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  List of data science software

  This is a list of data science software and platforms used in data science, which includes programming languages, programming environments, machine learning frameworks, data engineering tools, statistical software, data analysis, plotting, MLOps systems, and more. == Programming languages == == Development environments == These interactive notebooks, IDEs, and platforms provide specialised development environments. Apache Zeppelin Architect — Eclipse (software) CoCalc Dataiku Data Science Studio FreeMat GNU Octave Google Colab DataSpell Jupyter Notebook / JupyterLab Kaggle Notebooks MATLAB O-Matrix PyCharm RStudio SAS (software) and SAS Studio Spyder Visual Studio Code == Machine and deep learning software == The Machine learning / deep learning tools support development in those fields. == Data engineering == Examples of Data engineering tools. Apache Airflow Apache Flink Apache Hadoop Apache Kafka Apache NiFi Apache Spark Dask Data build tool (dbt) == Data mining == Examples of Data mining tools. === Free and open-source === === Proprietary === == Database management == === List of RDBMS === ==== Proprietary ==== == Data warehouses == Data warehouse environments include: Amazon Redshift Snowflake Google BigQuery Microsoft Azure Synapse Teradata Vertica == Data lakes == Data lake environments include: Apache Hadoop Cloudera Databricks Delta Lake Amazon S3 Google Cloud Storage Azure Data Lake == Algorithms == Apriori algorithm – frequent itemset mining and association rule learning in market basket analysis Backpropagation – algorithm for training artificial neural networks using gradient descent Decision Trees – tree-based algorithm for classification and regression Expectation–maximization algorithm – iterative procedure for maximum likelihood estimation with latent variables Gradient descent – iterative optimization algorithm for minimizing a loss function ID3 algorithm – used to generate a decision tree from a dataset K-Means – clustering algorithm based on minimizing within-cluster distances K-Nearest Neighbors (KNN) – instance-based learning and classification method Linear regression – estimation method for predicting a dependent variable based on independent variables Logistic regression – classification algorithm for predicting a binary outcome Naive Bayes – probabilistic classifier based on Bayes' theorem Ordinary least squares – estimation method for parameters in linear regression PageRank – graph-based algorithm for link analysis and search ranking Principal component analysis – technique to reduce high-dimensional data while preserving variance Q-learning – reinforcement learning algorithm for learning optimal actions Random forest – ensemble of decision trees for improved classification or regression Sequential minimal optimization – solver for training support vector machines Stochastic gradient descent – randomized variant of gradient descent for large-scale machine learning Support Vector Machines (SVM) – algorithm for finding a hyperplane to separate classes == Statistical software == === Open-source === === Public domain === CSPro Dataplot Epi Map X-13ARIMA-SEATS === Freeware === BV4.1 MINUIT WinBUGS Winpepi === Proprietary === == Data processing == Tools for Data processing and analysis: == Data and information visualization == Software for Data visualization: == Plotting software == Software for plotting data to support processing and visualise results. == Maps and geospatial visualization == ArcGIS Carto Epi Map GeoDA Google Earth Engine Leaflet Mapbox MountainsMap QGIS == Machine learning == MLOps and model deployment: BentoML Data Version Control (DVC) Kubeflow MLflow Seldon Core Streamlit TensorFlow Serving Weights & Biases == Data repositories == Kaggle – platform for data science competitions, datasets, and notebooks. OpenML – collaborative platform for sharing datasets, algorithms, and experiments. University of California, Irvine Machine Learning Repository Zenodo – open-access repository supported by CERN and the EU. == Educational data science software == Kaggle – online platform for data science education, competitions, datasets, and collaborative learning. KNIME – open-source data analytics platform used for teaching data science, machine learning, and workflow-based analysis. RapidMiner – used in academic research and education for data mining and machine learning. Statistics Online Computational Resource (SOCR) – online tools and instructional resources for statistics education. Tanagra (machine learning) – data mining software developed for research and teaching purposes. TinkerPlots – explore and analyze data through visual modeling.

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  AARON

  AARON is the collective name for a series of computer programs written by artist Harold Cohen that create original artistic images autonomously, which set it apart from previous programs. Proceeding from Cohen's initial question "What are the minimum conditions under which a set of marks functions as an image?", AARON was in development between 1972 and the 2010s. As the software is not open source, its development effectively ended with Cohen's death in 2016. The name "AARON" does not seem to be an acronym; rather, it was a name chosen to start with the letter "A" so that the names of successive programs could follow it alphabetically. However, Cohen did not create any other major programs. Initial versions of AARON created abstract drawings that grew more complex through the 1970s. More representational imagery was added in the 1980s; first rocks, then plants, then people. In the 1990s more representational figures set in interior scenes were added, along with color. AARON returned to more abstract imagery, this time in color, in the early 2000s. Cohen used machines that allowed AARON to produce physical artwork. The first machines drew in black and white using a succession of custom-built "turtle" and flatbed plotter devices. Cohen would sometimes color these images by hand in fabric dye (Procion), or scale them up to make larger paintings and murals. In the 1990s Cohen built a series of digital painting machines to output AARON's images in ink and fabric dye. His later work used a large-scale inkjet printer on canvas. Development of AARON began in the C programming language then switched to Lisp in the early 1990s. Cohen credits Lisp with helping him solve the challenges he faced in adding color capabilities to AARON. An article about Cohen appeared in Computer Answers that describes AARON and shows two line drawings that were exhibited at the Tate gallery. The article goes on to describe the workings of AARON, then running on a DEC VAX 750 minicomputer. Raymond Kurzweil's company has produced a downloadable screensaver of AARON for Microsoft Windows PCs. This version of AARON can also produce printable images. AARON's source code is not publicly available, but Cohen has described AARON's operations in various essays and it is discussed in abstract in Pamela McCorduck's book. AARON cannot learn new styles or imagery on its own; each new capability must be hand-coded by Cohen. It is capable of producing a practically infinite supply of distinct images in its own style. Examples of these images have been exhibited in galleries worldwide. AARON's artwork has been used as an artistic equivalent of the Turing test. It does seem however that AARON's output follows a noticeable formula (figures standing next to a potted plant, framed within a colored square is a common theme). Cohen is very careful not to claim that AARON is creative. But he does ask "If what AARON is making is not art, what is it exactly, and in what ways, other than its origin, does it differ from the 'real thing?' If it is not thinking, what exactly is it doing?" — The further exploits of AARON, Painter. The Whitney Museum featured AARON in 2024, showcasing the evolution of AARON as the earliest artificial intelligence (AI) program for artmaking.

