specified. Several discretizations of the Laplace operator exist (see Discrete Laplace operator) for the different types of geometry representations. Many of these operators do not approximate well the underlying continuous operator. == Spectral shape descriptors == === ShapeDNA and its variants === The ShapeDNA is one of the first spectral shape descriptors. It is the normalized beginning sequence of the eigenvalues of the Laplace–Beltrami operator. Its main advantages are the simple representation (a vector of numbers) and comparison, scale invariance, and in spite of its simplicity a very good performance for shape retrieval of non-rigid shapes. Competitors of shapeDNA include singular values of Geodesic Distance Matrix (SD-GDM) and Reduced BiHarmonic Distance Matrix (R-BiHDM). However, the eigenvalues are global descriptors, therefore the shapeDNA and other global spectral descriptors cannot be used for local or partial shape analysis. === Global point signature (GPS) === The global point signature at a point x {\displaystyle x} is a vector of scaled eigenfunctions of the Laplace–Beltrami operator computed at x {\displaystyle x} (i.e. the spectral embedding of the shape). The GPS is a global feature in the sense that it cannot be used for partial shape matching. === Heat kernel signature (HKS) === The heat kernel signature makes use of the eigen-decomposition of the heat kernel: h t ( x , y ) = ∑ i = 0 ∞ exp ( − λ i t ) φ i ( x ) φ i ( y ) . {\displaystyle h_{t}(x,y)=\sum _{i=0}^{\infty }\exp(-\lambda _{i}t)\varphi _{i}(x)\varphi _{i}(y).} For each point on the surface the diagonal of the heat kernel h t ( x , x ) {\displaystyle h_{t}(x,x)} is sampled at specific time values t j {\displaystyle t_{j}} and yields a local signature that can also be used for partial matching or symmetry detection. === Wave kernel signature (WKS) === The WKS follows a similar idea to the HKS, replacing the heat equation with the Schrödinger wave equation. === Improved wave kernel signature (IWKS) === The IWKS improves the WKS for non-rigid shape retrieval by introducing a new scaling function to the eigenvalues and aggregating a new curvature term. === Spectral graph wavelet signature (SGWS) === SGWS is a local descriptor that is not only isometric invariant, but also compact, easy to compute and combines the advantages of both band-pass and low-pass filters. An important facet of SGWS is the ability to combine the advantages of WKS and HKS into a single signature, while allowing a multiresolution representation of shapes. == Spectral Matching == The spectral decomposition of the graph Laplacian associated with complex shapes (see Discrete Laplace operator) provides eigenfunctions (modes) which are invariant to isometries. Each vertex on the shape could be uniquely represented with a combinations of the eigenmodal values at each point, sometimes called spectral coordinates: s ( x ) = ( φ 1 ( x ) , φ 2 ( x ) , … , φ N ( x ) ) for vertex x . {\displaystyle s(x)=(\varphi _{1}(x),\varphi _{2}(x),\ldots ,\varphi _{N}(x)){\text{ for vertex }}x.} Spectral matching consists of establishing the point correspondences by pairing vertices on different shapes that have the most similar spectral coordinates. Early work focused on sparse correspondences for stereoscopy. Computational efficiency now enables dense correspondences on full meshes, for instance between cortical surfaces. Spectral matching could also be used for complex non-rigid image registration, which is notably difficult when images have very large deformations. Such image registration methods based on spectral eigenmodal values indeed capture global shape characteristics, and contrast with conventional non-rigid image registration methods which are often based on local shape characteristics (e.g., image gradients).
