Vinted Group UAB is a Lithuanian technology company best known for its online marketplace Vinted. Vinted is the leading second-hand fashion marketplace in Europe and a go-to destination for all kinds of second-hand items. According to the company, its mission is to make second-hand the first choice worldwide. The company operates as an ecosystem of businesses, including the Vinted Marketplace (its peer-to-peer resale platform), Vinted Go (logistics and shipping services), Vinted Pay (in-app payment solutions), and Vinted Ventures (an investment arm supporting the circular economy). Headquartered in Vilnius, Lithuania, it also has offices in Germany and the Netherlands and employs more than 2,200 people. == History == Vinted was co-founded in 2008 by Milda Mitkute and Justas Janauskas in Vilnius, Lithuania. The idea originated when Mitkute was moving house and wanted a way to sell clothes she no longer needed. Janauskas helped her create a website where users could trade clothing items. In 2016, Dutch entrepreneur Thomas Plantenga joined Vinted as a strategy consultant and later became Chief Executive Officer, leading the company through a period of international growth. In 2019, Vinted became Lithuania’s first technology unicorn after raising €128 million at a €1 billion valuation in a funding round led by Lightspeed Venture Partners. In October 2020, it acquired United Wardrobe, a Dutch competitor, and in November 2020 German Kleiderkreisel and Mamikreisel were officially merged into the Vinted platform. In 2024 it acquired Trendsales, a Danish resale platform. According to Vogue Business, Vinted’s revenue grew 61% between 2022 and 2023 and the company posted a net profit of €17.8 million in 2023. Usage of Vinted in the UK has grown from 1.2 million users in 2021, to 8 million in 2023. In 2024, the group reported consolidated revenue of €813.4 million (up 36% from 2023) and a net profit of €76.7 million, up 330% from 2023. As of 2024, Vinted was valued at approximately €5 billion, operating in more than 26 markets worldwide and announcing plans to launch in Ireland, Greece, Latvia, Slovenia, and Estonia in 2025. As of 2025 the company employed more than 2,200 people. In April 2026, Vinted completed a secondary share transaction of €880m, valuing the company at €8bn. == Products and operations == Vinted primarily resells clothing but now supports multiple categories including homeware, kidswear, electronics, books, collectibles, and high-value fashion. Vinted has worked with public figures such as Paul Mescal and Alexa Chung on exclusive wardrobe sales and has also partnered directly with charities including Oxfam on initiatives which promote the social and environmental value of second-hand fashion, such as the Style for Change fashion show at London Fashion Week. In 2025, Vinted produced its first television format, the second-hand fashion competition series RE/Style, hosted by Emma Willis. The show features emerging fashion designers from across Europe creating runway-ready looks from second-hand garments and aired on Prime Video UK. In 2025, Vinted was reported as France’s top clothing retailer by sales volume. == Criticism == Vinted has faced scrutiny from European data protection authorities in France, Lithuania, and Poland following complaints regarding GDPR compliance and account blocking practices. In July 2024, the Lithuanian authority fined the company €2,375,276. The case was coordinated by a dedicated Vinted Working Group under the European Data Protection Board. In early 2024, Swedish police reported around 300 fraud cases linked to the platform, in which users’ bank accounts were targeted by scammers. In October 2024, Channel 4 in the United Kingdom aired a documentary examining safety and privacy concerns related to the platform, including the sexualisation of underage users’ images and risks associated with second-hand baby products lacking safety certification. In November 2025, BBC News reported that Vinted’s update to its sizing system in the United Kingdom led to widespread user criticism. Vinted said the update was intended to standardise sizing across international brands.