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  BeeSafe

  BeeSafe is a personal safety mobile app launched in 2015 as a Slovak startup. It is a location-based security service that notifies family members and friends in case the user of the app gets in danger. The app has received numerous awards. The app has more than 700 downloads and 250 active logins from more than 60 countries worldwide. == History == BeeSafe was founded on March 20, 2015 by Peter Stražovec and Michal Kačerík. The project was a winner of Žilina’s Startup Weekend 2013 and a StartupAwards.SK 2015 finalist. Later on, the app was released in the Android and iOS marketplace. The whole BeeSafe project was in The Spot booster and incubator in Bratislava for three months. BeeSafe entered into an agreement with the city of Piešťany in November 2015 to increase the security of its citizen by connecting the mobile app with the police platform. It is the first city that started using the BeeSafe platform. Further on, the application tries to help people in other Slovak cities. The cities can see the users only if they are in danger. == Awards == BeeSafe app received the Via Bona award, it is a winner of a Slovak startup and has other nominations too.

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  Super-resolution optical fluctuation imaging

  Super-resolution optical fluctuation imaging (SOFI) is a post-processing method for the calculation of super-resolved images from recorded image time series that is based on the temporal correlations of independently fluctuating fluorescent emitters. SOFI has been developed for super-resolution of biological specimen that are labelled with independently fluctuating fluorescent emitters (organic dyes, fluorescent proteins). In comparison to other super-resolution microscopy techniques such as STORM or PALM that rely on single-molecule localization and hence only allow one active molecule per diffraction-limited area (DLA) and timepoint, SOFI does not necessitate a controlled photoswitching and/ or photoactivation as well as long imaging times. Nevertheless, it still requires fluorophores that are cycling through two distinguishable states, either real on-/off-states or states with different fluorescence intensities. In mathematical terms SOFI-imaging relies on the calculation of cumulants, for what two distinguishable ways exist. For one thing an image can be calculated via auto-cumulants that by definition only rely on the information of each pixel itself, and for another thing an improved method utilizes the information of different pixels via the calculation of cross-cumulants. Both methods can increase the final image resolution significantly although the cumulant calculation has its limitations. Actually SOFI is able to increase the resolution in all three dimensions. == Principle == Likewise to other super-resolution methods SOFI is based on recording an image time series on a CCD- or CMOS camera. In contrary to other methods the recorded time series can be substantially shorter, since a precise localization of emitters is not required and therefore a larger quantity of activated fluorophores per diffraction-limited area is allowed. The pixel values of a SOFI-image of the n-th order are calculated from the values of the pixel time series in the form of a n-th order cumulant, whereas the final value assigned to a pixel can be imagined as the integral over a correlation function. The finally assigned pixel value intensities are a measure of the brightness and correlation of the fluorescence signal. Mathematically, the n-th order cumulant is related to the n-th order correlation function, but exhibits some advantages concerning the resulting resolution of the image. Since in SOFI several emitters per DLA are allowed, the photon count at each pixel results from the superposition of the signals of all activated nearby emitters. The cumulant calculation now filters the signal and leaves only highly correlated fluctuations. This provides a contrast enhancement and therefore a background reduction for good measure. As it is implied in the figure on the left the fluorescence source distribution: ∑ k = 1 N δ ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) {\displaystyle \sum _{k=1}^{N}\delta ({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t)} is convolved with the system's point spread function (PSF) U(r). Hence the fluorescence signal at time t and position r → {\displaystyle {\vec {r}}} is given by F ( r → , t ) = ∑ k = 1 N U ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) . {\displaystyle F({\vec {r}},t)=\sum _{k=1}^{N}U({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t).} Within the above equations N is the amount of emitters, located at the positions r → k {\displaystyle {\vec {r}}_{k}} with a time-dependent molecular brightness ε k ⋅ s k {\displaystyle \varepsilon _{k}\cdot s_{k}} where ε k {\displaystyle \varepsilon _{k}} is a variable for the constant molecular brightness and s k ( t ) {\displaystyle s_{k}(t)} is a time-dependent fluctuation function. The molecular brightness is just the average fluorescence count-rate divided by the number of molecules within a specific region. For simplification it has to be assumed that the sample is in a stationary equilibrium and therefore the fluorescence signal can be expressed as a zero-mean fluctuation: δ F ( r → , t ) = F ( r → , t ) − ⟨ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=F({\vec {r}},t)-\langle F({\vec {r}},t)\rangle _{t}} where ⟨ ⋯ ⟩ t {\displaystyle \langle \cdots \rangle _{t}} denotes time-averaging. The auto-correlation here e.g. the second-order can then be described deductively as follows for a certain time-lag τ {\displaystyle \tau } : δ F ( r → , t ) = ⟨ δ F ( r → , t + τ ) ⋅ δ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=\langle \delta F({\vec {r}},t+\tau )\cdot \delta F({\vec {r}},t)\rangle _{t}} From these equations it follows that the PSF of the optical system has to be taken to the power of the order of the correlation. Thus in a second-order correlation the PSF would be reduced along all dimensions by a factor of 2 {\displaystyle {\sqrt {2}}} . As a result, the resolution of the SOFI-images increases according to this factor. === Cumulants versus correlations === Using only the simple correlation function for a reassignment of pixel values, would ascribe to the independency of fluctuations of the emitters in time in a way that no cross-correlation terms would contribute to the new pixel value. Calculations of higher-order correlation functions would suffer from lower-order correlations for what reason it is superior to calculate cumulants, since all lower-order correlation terms vanish. == Cumulant-calculation == === Auto-cumulants === For computational reasons it is convenient to set all time-lags in higher-order cumulants to zero so that a general expression for the n-th order auto-cumulant can be found: A C n ( r → , τ 1 … n − 1 = 0 ) = ∑ k = 1 N U n ( r → − r → k ) ε k n w k ( 0 ) {\displaystyle AC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\sum _{k=1}^{N}U^{n}({\vec {r}}-{\vec {r}}_{k})\varepsilon _{k}^{n}w_{k}(0)} w k {\displaystyle w_{k}} is a specific correlation based weighting function influenced by the order of the cumulant and mainly depending on the fluctuation properties of the emitters. Albeit there is no fundamental limitation in calculating very high orders of cumulants and thereby shrinking the FWHM of the PSF there are practical limitations according to the weighting of the values assigned to the final image. Emitters with a higher molecular brightness will show a strong increase in terms of the pixel cumulant value assigned at higher-orders as well as this performance can be expected from a diverse appearance of fluctuations of different emitters. A wide intensity range of the resulting image can therefore be expected and as a result dim emitters can get masked by bright emitters in higher-order images:. The calculation of auto-cumulants can be realized in a very attractive way in a mathematical sense. The n-th order cumulant can be calculated with a basic recursion from moments K n ( r → ) = μ n ( r → ) − ∑ i = 1 n − 1 ( n − 1 i ) K n − i ( r → ) μ i ( r → ) {\displaystyle K_{n}({\vec {r}})=\mu _{n}({\vec {r}})-\sum _{i=1}^{n-1}{\begin{pmatrix}n-1\\i\end{pmatrix}}K_{n-i}({\vec {r}})\mu _{i}({\vec {r}})} where K is a cumulant of the index's order, likewise μ {\displaystyle \mu } represents the moments. The term within the brackets indicates a binomial coefficient. This way of computation is straightforward in comparison with calculating cumulants with standard formulas. It allows for the calculation of cumulants with only little time of computing and is, as it is well implemented, even suitable for the calculation of high-order cumulants on large images. === Cross-cumulants === In a more advanced approach cross-cumulants are calculated by taking the information of several pixels into account. Cross-cumulants can be described as follows: C C n ( r → , τ 1 … n − 1 = 0 ) = ∏ j < l n U ( r → j − r → l n ) ⋅ ∑ i = 1 N U n ( r → i − ∑ k n r → k n ) ε i n w i ( 0 ) {\displaystyle CC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\prod _{j Read more →