Video browsing
Video browsing, also known as exploratory video search, is the interactive process of skimming through video content in order to satisfy some information need or to interactively check if the video content is relevant. While originally proposed to help users inspecting a single video through visual thumbnails, modern video browsing tools enable users to quickly find desired information in a video archive by iterative human–computer interaction through an exploratory search approach. Many of these tools presume a smart user that wants features to interactively inspect video content, as well as automatic content filtering features. For that purpose, several video interaction features are usually provided, such as sophisticated navigation in video or search by a content-based query. Video browsing tools often build on lower-level video content analysis, such as shot transition detection, keyframe extraction, semantic concept detection, and create a structured content overview of the video file or video archive. Furthermore, they usually provide sophisticated navigation features, such as advanced timelines, visual seeker bars or a list of selected thumbnails, as well as means for content querying. Examples of content queries are shot filtering through visual concepts (e.g., only shots showing cars), through some specific characteristics (e.g., color or motion filtering), through user-provided sketches (e.g., a visually drawn sketch), or through content-based similarity search. == History == Video browsing was originally proposed by Iranian engineer Farshid Arman, Taiwanese computer scientist Arding Hsu, and computer scientist Ming-Yee Chiu, while working at Siemens, and it was presented at the ACM International Conference in August 1993. They described a shot detection algorithm for compressed video that was originally encoded with discrete cosine transform (DCT) video coding standards such as JPEG, MPEG and H.26x. The basic idea was that, since the DCT coefficients are mathematically related to the spatial domain and represent the content of each frame, they can be used to detect the differences between video frames. In the algorithm, a subset of blocks in a frame and a subset of DCT coefficients for each block are used as motion vector representation for the frame. By operating on compressed DCT representations, the algorithm significantly reduces the computational requirements for decompression and enables effective video browsing. The algorithm represents separate shots of a video sequence by an r-frame, a thumbnail of the shot framed by a motion tracking region. A variation of this concept was later adopted for QBIC video content mosaics, where each r-frame is a salient still from the shot it represents. === Video Notebook === Modern video browsing solutions include Video Notebook, a Menlo Park startup founded in 2021 by Mike Lanza, which uses computer vision to extract slides and optical character recognition and speech recognition to facilitate video search. The software can be either used on the client side (using a browser extension), where the slides and text are extracted while the video is watched (e.g. on a video platform like YouTube or Udemy), or on the server side. Processed videos, which can be viewed in the Video Notebook web app, feature a video browsing user interface with extracted timestamped slides, a search bar for querying the video (or a collection of videos), and text chapters. Video Notebook customers include organisations like Ernst & Young. === Video Browser Showdown === The Video Browser Showdown (VBS) is an annual live evaluation competition for exploratory video search tools, where international researchers use video browsing tools to solve ad-hoc video search tasks on a moderately large data set as fast as possible. The main goal of the VBS, which started in 2012 at the International Conference on MultiMedia Modeling (MMM), is to advance the performance of video browsing tools. Since 2016, the VBS also collaborates with TRECVID. The aim of the VBS is to evaluate video browsing tools for efficiency at known-item search (KIS) tasks with a well-defined data set in direct comparison to other tools.
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.
Line integral convolution
In scientific visualization, line integral convolution (LIC) is a method to visualize a vector field (such as fluid motion) at high spatial resolutions. The LIC technique was first proposed by Brian Cabral and Leith Casey Leedom in 1993. In LIC, discrete numerical line integration is performed along the field lines (curves) of the vector field on a uniform grid. The integral operation is a convolution of a filter kernel and an input texture, often white noise. In signal processing, this process is known as a discrete convolution. == Overview == Traditional visualizations of vector fields use small arrows or lines to represent vector direction and magnitude. This method has a low spatial resolution, which limits the density of presentable data and risks obscuring characteristic features in the data. More sophisticated methods, such as streamlines and particle tracing techniques, can be more revealing but are highly dependent on proper seed points. Texture-based methods, like LIC, avoid these problems since they depict the entire vector field at point-like (pixel) resolution. Compared to other integration-based techniques that compute field lines of the input vector field, LIC has the advantage that all structural features of the vector field are displayed, without the need to adapt the start and end points of field lines to the specific vector field. In other words, it shows the topology of the vector field. In user testing, LIC was found to be particularly good for identifying critical points. == Algorithm == === Informal description === LIC causes