Image analysis
Image analysis or imagery analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques. Image analysis tasks can be as simple as reading bar coded tags or as sophisticated as identifying a person from their face. Computers are indispensable for the analysis of large amounts of data, for tasks that require complex computation, or for the extraction of quantitative information. On the other hand, the human visual cortex is an excellent image analysis apparatus, especially for extracting higher-level information, and for many applications — including medicine, security, and remote sensing — human analysts still cannot be replaced by computers. For this reason, many important image analysis tools such as edge detectors and neural networks are inspired by human visual perception models. == Digital == Digital Image Analysis or Computer Image Analysis is when a computer or electrical device automatically studies an image to obtain useful information from it. Note that the device is often a computer but may also be an electrical circuit, a digital camera or a mobile phone. It involves the fields of computer or machine vision, and medical imaging, and makes heavy use of pattern recognition, digital geometry, and signal processing. This field of computer science developed in the 1950s at academic institutions such as the MIT A.I. Lab, originally as a branch of artificial intelligence and robotics. It is the quantitative or qualitative characterization of two-dimensional (2D) or three-dimensional (3D) digital images. 2D images are, for example, to be analyzed in computer vision, and 3D images in medical imaging. The field was established in the 1950s—1970s, for example with pioneering contributions by Azriel Rosenfeld, Herbert Freeman, Jack E. Bresenham, or King-Sun Fu. == Techniques == There are many different techniques used in automatically analysing images. Each technique may be useful for a small range of tasks, however there still aren't any known methods of image analysis that are generic enough for wide ranges of tasks, compared to the abilities of a human's image analysing capabilities. Examples of image analysis techniques in different fields include: 2D and 3D object recognition, image segmentation, motion detection e.g. Single particle tracking, video tracking, optical flow, medical scan analysis, 3D Pose Estimation. == Deep learning == Since the early 2010s, deep learning methods have substantially advanced the field of image analysis. In 2012, a deep convolutional neural network (CNN) known as AlexNet achieved a significant reduction in error rates on the ImageNet large-scale image classification benchmark, demonstrating the effectiveness of deep learning for visual recognition tasks. Subsequent architectures such as ResNet introduced residual connections that enabled training of much deeper networks, further improving accuracy across image analysis tasks. Real-time object detection became practical with frameworks such as YOLO (You Only Look Once), which unified detection and classification into a single network pass. In 2020, the Vision Transformer (ViT) demonstrated that transformer architectures, originally developed for natural language processing, could achieve competitive results on image classification when applied directly to sequences of image patches. More recently, foundation models trained on large-scale datasets have enabled zero-shot generalisation across image analysis tasks. The Segment Anything Model (SAM), trained on over one billion masks, can segment arbitrary objects in images without task-specific fine-tuning. These advances have made image analysis techniques increasingly accessible through browser-based tools and open-source implementations. == Applications == The applications of digital image analysis are continuously expanding through all areas of science and industry, including: anatomy, allows for precise measurements, visualization, and statistical analysis of anatomical structures. assay micro plate reading, such as detecting where a chemical was manufactured. astronomy, such as calculating the size of a planet. automated species identification (e.g. plant and animal species) defense error level analysis filtering machine vision, such as to automatically count items in a factory conveyor belt. materials science, such as determining if a metal weld has cracks. medicine, such as detecting cancer in a mammography scan. metallography, such as determining the mineral content of a rock sample. microscopy, such as counting the germs in a swab. automatic number plate recognition; optical character recognition, such as automatic license plate detection. remote sensing, such as detecting intruders in a house, and producing land cover/land use maps. robotics, such as to avoid steering into an obstacle. security, such as detecting a person's eye color or hair color. == Object-based == Object-based image analysis (OBIA) involves two typical processes, segmentation and classification. Segmentation helps to group pixels into homogeneous objects. The objects typically correspond to individual features of interest, although over-segmentation or under-segmentation is very likely. Classification then can be performed at object levels, using various statistics of the objects as features in the classifier. Statistics can include geometry, context and texture of image objects. Over-segmentation is often preferred over under-segmentation when classifying high-resolution images. Object-based image analysis has been applied in many fields, such as cell biology, medicine, earth sciences, and remote sensing. For example, it can detect changes of cellular shapes in the process of cell differentiation.; it has also been widely used in the mapping community to generate land cover. When applied to earth images, OBIA is known as geographic object-based image analysis (GEOBIA), defined as "a sub-discipline of geoinformation science devoted to (...) partitioning remote sensing (RS) imagery into meaningful image-objects, and assessing their characteristics through spatial, spectral and temporal scale". The international GEOBIA conference has been held biannually since 2006. OBIA techniques are implemented in software such as eCognition or the Orfeo toolbox.