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  Azure Stream Analytics

  Microsoft Azure Stream Analytics is a serverless scalable complex event processing engine by Microsoft that enables users to develop and run real-time analytics on multiple streams of data from sources such as devices, sensors, web sites, social media, and other applications. Users can set up alerts to detect anomalies, predict trends, trigger necessary workflows when certain conditions are observed, and make data available to other downstream applications and services for presentation, archiving, or further analysis. == Query Language == Users can author real-time analytics using a simple declarative SQL-like language with embedded support for temporal logic. Callouts to custom code with JavaScript user defined functions extend the streaming logic written in SQL. Callouts to Azure Machine Learning helps with predictive scoring on streaming data. == Scalability == Azure Stream Analytics is a serverless job service on Azure that eliminates the need for infrastructure, servers, virtual machines, or managed clusters. Users only pay for the processing used for the running jobs. == IoT applications == Azure Stream Analytics integrates with Azure IoT Hub to enable real-time analytics on data from IoT devices and applications. == Real-time Dashboards == Users can build real-time dashboards with Power BI for a live command and control view. Real-time dashboards help transform live data into actionable and insightful visuals. == Data Input Sources == Stream Analytics supports three different types of input sources - Azure Event Hubs, Azure IoT Hubs, and Azure Blob Storage. Additionally, stream analytics supports Azure Blob storage as the input reference data to help augment fast moving event data streams with static data. Stream analytics supports a wide variety of output targets. Support for Power BI allows for real-time dashboarding. Event Hub, Service bus topics and queues help trigger downstream workflows. Support for Azure Table Storage, Azure SQL Databases, Azure SQL Data Warehouse, Azure SQL, Document DB, Azure Data Lake Store enable a variety of downstream analysis and archiving capabilities.