output values to be strongly correlated along the field lines, but uncorrelated in orthogonal directions. As a result, the field lines contrast each other and stand out visually from the background. Intuitively, the process can be understood with the following example: the flow of a vector field can be visualized by overlaying a fixed, random pattern of dark and light paint. As the flow passes by the paint, the fluid picks up some of the paint's color, averaging it with the color it has already acquired. The result is a randomly striped, smeared texture where points along the same streamline tend to have a similar color. Other physical examples include: whorl patterns of paint, oil, or foam on a river visualisation of magnetic field lines using randomly distributed iron filings fine sand being blown by strong wind === Formal mathematical description === Although the input vector field and the result image are discretized, it pays to look at it from a continuous viewpoint. Let v {\displaystyle \mathbf {v} } be the vector field given in some domain Ω {\displaystyle \Omega } . Although the input vector field is typically discretized, we regard the field v {\displaystyle \mathbf {v} } as defined in every point of Ω {\displaystyle \Omega } , i.e. we assume an interpolation. Streamlines, or more generally field lines, are tangent to the vector field in each point. They end either at the boundary of Ω {\displaystyle \Omega } or at critical points where v = 0 {\displaystyle \mathbf {v} =\mathbf {0} } . For the sake of simplicity, critical points and boundaries are ignored in the following. A field line σ {\displaystyle {\boldsymbol {\sigma }}} , parametrized by arc length s {\displaystyle s} , is defined as d σ ( s ) d s = v ( σ ( s ) ) | v ( σ ( s ) ) | . {\displaystyle {\frac {d{\boldsymbol {\sigma }}(s)}{ds}}={\frac {\mathbf {v} ({\boldsymbol {\sigma }}(s))}{|\mathbf {v} ({\boldsymbol {\sigma }}(s))|}}.} Let σ r ( s ) {\displaystyle {\boldsymbol {\sigma }}_{\mathbf {r} }(s)} be the field line that passes through the point r {\displaystyle \mathbf {r} } for s = 0 {\displaystyle s=0} . Then the image gray value at r {\displaystyle \mathbf {r} } is set to D ( r ) = ∫ − L / 2 L / 2 k ( s ) N ( σ r ( s ) ) d s {\displaystyle D(\mathbf {r} )=\int _{-L/2}^{L/2}k(s)N({\boldsymbol {\sigma }}_{\mathbf {r} }(s))ds} where k ( s ) {\displaystyle k(s)} is the convolution kernel, N ( r ) {\displaystyle N(\mathbf {r} )} is the noise image, and L {\displaystyle L} is the length of field line segment that is followed. D ( r ) {\displaystyle D(\mathbf {r} )} has to be computed for each pixel in the LIC image. If carried out naively, this is quite expensive. First, the field lines have to be computed using a numerical method for solving ordinary differential equations, like a Runge–Kutta method, and then for each pixel the convolution along a field line segment has to be calculated. The final image will normally be colored in some way. Typically, some scalar field in Ω {\displaystyle \Omega } (like the vector length) is used to determine the hue, while the grayscale LIC output determines the brightness. Different choices of convolution kernels and random noise produce different textures; for example, pink noise produces a cloudy pattern where areas of higher flow stand out as smearing, suitable for weather visualization. Further refinements in the convolution can improve the quality of the image. === Programming description === Algorithmically, LIC takes a vector field and noise texture as input, and outputs a texture. The process starts by generating in the domain of the vector field a random gray level image at the desired output resolution. Then, for every pixel in this image, the forward and backward streamline of a fixed arc length is calculated. The value assigned to the current pixel is computed by a convolution of a suitable convolution kernel with the gray levels of all the noise pixels lying on a segment of this streamline. This creates a gray level LIC image. == Versions == === Basic === Basic LIC images are grayscale images, without color and animation. While such LIC images convey the direction of the field vectors, they do not indicate orientation; for stationary fields, this can be remedied by animation. Basic LIC images do not show the length of the vectors (or the strength of the field). === Color === The length of the vectors (or the strength of the field) is usually coded in color; alternatively, animation can be used. === Animation === LIC images can be animated by using a kernel that changes over time. Samples at a constant time from the streamline would still be used, but instead of averaging all pixels in a streamline with a static kernel, a ripple-like kernel constructed from a periodic function multiplied by a Hann function acting as a window (in order to prevent artifacts) is used. The periodic function is then shifted along the period to create an animation. === Fast LIC (FLIC) === The computation can be significantly accelerated by re-using parts of already computed field lines, specializing to a box function as convolution kernel k ( s ) {\displaystyle k(s)} and avoiding redundant computations during convolution. The resulting fast LIC method can be generalized to convolution kernels that are arbitrary polynomials. === Oriented Line Integral Convolution (OLIC) === Because LIC does not encode flow orientation, it cannot distinguish between streamlines of equal direction but opposite orientation. Oriented Line Integral Convolution (OLIC) solves this issue by using a ramp-like asymmetric kernel and a low-density noise texture. The kernel asymmetrically modulates the intensity along the streamline, producing a trace that encodes orientation; the low-density of the noise texture prevents smeared traces from overlapping, aiding readability. Fast Rendering of Oriented