Automated restaurant
An automated restaurant or robotic restaurant is a restaurant that uses robots to do tasks such as delivering food and drink to the tables or cooking the food. Restaurant automation means the use of a restaurant management system to automate some or occasionally all of the major operations of a restaurant establishment. More recently, restaurants are opening that have completely or partially automated their services. These may include: taking orders, preparing food, serving, and billing. A few fully automated restaurants operate without any human intervention whatsoever. Robots are designed to help and sometimes replace human labour (such as waiters and chefs). The automation of restaurants may also allow for the option for greater customization of an order. == History == === Vending machines === In the late 19th and early 20th century a number of restaurants served food solely through vending machines. These restaurants were called automats or, in Japan, shokkenki. Customers ordered their food directly through the machines. === Sushi conveyors === Yoshiaki Shiraishi is a Japanese innovator who is known for the creation of conveyor belt sushi. He had the idea following difficulty staffing his small sushi restaurant and managing the restaurant on his own. He was inspired seeing beer bottles on a conveyor belt in an Asahi brewery. Yoshiaki's restaurants are an early example of restaurant automation; they used a conveyor belt to distribute dishes around the restaurant, eliminating the need for waiters. This example of automation dates back to the Japanese economic miracle; the first of Yoshiaki's conveyor belt sushi restaurants was opened under the name Mawaru Genroku Sushi in 1958, in Osaka. === Partial automation === As of 2011, across Europe, McDonald's had already begun implementing 7,000 touch screen kiosks that could handle cashiering duties. From 2015 to 2020, Zume had an automated pizza parlor. Later companies would try to produce smaller, less ambitious devices, with one robotics company producing a machine that could automate the slowest and most repetitive parts of assembling a pizza, such as spreading pizza sauce or placing slices of pepperoni, while leaving other customizations to employees. In 2020, a restaurant in the Netherlands began trialling the use of a robot to serve guests. In September 2021, Karakuri's 'Semblr' food service robot served personalised lunches for the 4,000 employees of grocery technology solutions provider ocado Group's head offices in Hatfield, UK. 2,700 different combinations of dishes were on offer. Customers could specify in grams what hot and cold items, proteins, sauces and fresh toppings they wanted. In 2021, Columbia University School of Engineering and Applied Science engineers developed a method of cooking 3D printed chicken with software-controlled robotic lasers. The “Digital Food” team exposed raw 3D printed chicken structures to both blue and infrared light. They then assessed the cooking depth, colour development, moisture retention and flavour differences of the laser-cooked 3D printed samples in comparison to stove-cooked meat. In June 2022 a California nonprofit chain of residential communities, Front Porch, experimented with robots in dining rooms at two locations to supplement wait staff by carrying plated food and drink to tables, and removing dishes. 65% of residents found the robots helpful, with 51% saying they let the staff spend more quality time with diners. 51% of staff were "excited" and 58% said they enabled more quality time with diners. The chain has 19 senior living communities (and 35 affordable housing communities), so it has potential to expand robots to more dining rooms. It is shifting to memory care, which may affect plans. == Rationales == === Advantages === Efficiency: Automated restaurants can significantly enhance operational efficiency by minimizing human error and reducing service time. With automated ordering, payment, and food preparation systems, customers can enjoy faster service and reduced waiting times. Cost savings: By reducing the need for human staff, automated restaurants can potentially lower labor costs. This can be particularly beneficial in areas with high labor expenses, as it allows for better resource allocation and cost management. Consistency: Automation ensures consistency in food quality and presentation. With precise portion control and standardized cooking methods, customers can expect the same quality and taste in their meals every time they visit. Enhanced customer experience: Self-service kiosks and automated systems provide customers with control and convenience. They can customize their orders, browse through menu options, and pay seamlessly, creating a more interactive and satisfying dining experience. === Disadvantages === Lack of personal touch: Automated restaurants may lack the personal interaction and warmth that traditional restaurants provide. Some customers prefer the human touch, personalized recommendations, and the social aspect of dining out. Technical issues: Reliance on technology means that technical glitches and malfunctions can occur, resulting in service disruptions or delays. Maintenance and technical support become critical in ensuring smooth operations. Limited menu complexity: The automation