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  DeepRoute.ai

  DeepRoute.ai (Chinese: 元戎启行) is a Chinese autonomous driving company founded in 2019 and headquartered in Shenzhen, China. The company develops full-stack self-driving solutions including perception, decision-making, and control systems. == History == DeepRoute.ai was founded in February 2019 in Shenzhen, China, by Zhou Guang (周光), who serves as the company's CEO. In September 2019, the company collaborated with Dongfeng for a live-streamed autonomous driving demonstration. In October 2019, during the 7th Military World Games, DeepRoute.ai conducted Robotaxi demonstration operations. In November 2019, it obtained an intelligent connected vehicle road test permit for public roads in Shenzhen. In October 2020, DeepRoute.ai signed an "Autonomous Driving Leadership Project" with Dongfeng to build one of China's largest autonomous fleets. In August 2020, DeepRoute.ai announced its partnership with Cao Cao Mobility, a Geely-backed ride-hailing company, to test Robotaxis in Hangzhou for daily operations, planning to provide Robotaxis during the 2022 Asian Games. In September 2021, DeepRoute.ai secured US$300 million in a Series B funding round led by Alibaba. In December 2021, the company unveiled its DeepRoute-Driver 2.0, an L4-level autonomous driving solution comprising five solid-state lidar sensors, eight cameras, a proprietary computing system and an optional millimeter-wave radar. with a production cost of under US$10,000. In June 2022, it partnered with Deppon Express to provide autonomous light truck freight transfer services. In March 2023, the company launched its high-precision map-free intelligent driving solution, DeepRoute-Driver 3.0. In November 2024, Great Wall Motor announced a $100 million Series C funding round for Deeproute. With this, Deeproute has completed five rounds of financing, raising a cumulative total of over $500 million. Its shareholders include Fosun RZ Capital, Yunqi Partners, Alibaba, Vision Plus Capital, and Dongfeng, among others. In the same month, Deeproute.ai emphasised that they were in "deep cooperation" with Nvidia and spoke on being part of the first batch of companies in China to get a hold of Nvidia's newer Thor chip for cars which will be used in a new system released next year. This new system will help manage more complex driving scenarios through visual cues. == Products == === VLA Model === VLA Model is a Vision–language–action model designed for autonomous driving systems. It integrates visual perception, semantic understanding, and action decision-making into a unified framework, aiming to enhance the safety and adaptability of advanced driver-assistance systems (ADAS) in complex road environments. The model was officially launched on August 26, 2025, as the core of DeepRoute.ai's DeepRoute IO 2.0 platform. The VLA model is characterized by its "visual-language-action" architecture, which incorporates a chain-of-thought (CoT) reasoning capability inspired by large language models. This design is intended to address the "black box" limitations of traditional end-to-end autonomous driving systems by enabling the model to analyze information, infer causality, and make decisions in a more transparent and interpretable manner. === Appliance === The company has partnered with several automakers including Dongfeng Motor Corporation and Geely to develop and test autonomous vehicles.

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  Kernel (image processing)