Line Integral Convolution (FROLIC) is a variation that approximates OLIC by rendering each trace in discrete steps instead of as a continuous smear. === Unsteady Flow LIC (UFLIC) === For time-dependent vector fields (unsteady flow), a variant called Unsteady Flow LIC has been designed that maintains the coherence of the flow animation. An interactive GPU-based implementation of UFLIC has been presented. === Parallel === Since the computation of an LIC image is expensive but inherently parallel, the process has been parallelized and, with availability of GPU-based implementations, interactive on PCs. === Multidimensional === Note that the domain Ω {\displaystyle \Omega } does not have to be a 2D domain: the method is applicable to higher dimensional domains using multidimensional noise fields. However, the visualization of the higher-dimensional LIC texture is problematic; one way is to use interactive exploration with 2D slices that are manually positioned and rotated. The domain Ω {\displaystyle \Omega } does not have to be flat either; the LIC texture can be computed also for arbitrarily shaped 2D surfaces in 3D space. == Applications == This technique has been applied to a wide range of problems since it first was published in 1993, both scientific and creative, including: Representing vector fields: visualization of steady (time-independent) flows (streamlines) visual exploration of 2D autonomous dynamical systems wind mapping water flow mapping Artistic effects for image generation and stylization: pencil drawing (auto
Clip Studio Paint
Clip Studio Paint (previously marketed as Manga Studio in North America), informally known in Japan as Kurisuta (クリスタ), is a family of software applications developed by Japanese graphics software company Celsys. It is used for the digital creation of comics, general illustration, and 2D animation. The software is available in versions for macOS, Windows, iOS, iPadOS, Android, and ChromeOS. The program is widely used by amateur and professional comics creators, and animation studios. The application is sold in editions with varying feature sets. The full-featured edition is a page-based, layered drawing program, with support for bitmap and vector art, text, imported 3D models, and frame-by-frame animation. It is designed for use with a stylus and a graphics tablet or tablet computer. It has drawing tools which emulate natural media such as pencils, ink pens, and brushes, as well as patterns and decorations. It is distinguished from similar programs by features designed for creating comics: tools for creating panel layouts, perspective rulers, sketching, inking, applying tones and textures, coloring, and creating word balloons and captions. == History == The application has it origins in a program for macOS and Windows, released in Japan in 2001 as "Comic Studio". It was sold as "Manga Studio" in the Western market by E Frontier America until 2007, then by Smith Micro Software. Early versions were designed for creating black and white art with only spot color (a typical format for Japanese manga), with version 4 adding support for full-color art. Celsys developed Clip Studio Paint as a replacement for this product, based on the company's Illust Studio application, and it was released on May 31, 2012. It was initially distributed in Western markets as "Manga Studio 5", but in 2016, the branding was unified worldwide as "Clip Studio Paint". At this time, version 1.5.4 introduced a new file format (extension .clip) and frame-by-frame animation. In late 2017, Celsys took over direct support for the software worldwide, and ceased its relationship with Smith Micro. In July 2018, Celsys began a partnership with Graphixly for distribution in North America, South America, and Europe. Clip Studio Paint for the Apple iPad was introduced in November 2017, and for the iPhone in December 2019. Clip Studio Paint for Samsung Galaxy tablets and smartphones was released in August 2020 on the Galaxy Store, with versions for other Android devices and Chromebooks released in December. The Windows and macOS versions of the software have been sold and distributed either from the developer's web site or on DVD, and purchased either with a perpetual license or an ongoing subscription. The versions for iPhone, iPad, and Android-based devices are distributed through the corresponding app stores free of charge, but require a subscription – which includes cloud storage – for unrestricted use. Without a subscription, the tablet versions can be used only for a specified number of months, and the phone versions can be used only for 30 hours per month. From 2013 to 2023, regular updates for version 1 were distributed free of additional charge to both perpetual and subscription users. Since the release of version 2 in 2023, feature updates are included only in subscription plans and are available to perpetual licenses at an additional cost. Perpetual licenses can be upgraded permanently or with an annual "update pass". The "update pass" provides early access to features to be included in subsequent perpetual licenses for 12 months, after which the software reverts to the original license if not renewed. In March 2024, version 3 was released, and version 4 introduced additional features in March 2025. == Editions == Clip Studio Paint is available in three editions, with differing feature sets and prices: Debut (bundle-only grade), Pro (adding support for vector-based drawing, custom textures, and comics-focused features), and EX (adding support for multi-page documents, book exporting, and 2D animation). Companion programs include Clip Studio (for managing and sharing digital assets distributed through the Clip Studio web site, managing licenses, and getting updates and support) and Clip Studio Modeler (for setting up 3D materials to use in Clip Studio Paint).