process may be better suited for standardized menu items rather than complex or customized dishes. The ability to cater to unique dietary preferences or accommodate special requests may be limited. Employment implications: Automated restaurants may result in job losses for traditional restaurant staff, potentially impacting the local workforce. It is important to consider the social and economic implications of adopting such technology. == Locations == Automated restaurants have been opening in many countries. Examples include: Nala Restaurant in Naperville, Illinois Fritz's Railroad Restaurant in Kansas City, Kansas Výtopna, a Railway Restaurant using model trains: franchise of various restaurants and coffeehouses in the Czech Republic Bagger's Restaurant in Nuremberg, Germany FuA-Men Restaurant, a ramen restaurant located in Nagoya, Japan Fōster Nutrition in Buenos Aires, Argentina Dalu Robot Restaurant in Jinan, China Haohai Robot Restaurant in Harbin, China Robot Kitchen Restaurant in Hong Kong Robo-Chef restaurant in Tehran, Iran, started in 2017, is the first robotic and "waiterless" restaurant of the Middle East. MIT graduates opened Spyce Kitchens in downtown Boston, Massachusetts, in 2018 Foodom, under Country Garden Holdings, opened January 12, 2020, in Guangzhou, China Robot Chacha, the first robot restaurant of India, is planning to open in the capital city of New Delhi. Kura Revolving Sushi Bar, with a number of locations in the United States, uses a tablets at tables for ordering, a conveyor belt to deliver food, and robots to deliver drinks and condiments. Chipotle Mexican Grill is beginning to deploy the Hyphen Makeline, which assembles up to 350 bowls and salads automatically per hour, and Chippy, an automatic tortilla chip fryer made by Miso Robotics. Serious Dumplings in Boca Raton, Florida
Continuous Function Chart
A Continuous Function Chart (CFC) is a graphic editor that can be used in conjunction with the STEP 7 software package or with other tools, such as CODESYS. It is used to create the entire software structure of the CPU from ready-made blocks. When working with the editor, you place blocks on function charts, assign parameters to them, and interconnect them. Interconnecting means, for example, that values are transferred from one output to one or more inputs during communication between the blocks. Continuous function charts are basically used for controlling continuous processes, where all the logic is executed and outputs are calculated in each PLC scan. Whereas in SFC, execution will be sequential as done is batch processes.
Lucy–Hook coaddition method
The Lucy–Hook coaddition method is an image processing technique for combining sub-stepped astronomical image data onto a finer grid. The method allows the option of resolution and contrast enhancement or the choice of a conservative, re-convolved, output. Tests with very deep Hubble Space Telescope Wide Field and Planetary Camera 2 (WFPC2) imaging data of excellent quality show that these methods can be very effective and allow fine-scale features to be studied better than on the unprocessed images. The Lucy–Hook coaddition method is an extension of the standard Richardson–Lucy deconvolution iterative restoration method. For many purposes it may be more convenient to combine dithered datasets using the Drizzle method.
Convolutional neural network
A convolutional neural network (CNN) is a type of feedforward neural network that learns features via filter (or kernel) optimization. This type of deep learning network has been applied to process and make predictions from many different types of data including text, images and audio. CNNs are the de-facto standard in deep learning-based approaches to computer vision and image processing, and have only recently been replaced—in some cases—by newer architectures such as the transformer. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by the regularization that comes from using shared weights over fewer connections. For example, for each neuron in the fully-connected layer, 10,000 weights would be required for processing an image sized 100 × 100 pixels. However, applying cascaded convolution (or cross-correlation) kernels, only 25 weights for each convolutional layer are required to process 5x5-sized tiles. Higher-layer features are extracted from wider context windows, compared to lower-layer features. Some applications of CNNs include: image and video recognition, recommender systems, image classification, image segmentation, medical image analysis, natural language processing, brain–computer interfaces, and financial time series. CNNs are also known as shift invariant or space invariant artificial neural networks, based on the shared-weight architecture of the convolution kernels or filters that slide along input features and provide translation-equivariant responses known as feature maps. Counter-intuitively, most convolutional neural networks are not invariant to translation, due to the downsampling operation they apply to the input. Feedforward neural networks are usually fully connected networks, that is, each neuron in one layer is connected to all neurons in the next layer. The "full connectivity" of these networks makes them prone to overfitting data. Typical ways of regularization, or preventing