  In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This is accomplished by doing a convolution between the kernel and an image. Or more simply, when each pixel in the output image is a function of the nearby pixels (including itself) in the input image, the kernel is that function. == Details == The general expression of a convolution is g x , y = ω ∗ f x , y = ∑ i = − a a ∑ j = − b b ω i , j f x − i , y − j , {\displaystyle g_{x,y}=\omega f_{x,y}=\sum _{i=-a}^{a}{\sum _{j=-b}^{b}{\omega _{i,j}f_{x-i,y-j}}},} where g ( x , y ) {\displaystyle g(x,y)} is the filtered image, f ( x , y ) {\displaystyle f(x,y)} is the original image, ω {\displaystyle \omega } is the filter kernel. Every element of the filter kernel is considered by − a ≤ i ≤ a {\displaystyle -a\leq i\leq a} and − b ≤ j ≤ b {\displaystyle -b\leq j\leq b} . Depending on the element values, a kernel can cause a wide range of effects: The above are just a few examples of effects achievable by convolving kernels and images. === Origin === The origin is the position of the kernel which is above (conceptually) the current output pixel. This could be outside of the actual kernel, though usually it corresponds to one of the kernel elements. For a symmetric kernel, the origin is usually the center element. == Convolution == Convolution is the process of adding each element of the image to its local neighbors, weighted by the kernel. This is related to a form of mathematical convolution. The matrix operation being performed—convolution—is not traditional matrix multiplication, despite being similarly denoted by . For example, if we have two three-by-three matrices, the first a kernel, and the second an image piece, convolution is the process of flipping both the rows and columns of the kernel and multiplying locally similar entries and summing. The element at coordinates [2, 2] (that is, the central element) of the resulting image would be a weighted combination of all the entries of the image matrix, with weights given by the kernel: ( [ a b c d e f g h i ] ∗ [ 1 2 3 4 5 6 7 8 9 ] ) [ 2 , 2 ] = {\displaystyle \left({\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}}{\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}}\right)[2,2]=} ( i ⋅ 1 ) + ( h ⋅ 2 ) + ( g ⋅ 3 ) + ( f ⋅ 4 ) + ( e ⋅ 5 ) + ( d ⋅ 6 ) + ( c ⋅ 7 ) + ( b ⋅ 8 ) + ( a ⋅ 9 ) . {\displaystyle (i\cdot 1)+(h\cdot 2)+(g\cdot 3)+(f\cdot 4)+(e\cdot 5)+(d\cdot 6)+(c\cdot 7)+(b\cdot 8)+(a\cdot 9).} The other entries would be similarly weighted, where we position the center of the kernel on each of the boundary points of the image, and compute a weighted sum. The values of a given pixel in the output image are calculated by multiplying each kernel value by the corresponding input image pixel values. This can be described algorithmically with the following pseudo-code: for each image row in input image: for each pixel in image row: set accumulator to zero for each kernel row in kernel: for each element in kernel row: if element position corresponding to pixel position then multiply element value corresponding to pixel value add result to accumulator endif set output image pixel to accumulator corresponding input image pixels are found relative to the kernel's origin. If the kernel is symmetric then place the center (origin) of the kernel on the current pixel. The kernel will overlap the neighboring pixels around the origin. Each kernel element should be multiplied with the pixel value it overlaps with and all of the obtained values should be summed. This resultant sum will be the new value for the current pixel currently overlapped with the center of the kernel. If the kernel is not symmetric, it has to be flipped both around its horizontal and vertical axis before calculating the convolution as above. The general form for matrix convolution is [ x 11 x 12 ⋯ x 1 n x 21 x 22 ⋯ x 2 n ⋮ ⋮ ⋱ ⋮ x m 1 x m 2 ⋯ x m n ] ∗ [ y 11 y 12 ⋯ y 1 n y 21 y 22 ⋯ y 2 n ⋮ ⋮ ⋱ ⋮ y m 1 y m 2 ⋯ y m n ] = ∑ i = 0 m − 1 ∑ j = 0 n − 1 x ( m − i ) ( n − j ) y ( 1 + i ) ( 1 + j ) {\displaystyle {\begin{bmatrix}x_{11}&x_{12}&\cdots &x_{1n}\\x_{21}&x_{22}&\cdots &x_{2n}\\\vdots &\vdots &\ddots &\vdots \\x_{m1}&x_{m2}&\cdots &x_{mn}\\\end{bmatrix}}{\begin{bmatrix}y_{11}&y_{12}&\cdots &y_{1n}\\y_{21}&y_{22}&\cdots &y_{2n}\\\vdots &\vdots &\ddots &\vdots \\y_{m1}&y_{m2}&\cdots &y_{mn}\\\end{bmatrix}}=\sum _{i=0}^{m-1}\sum _{j=0}^{n-1}x_{(m-i)(n-j)}y_{(1+i)(1+j)}} === Edge handling === Kernel convolution usually requires values from pixels outside of the image boundaries. There are a variety of methods for handling image edges. Extend The nearest border pixels are conceptually extended as far as necessary to provide values for the convolution. Corner pixels are extended in 90° wedges. Other edge pixels are extended in lines. Wrap The image is conceptually wrapped (or tiled) and values are taken from the opposite edge or corner. Mirror The image is conceptually mirrored at the edges. For example, attempting to read a pixel 3 units outside an edge reads one 3 units inside the edge instead. Crop / Avoid overlap Any pixel in the output image which would require values from beyond the edge is skipped. This method can result in the output image being slightly smaller, with the edges having been cropped. Move kernel so that values from outside of image is never required. Machine learning mainly uses this approach. Example: Kernel size 10x10, image size 32x32, result image is 23x23. Kernel Crop Any pixel in the kernel that extends past the input image isn't used and the normalizing is adjusted to compensate. Constant Use constant value for pixels outside of image. Usually black or sometimes gray is used. Generally this depends on application. === Normalization === Normalization is defined as the division of each element in the kernel by the sum of all kernel elements, so that the sum of the elements of a normalized kernel is unity. This will ensure the average pixel in the modified image is as bright as the average pixel in the original image. === Optimization === Fast convolution algorithms include: separable convolution ==== Separable convolution ==== 2D convolution with an M × N kernel requires M × N multiplications for each sample (pixel). If the kernel is separable, then the computation can be reduced to M + N multiplications. Using separable convolutions can significantly decrease the computation by doing 1D convolution twice instead of one 2D convolution. === Implementation === Here a concrete convolution implementation done with the GLSL shading language :

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  Smoothing

  In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adjacent points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased, leading to a smoother signal. Reducing noise by smoothing may aid in data analysis in two notable ways: Help uncover more meaningful information from the underlying data, such as trends. Provide analyses that are both flexible and robust. Many different algorithms are used in smoothing, most commonly binning, kernels, and local weighted regression. == Compared to curve fitting == Smoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways: curve fitting often involves the use of an explicit function form for the result, whereas the immediate results from smoothing are the "smoothed" values with no later use made of a functional form if there is one; the aim of smoothing is to give a general idea of relatively slow changes of value with little attention paid to the close matching of data values, while curve fitting concentrates on achieving as close a match as possible. smoothing methods often have an associated tuning parameter which is used to control the extent of smoothing. Curve fitting will adjust any number of parameters of the function to obtain the 'best' fit. == Linear smoothers == In the case that the smoothed values can be written as a linear transformation of the observed values, the smoothing operation is known as a linear smoother; the matrix representing the transformation is known as a smoother matrix or hat matrix. The operation of applying such a matrix transformation is called convolution. Thus the matrix is also called convolution matrix or a convolution kernel. In the case of simple series of data points (rather than a multi-dimensional image), the convolution kernel is a one-dimensional vector. == Algorithms == One of the most common algorithms is the "moving average", often used to try to capture important trends in repeated statistical surveys. In image processing and computer vision, smoothing ideas are used in scale space representations. The simplest smoothing algorithm is the "rectangular" or "unweighted sliding-average smooth". This method replaces each point in the signal with the average of "m" adjacent points, where "m" is a positive integer called the "smooth width". Usually m is an odd number. The triangular smooth is like the rectangular smooth except that it implements a weighted smoothing function. Some specific smoothing and filter types, with their respective uses, pros and cons are:

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  Taimi

  Taimi ( TAY-mee) is a dating app that caters to the LGBTQI+ community. The network matches its registered users based on their selected preferences and location. Originally an online dating service for gay men, by 2022 Taimi had become an app for all members of the LGBTQI+ community. It operates in more than 138 countries, including the US, UK, the Netherlands, Spain, Central and South America, Ukraine, and other European and Asian countries. Taimi runs on iOS and Android. The mobile app has a free and subscription-based premium version and offers a number of services for communication, including live streaming, chatting, and video calling. There is also an active blog that regularly posts articles and news about events of interest to the LGBTQ+ community. The application does not provide for non-Google e-mail log option, either phone number or Facebook account, during the registration process. The data controller for the non EU/UK users is based in a company, called Social Impact Inc., with its registered address at 1180 North Town Center Drive Suite 100, Las Vegas, Nevada, 89144, United States of America. == History == Taimi was launched in 2017 by Social Impact, Inc. in Las Vegas. Its founder, Alex Pasykov, originally called the app "Tame Me," a name that gradually morphed into Taimi. Over time, Taimi expanded into other countries, and expanding its reach to the LGBTQ+ community, so that, by 2022, it was fully inclusive of the entire queer community. In November 2020 the app was redesigned, with a new interface, branding, and logo. As of 2024, there are over 25 million registered users of Taimi worldwide. Pasykov states that he is an ally of the LGBTQ+ community and that he is focused on, among other things, partnering with NGOs to fight Homophobia and "regressive policies and laws" that negatively impact the community. == Features == Users register on the app and complete a profile, including personal information and preferences for compatibility, dating style, and relationship goals. An algorithm then finds and presents recommendations that a user accepts or rejects. Users are then free to chat via text or video with people they have connected with. Safety and security features include a two-step authentication process and an automated account verification along with a clear reporting system when breaches or policy violations occur. User responses to new features and policies drive changes and modifications that are made to all aspects of the site. == Partnerships and Collaborations == Taimi has a long history of collaborations and partnerships in Pride events, both in the US and abroad, including fund-raising efforts. Taimi has partnered with Rakuten Viber to create a bot focused on educating its members on key LGBTQ+ topics and to allow queer Viber users to connect. In 2023, Taimi collaborated with the Known Agency in an "America the Beautiful" campaign to shine a spotlight on current anti-LGBTQ+ policies and laws in a number of US states, and to counter these by highlighting the values and freedoms upon which America was founded. The campaign was nominated for The Drum Awards in the category "OOH For Good" and honored with the ANA Multicultural Excellence Award. Taimi also partnered with Goodparts, a queer-owned and operated retailer, in a "Body Beautiful" campaign focused on love and acceptance of all body types. In this campaign, well-known LGBTQ+ artists are providing artwork for Goodpart's product packaging. From October 31 to December 13, 2023, Taimi showed the "Taimi Moments" video, created in collaboration with Raygun Agency, on large screens between performances of LGBTQ+ artists Doja Cat, Ice Spice, and Doechii on their Scarlet Tour. In spring 2024, Taimi launched Queer Paradise, a series of live events in Southern California to celebrate diversity, sexual exploration, and dating fluidity. Each event in the series was curated to give the full spectrum of groups within the LGBTQ+ community a space to express their authentic selves. Taimi's partners for Queer Paradise include Hawtmess Productions, Eden Entertainment Group, Hump Events, Girls Gays & Theys, Damn Good Dyke Nights, and Gaybors Agency. In summer 2024, with support from GLAAD, Taimi has updated features and self-expression tools to better serve the LGBTQ+ people seeking connection in the app. Taimi allowed members to select multiple sexualities, unified the list of sexualities across all genders, added more pronoun options, and created a more inclusive and improved list of subcategories for non-binary users. Also, in summer 2024, Taimi has partnered with gender-affirming underwear brand Urbody to release a capsule collection. Focused on gender inclusivity and sexual fluidity, the capsule collection includes a range of underwear and compression tops intended to promote "joy, self-love and empowerment."

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  GamePigeon

  GamePigeon is a mobile app for iOS devices, developed by Vitalii Zlotskii and released on September 13, 2016. The game takes advantage of the iOS 10 update, which expanded how users could interact with Apple's Messages app. GamePigeon is only available through the Messages app, which allows players to start and respond to different party games in conversations. == Release == The app was first released on September 13, 2016, coinciding with the launch of iOS 10. The app was released for free, although it includes in-app purchases to unlock additional items, such as cosmetic skins, avatar items, new game modes, and an option to remove ads. == Games in the app == The following is a list of games that users can play within GamePigeon: Sources: Poker was one of the games included in GamePigeon at launch, although it has since been removed and is no longer listed on the game's App Store description. == Reception == GamePigeon has enjoyed commercial success, with VentureBeat noting that GamePigeon was ranked number-one in the "Top Free" category of the iMessage App Store, six months after its release. Critically, GamePigeon has been generally well received, being highlighted by online media publications early on shortly after the iOS 10 launch. It has since been included on many "best iMessage apps" lists. Based on over 162,000 ratings, the game holds a 4.0 out of 5 rating on the App Store. Julian Chokkattu of Digital Trends wrote "GamePigeon should be like the pre-installed versions of Solitaire and Minesweeper that used to come with older iterations of Windows." On its launch day, Boy Genius Report included it on a list of "10 of the best iMessage apps, games and stickers for iOS 10 on launch day." The Daily Dot wrote, "GamePigeon is easily the best current gaming option within iMessages." 8-ball and cup pong have been particularly well received by media outlets. The Daily Dot had specific praise for the app's billiards game: "8-Ball controls shockingly smoothly with your fingers, and there’s nothing quite like destroying a dear friend in poker." During his 2020 U.S. presidential campaign, Cory Booker was cited as playing the game with his family. In 2017, CNBC cited one teenager who expressed that GamePigeon was one of just a few reasons that those in her age range use the iMessage app. The game has received particular positive reception for allowing introverted individuals to exercise a form social activity; similarly, the game was highlighted as a way to maintain social distancing guidelines during the COVID-19 pandemic. As an April Fools' Day joke in 2020, The Chronicle, a Duke University newspaper, published that Duke's athletic program adopted GamePigeon's Cup Pong as an official varsity sport.