overfitting, include: penalizing parameters during training (such as weight decay) or trimming connectivity (skipped connections, dropout, etc.) Robust datasets also increase the probability that CNNs will learn the generalized principles that characterize a given dataset rather than the biases of a poorly-populated set. Convolutional networks were inspired by biological processes in that the connectivity pattern between neurons resembles the organization of the animal visual cortex. Individual cortical neurons respond to stimuli only in a restricted region of the visual field known as the receptive field. The receptive fields of different neurons partially overlap such that they cover the entire visual field. CNNs use relatively little pre-processing compared to other image classification algorithms. This means that the network learns to optimize the filters (or kernels) through automated learning, whereas in traditional algorithms these filters are hand-engineered. This simplifies and automates the process, enhancing efficiency and scalability overcoming human-intervention bottlenecks. == Architecture == A convolutional neural network consists of an input layer, hidden layers and an output layer. In a convolutional neural network, the hidden layers include one or more layers that perform convolutions. Typically this includes a layer that performs a dot product of the convolution kernel with the layer's input matrix. This product is usually the Frobenius inner product, and its activation function is commonly ReLU. As the convolution kernel slides along the input matrix for the layer, the convolution operation generates a feature map, which in turn contributes to the input of the next layer. This is followed by other layers such as pooling layers, fully connected layers, and normalization layers. Here it should be noted how close a convolutional neural network is to a matched filter. === Convolutional layers === In a CNN, the input is a tensor with shape: (number of inputs) × (input height) × (input width) × (input channels) After passing through a convolutional layer, the image becomes abstracted to a feature map, also called an activation map, with shape: (number of inputs) × (feature map height) × (feature map width) × (feature map channels). Convolutional layers convolve the input and pass its result to the next layer. This is similar to the response of a neuron in the visual cortex to a specific stimulus. Each convolutional neuron processes data only for its receptive field. Although fully connected feedforward neural networks can be used to learn features and classify data, this architecture is generally impractical for larger inputs (e.g., high-resolution images), which would require massive numbers of neurons because each pixel is a relevant input feature. A fully connected layer for an image of size 100 × 100 has 10,000 weights for each neuron in the second layer. Convolution reduces the number of free parameters, allowing the network to be deeper. For example, using a 5 × 5 tiling region, each with the same shared weights, requires only 25 neurons. Using shared weights means there are many fewer parameters, which helps avoid the vanishing gradients and exploding gradients problems seen during backpropagation in earlier neural networks. To speed processing, standard convolutional layers can be replaced by depthwise separable convolutional layers, which are based on a depthwise convolution followed by a pointwise convolution. The depthwise convolution is a spatial convolution applied independently over each channel of the input tensor, while the pointwise convolution is a standard convolution restricted to the use of 1 × 1 {\displaystyle 1\times 1} kernels. === Pooling layers === Convolutional networks may include local and/or global pooling layers along with traditional convolutional layers. Pooling layers reduce the dimensions of data by combining the outputs of neuron clusters at one layer into a single neuron in the next layer. Local pooling combines small clusters, tiling sizes such as 2 × 2 are commonly used. Global pooling acts on all the neurons of the feature map. There are two common types of pooling in popular use: max and average. Max pooling uses the maximum value of each local cluster of neurons in the feature map, while average pooling takes the average value. === Fully connected layers === Fully connected layers connect every neuron in one layer to every neuron in another layer. It is the same as a traditional multilayer perceptron neural network (MLP). Each neuron in the fully connected layer receives input from all the neurons in the previous layer. These inputs are weighted and summed with the corresponding biases, and then passed through an activation function to perform a nonlinear transformation, generating the output. The flattened matrix goes through a fully connected layer to classify the images. === Receptive field === In neural networks, each neuron receives input from some number of locations in the previous layer. In a convolutional layer, each neuron receives input from only a restricted area of the previous layer called the neuron's receptive field. Typically the area is a square (e.g. 5 by 5 neurons). Whereas, in a fully connected layer, the receptive field is the entire previous layer. Thus, in each convolutional