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  Prequel (mobile application)

  Prequel, Inc. is an American technology company and mobile app developer known for developing the Prequel mobile application, which enables editing photos and videos with filters and effects generated using artificial intelligence. Prequel was founded in 2018 by Serge Aliseenko and Timur Khabirov, who currently serves as the company's CEO. It is headquartered in New York City. As of August 2022, it had been downloaded more than 100 million times. == History == In 2016, entrepreneur Timur Khabirov and investor Serge Aliseenko registered a US corporation named AIAR Labs Inc, which was developing AR solutions as an outsourced contractor. Of several proprietary products, Prequel was selected for beta-testing as a product focused on editing photos and videos. In 2018, Prequel was released on the Apple App Store. The launch cost $3 million USD, financed with the founders’ personal funds. The first release included approximately 10 filters for photos and the same amount of effects that augmented images with rose petals, rain and snow, VHS and film reel simulations, glitch, grain, sun puddles, and lomography. By June 2020, the app had also been released for Android. In 2021, Prequel founders Timur Khabirov and Serge Aliseenko launched a venture studio for startups working with artificial, computer vision, and AR-based visual art. In December 2022, Prequel reached the number 14 slot on the global rankings for Apple App Store’s Top Charts and the number 5 slot on the App Store’s U.S. charts. In March 2023, Prequel launched a new app called Artique, which is an AI-powered image editing app for businesses. Artique provides advertising and marketing graphic design using ready-made templates that users can customize, while giving suggestions and visual cues through artificial intelligence. Prequel was also one of the companies participating in discussions about artificial intelligence at SXSW 2023. == Features == Prequel describes its app as an "Aesthetic Pic Editor. The app uses artificial intelligence to create and edit content. Prequel can be used to touch up faces on images and videos and can also tie various decorative elements to certain points on the human body and face. Prequel filters include the "Cartoon" filter, which converts selfies into cartoon-style pictures. Other filters include Kidcore, Dust, Grain, Fisheye, Retro Style, Miami, Disco, and VHS-style filters, as well as the ability to create Renaissance-style pictures. Prequel also gives users the ability to apply color correction tools and to make moving images with 3D effects out of 2D images. Prequel allows users to take photos and videos directly through the app and apply filters and effects in real time. The app also comes with manual editing options for photos, such as adjusting the brightness and/or exposure and cropping photos, as well as an option to automatically apply adjustments. The Prequel app uses the Core ML, MNN, and TFLight frameworks to work with its neural networks. Some AI solutions are launched server-side, and some on the user's mobile device. A resulting photo or video edited with the app is called "a prequel." The app daily generates over 2 million such prequels, which are published by users in Instagram, TikTok, and other social media. As of 2022, the app has more than 800 filters and effects, along with video templates and support for GIFs and stickers. Prequel is free-to-use, but has a premium version that gives users access to more effects, filters, and beauty tools. Since its launch in 2018, Prequel has been downloaded more than 100 million times.

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  Desktop video

  Desktop video refers to a phenomenon lasting from the mid-1980s to the early 1990s when the graphics capabilities of personal computers such as the Amiga, Macintosh II, and specially-upgraded IBM PC compatibles had advanced to the point where individuals and local broadcasters could use them for analog non-linear editing and vision mixing in video production. Despite the use of computers, desktop video should not be confused with digital video since the video data remained analog, and it uses items like a VCR and a camcorder to record the video. Full-screen, full-motion video's vast storage requirements meant that the promise of digital encoding would not be realized on desktop computers for at least another decade. == Description == There were multiple models of genlock cards available to synchronize the content; the Newtek Video Toaster was commonly used in Amiga in countries that used NTSC (PAL-M in Brazil), while PCs had Truevision and Matrox Illuminator cards and Mac systems had the SuperMac Video Spigot and Radius VideoVision cards. Apple later introduced the Macintosh Quadra 840AV and Centris 660AV systems to specifically address this market. Desktop video was a parallel development to desktop publishing and enabled many small production houses and local TV stations to produce their own original content for the first time. Along with the advent of public-access cable channels, desktop video meant that television advertising became affordable for local businesses such as retailers, restaurants, real estate agents, contractors and auto dealers. As with the phrase desktop publishing, use of the term died out as the technologies to which it referred become the norm for any kind of video production.

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  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

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  CamScanner

  CamScanner is a Chinese mobile app first released in 2010 that allows iOS and Android devices to be used as image scanners. It allows users to 'scan' documents (by taking a photo with the device's camera) and share the photo as either a JPEG or PDF. This app is available free of charge on the Google Play Store and the Apple App Store. The app is based on freemium model, with ad-supported free version and a premium version with additional functions. == History == On August 27, 2019, Russian cyber security company Kaspersky Lab discovered that recent versions of the Android app distributed an advertising library containing a Trojan Dropper, which was also included in some apps preinstalled on several Chinese mobiles. The advertising library decrypts a Zip archive which subsequently downloads additional files from servers controlled by hackers, allowing the hackers to control the device, including by showing intrusive advertising or charging paid subscriptions. Google took the app down after Kaspersky reported its findings. An updated version of the app with the advertising library removed was made available on the Google Play Store as of September 5, 2019. Kaspersky later acknowledged "We appreciate the willingness to cooperate that we've seen from CamScanner representatives, as well as the responsible attitude to user safety they demonstrated while eliminating the threat…The malicious modules were removed from the app immediately upon Kaspersky's warning, and Google Play has restored the app." In June 2020, as tensions along the Line of Actual Control between China and India continued, the Government of India decided to ban 118 Chinese apps, including TikTok and CamScanner citing data and privacy issues. On January 5, 2021, US President Donald Trump signed Executive Order 13971 banning Alipay, Tencent's QQ, QQ Wallet, WeChat Pay, CamScanner, Shareit, VMate and WPS Office to conduct US transactions. The Trump administration explained this act by saying that this move helps prevent personal information such as text, phone calls and photos collected from rivals. However, the Biden administration did not meet the February 2021 deadline for implementing the executive order, allowing these apps to operate in the US and revoked the previous executive order Executive Order 14034 of June 9, 2021.

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  Blackmagic Design

  Blackmagic Design Pty Ltd is an Australian company that develops digital cinema technology and manufactures professional video production hardware and software. Headquartered in South Melbourne, it is known for producing high-end digital movie cameras and a range of broadcast and post-production equipment. The company also develops software applications, including the DaVinci Resolve application for non-linear video editing, color correction, color grading, visual effects, and audio post-production. == History == Blackmagic Design Pty Ltd was founded on 7 September 2001 by Grant Petty. Its first product, DeckLink, introduced in 2002, was a video capture card for macOS that supported uncompressed 10-bit video, marking a shift toward professional-grade yet affordable video workflows. Subsequent versions—including the DeckLink 2, Pro SDI, HD Plus, and Multibridge—added capabilities such as color correction, Windows support, and compatibility with major editing software like Adobe Premiere Pro, to broaden the product's appeal. At the 2012 NAB Show, Blackmagic announced its first Cinema Camera, a digital movie camera. Blackmagic made several acquisitions over the next decade. In 2009, it acquired da Vinci Systems, known for its color-grading tools. In 2010, it acquired Echolab's ATEM switcher line, in 2014, it added eyeon Software (developer of the Blackmagic Fusion compositing software) and London's Cintel (film scanning and restoration), and in 2016, it acquired Fairlight, an audio technology company known for its CMI synthesizers as well as mixing consoles. == Products == List of all products developed by the company. Editing, Color Correction and Audio Post Production DaVinci Resolve (free version) and DaVinci Resolve Studio (paid version), computer software for non-linear video editing, color correction, color grading, visual effects, and audio post-production. Audio/Video Controller Consoles: Editor Keyboard, Speed Editor, DaVinci Resolve Replay Editor, Micro Panel, Mini Panel, DaVinci Resolve Micro Color Panel, Advanced Panel, Fairlight Console Channel Fader, Fairlight Console Channel Control, Fairlight Console LCD Monitor, Fairlight Console Audio Editor, Fairlight Desktop Audio Editor, Fairlight Desktop Console, Fairlight Audio Interface Cintel Film Scanner (Generations 1-3) Live Production Home Streaming: ATEM Mini, ATEM Mini Pro/ISO, ATEM Mini Extreme, ATEM Mini Extreme ISO (The ATEM Mini series has both HDMI and SDI variants) Production Switchers: ATEM 1,2 & 4 M/E Constellation HD, ATEM 1,2 & 4 M/E Constellation 4K, ATEM Constellation 8K, ATEM 1,2 & 4 M/E Production Studio 4K, ATEM Television Studio HD8 & HD8 ISO Switcher & Camera Controllers: ATEM Camera Control Panel, ATEM 1 M/E Advanced Panel, ATEM 2 M/E Advanced Panel, ATEM 4 M/E Advanced Panel Chroma Keyers: Ultimatte 12 HD Mini, Ultimatte 12 HD, Ultimatte 12 4K, Ultimatte 12 8K Recording and Storage: HyperDeck Studio HD Mini, HyperDeck Studio HD Plus, HyperDeck Studio HD Plus, HyperDeck Studio 4K Pro, HyperDeck Extreme 8K HDR, HyperDeck Extreme 4K HDR, HyperDeck Extreme Control, HyperDeck Shuttle HD, Duplicator 4K, MultiDock 10G, Video Assist 7" 12G HDR, Video Assist 5" 12G HDR Capture and Playback UltraStudio: 3G, HD Mini, 4K Mini, 4K Extreme 3 DeckLink (PCIe cards): Mini Recorder, Mini Monitor, Mini Monitor 4K, Mini Recorder 4K, Duo 2 Mini, Duo 2, Quad 2, SDI 4K, Studio 4K, 4K Extreme 12G, 8K Pro, Quad HDMI Recorder Network Storage Cloud Store Cloud Pod Broadcast Converters Micro Converter: BiDirectional SDI/HDMI 3G wPSU, HDMI to SDI 3G wPSU, SDI to HDMI 3G wPSU, BiDirectional SDI/HDMI 3G, HDMI to SDI 3G, SDI to HDMI 3G Mini Converters: Audio to SDI, Optical Fiber 12G, SDI Multiplex 4K, Quad SDI to HDMI 4K, SDI Distribution 4K, SDI to Analog 4K, Audio to SDI 4K, SDI to Audio 4K, HDMI to SDI 6G, SDI to HDMI 6G Teranex Mini: SDI Distribution 12G, SDI to HDMI 12G, Audio to SDI 12G, SDI to Analog 12G, SDI to HDMI 8K HDR, SDI to DisplayPort 8K HDR 2110 IP Converters Routing and Distribution Videohub

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