layer, each neuron takes input from a larger area in the input than previous layers. This is due to applying the convolution over and over, which takes the value of a pixel into account, as well as its surrounding pixels. When using dilated layers, the number of pixels in the receptive field remains constant, but the field is more sparsely populated as its dimensions grow when combining the effect of several layers. To manipulate the receptive field size as desired, there are some alternatives to the standard convolutional layer. For example, atrous or dilated convolution expands the receptive field size without increasing the number of parameters by interleaving visible and blind regions. Moreover, a single dilated convolutional layer can comprise filters with multiple dilation ratios, thus having a variable receptive field size. === Weights === Each neuron in a neural network computes an output value by applying a specific function to the input values received from the receptive field in the previous layer. The function that is applied to the input values is determined by a vector of weights and a bias (typically real numbers). Learning consists of iteratively adjusting these biases and weights. The vectors of weights and biases are called filters and represent particular features of the input (e.g., a particular shape). A distinguishing feature of CNNs is that many neurons can share the same filter. This reduces the memory footprint because a single bias and a single vector of weights are used across all receptive fields that share that filter, as opposed to each receptive field having its own bias and vector
Structural similarity index measure
The structural similarity index measure (SSIM) is a method for predicting the perceived quality of digital television and cinematic pictures, as well as other kinds of digital images and videos. It is also used for measuring the similarity between two images. The SSIM index is a full reference metric; in other words, the measurement or prediction of image quality is based on an initial uncompressed or distortion-free image as reference. SSIM is a perception-based model that considers image degradation as perceived change in structural information, while also incorporating important perceptual phenomena, including both luminance masking and contrast masking terms. This distinguishes from other techniques such as mean squared error (MSE) or peak signal-to-noise ratio (PSNR) that instead estimate absolute errors. Structural information is the idea that the pixels have strong inter-dependencies especially when they are spatially close. These dependencies carry important information about the structure of the objects in the visual scene. Luminance masking is a phenomenon whereby image distortions (in this context) tend to be less visible in bright regions, while contrast masking is a phenomenon whereby distortions become less visible where there is significant activity or "texture" in the image. == History == The predecessor of SSIM was called Universal Quality Index (UQI), or Wang–Bovik index, which was developed by Zhou Wang and Alan Bovik in 2001. This evolved, through their collaboration with Hamid Sheikh and Eero Simoncelli, into the current version of SSIM, which was published in April 2004 in the IEEE Transactions on Image Processing. In addition to defining the SSIM quality index, the paper provides a general context for developing and evaluating perceptual quality measures, including connections to human visual neurobiology and perception, and direct validation of the index against human subject ratings. The basic model was developed in the Laboratory for Image and Video Engineering (LIVE) at The University of Texas at Austin and further developed jointly with the Laboratory for Computational Vision (LCV) at New York University. Further variants of the model have been developed in the Image and Visual Computing Laboratory at University of Waterloo and have been commercially marketed. SSIM subsequently found strong adoption in the image processing community and in the television and social media industries. The 2004 SSIM paper has been cited over 50,000 times according to Google Scholar, making it one of the highest cited papers in the image processing and video engineering fields. It was recognized with the IEEE Signal Processing Society Best Paper Award for 2009. It also received the IEEE Signal Processing Society Sustained Impact Award for 2016, indicative of a paper having an unusually high impact for at least 10 years following its publication. Because of its high adoption by the television industry, the authors of the original SSIM paper were each accorded a Primetime Engineering Emmy Award in 2015 by the Television Academy. == Algorithm == The SSIM index is calculated between two windows of pixel values x {\displaystyle x} and y {\displaystyle y} of common size, from corresponding locations in two images to be compared. These SSIM values can be aggregated across the full images by averaging or other variations. === Special-case formula === In one simple special case, further explained in the next section, the SSIM measure between x {\displaystyle x} and y {\displaystyle y} is: SSIM ( x , y ) = ( 2 μ x μ y + c 1 ) ( 2 σ x y + c 2 ) ( μ x 2 + μ y 2 + c 1 ) ( σ x 2 + σ y 2 + c 2 ) {\displaystyle {\hbox{SSIM}}(x,y)={\frac {(2\mu _{x}\mu _{y}+c_{1})(2\sigma _{xy}+c_{2})}{(\mu _{x}^{2}+\mu _{y}^{2}+c_{1})(\sigma _{x}^{2}+\sigma _{y}^{2}+c_{2})}}} with: μ x {\displaystyle \mu _{x}} the pixel sample mean of x {\displaystyle x} ; μ y {\displaystyle \mu _{y}} the pixel sample mean of y {\displaystyle y} ; σ x 2 {\displaystyle \sigma _{x}^{2}} the sample variance of x {\displaystyle x} ; σ y 2 {\displaystyle \sigma _{y}^{2}} the sample variance of y {\displaystyle y} ; σ x y {\displaystyle \sigma _{xy}} the sample covariance of x {\displaystyle x} and y {\displaystyle y} ; c 1 = ( k 1 L ) 2 {\displaystyle c_{1}=(k_{1}L)^{2}} , c 2 = ( k 2 L ) 2 {\displaystyle c_{2}=(k_{2}L)^{2}} two variables to stabilize the division with weak denominator; L {\displaystyle L} the dynamic range of the pixel-values (typically this is 2 # b i t s p e r p i x e l − 1 {\displaystyle 2^{\#bits\ per\ pixel}-1} ); k 1 = 0.01 {\displaystyle k_{1}=0.01} and k 2 = 0.03 {\displaystyle k_{2}=0.03} by default. === General formula and components === The SSIM formula is based on three comparison measurements between the samples of x {\displaystyle x} and y {\displaystyle y} : luminance ( l {\displaystyle l} ), contrast ( c {\displaystyle c} ), and structure ( s {\displaystyle s} ). The individual comparison functions are: l ( x , y ) = 2 μ x μ y + c 1 μ x 2 + μ y 2 + c 1 {\displaystyle l(x,y)={\frac {2\mu _{x}\mu _{y}+c_{1}}{\mu _{x}^{2}+\mu _{y}^{2}+c_{1}}}} c ( x , y ) = 2 σ x σ y + c 2 σ x 2 + σ y 2 + c 2 {\displaystyle c(x,y)={\frac {2\sigma _{x}\sigma _{y}+c_{2}}{\sigma _{x}^{2}+\sigma _{y}^{2}+c_{2}}}} s ( x , y ) = σ x y + c 3 σ x σ y + c 3 {\displaystyle s(x,y)={\frac {\sigma _{xy}+c_{3}}{\sigma _{x}\sigma _{y}+c_{3}}}} The SSIM for each block is then a weighted combination of those comparative measures: SSIM ( x , y ) = l ( x , y ) α ⋅ c ( x , y ) β ⋅ s ( x , y ) γ {\displaystyle {\text{SSIM}}(x,y)=l(x,y)^{\alpha }\cdot c(x,y)^{\beta }\cdot s(x,y)^{\gamma }} Choosing the third denominator stabilizing constant as: c 3 = c 2 / 2 {\displaystyle c_{3}=c_{2}/2} leads to a simplification when combining the c and s components with equal exponents ( β = γ {\displaystyle \beta =\gamma } ), as the numerator of c is then twice the denominator of s, leading to a cancellation leaving just a 2. Setting the weights (exponents) α , β , γ {\displaystyle \alpha ,\beta ,\gamma } to 1, the formula can then be reduced to the special case shown above. === Mathematical properties === SSIM satisfies the identity of indiscernibles, and symmetry properties, but not the triangle inequality or non-negativity, and thus is not a distance function. However, under certain conditions, SSIM may be converted to a normalized root MSE measure, which is a distance function. The square of such a function is not convex, but is locally convex and quasiconvex, making SSIM a feasible target for optimization. === Application of the formula === In order to evaluate the image quality, this formula is usually applied only on luma, although it may also be applied on color (e.g., RGB) values or chromatic (e.g. YCbCr) values. The resultant SSIM index is a decimal value between -1 and 1, where 1 indicates perfect similarity, 0 indicates no similarity, and -1 indicates perfect anti-correlation. For an image, it is typically calculated using a sliding Gaussian window of size 11×11 or a block window of size 8×8. The window can be displaced pixel-by-pixel on the image to create an SSIM quality map of the image. In the case of video quality assessment, the authors propose to use only a subgroup of the possible windows to reduce the complexity of the calculation. === Variants === ==== Multi-scale SSIM ==== A more advanced form of SSIM, called Multiscale SSIM (MS-SSIM) is conducted over multiple scales through a process of multiple stages of sub-sampling, reminiscent of multiscale processing in the early vision system. It has been shown to perform equally well or better than SSIM on different subjective image and video databases. ==== Multi-component SSIM ==== Three-component SSIM (3-SSIM) is a form of SSIM that takes into account the fact that the human eye can see differences more precisely on textured or edge regions than on smooth regions. The resulting metric is calculated as a weighted average of SSIM for three categories of regions: edges, textures, and smooth regions. The proposed weighting is 0.5 for edges, 0.25 for the textured and smooth regions. The authors mention that a 1/0/0 weighting (ignoring anything but edge distortions) leads to results that are closer to subjective ratings. This suggests that edge regions play a dominant role in image quality perception. The authors of 3-SSIM have also extended the model into four-component SSIM (4-SSIM). The edge types are further subdivided into preserved and changed edges by their distortion status. The proposed weighting is 0.25 for all four components. ==== Structural dissimilarity ==== Structural dissimilarity (DSSIM) may be derived from SSIM, though it does not constitute a distance function as the triangle inequality is not necessarily satisfied. DSSIM ( x , y ) = 1 − SSIM ( x , y ) 2 {\displaystyle {\hbox{DSSIM}}(x,y)={\frac {1-{\hbox{SSIM}}(x,y)}{2}}} ==== Video quality metrics and temporal variants ==== It is worth noting that the original vers