In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.
Harris corner detector
The Harris corner detector is a corner detection operator that is commonly used in computer vision algorithms to extract corners and infer features of an image. It was first introduced by Chris Harris and Mike Stephens in 1988 upon the improvement of Moravec's corner detector. Compared to its predecessor, Harris' corner detector takes the differential of the corner score into account with reference to direction directly, instead of using shifting patches for every 45 degree angles, and has been proved to be more accurate in distinguishing between edges and corners. Since then, it has been improved and adopted in many algorithms to preprocess images for subsequent applications. == Introduction == A corner is a point whose local neighborhood stands in two dominant and different edge directions. In other words, a corner can be interpreted as the junction of two edges, where an edge is a sudden change in image brightness. Corners are the important features in the image, and they are generally termed as interest points which are invariant to translation, rotation and illumination. Although corners are only a small percentage of the image, they contain the most important features in restoring image information, and they can be used to minimize the amount of processed data for motion tracking, image stitching, building 2D mosaics, stereo vision, image representation and other related computer vision areas. In order to capture the corners from the image, researchers have proposed many different corner detectors including the Kanade-Lucas-Tomasi (KLT) operator and the Harris operator which are most simple, efficient and reliable for use in corner detection. These two popular methodologies are both closely associated with and based on the local structure matrix. Compared to the Kanade-Lucas-Tomasi corner detector, the Harris corner detector provides good repeatability under changing illumination and rotation, and therefore, it is more often used in stereo matching and image database retrieval. Although there still exist drawbacks and limitations, the Harris corner detector is still an important and fundamental technique for many computer vision applications. == Development of Harris corner detection algorithm == Source: Without loss of generality, we will assume a grayscale 2-dimensional image is used. Let this image be given by I {\displaystyle I} . Consider taking an image patch ( x , y ) ∈ W {\displaystyle (x,y)\in W} (window) and shifting it by ( Δ x , Δ y ) {\displaystyle (\Delta x,\Delta y)} . The sum of squared differences (SSD) between these two patches, denoted f {\displaystyle f} , is given by: f ( Δ x , Δ y ) = ∑ ( x k , y k ) ∈ W ( I ( x k , y k ) − I ( x k + Δ x , y k + Δ y ) ) 2 {\displaystyle f(\Delta x,\Delta y)={\underset {(x_{k},y_{k})\in W}{\sum }}\left(I(x_{k},y_{k})-I(x_{k}+\Delta x,y_{k}+\Delta y)\right)^{2}} I ( x + Δ x , y + Δ y ) {\displaystyle I(x+\Delta x,y+\Delta y)} can be approximated by a Taylor expansion. Let I x {\displaystyle I_{x}} and I y {\displaystyle I_{y}} be the partial derivatives of I {\displaystyle I} , such that I ( x + Δ x , y + Δ y ) ≈ I ( x , y ) + I x ( x , y ) Δ x + I y ( x , y ) Δ y {\displaystyle I(x+\Delta x,y+\Delta y)\approx I(x,y)+I_{x}(x,y)\Delta x+I_{y}(x,y)\Delta y} This produces the approximation f ( Δ x , Δ y ) ≈ ∑ ( x , y ) ∈ W ( I x ( x , y ) Δ x + I y ( x , y ) Δ y ) 2 , {\displaystyle f(\Delta x,\Delta y)\approx {\underset {(x,y)\in W}{\sum }}\left(I_{x}(x,y)\Delta x+I_{y}(x,y)\Delta y\right)^{2},} which can be written in matrix form: f ( Δ x , Δ y ) ≈ ( Δ x Δ y ) M ( Δ x Δ y ) , {\displaystyle f(\Delta x,\Delta y)\approx {\begin{pmatrix}\Delta x&\Delta y\end{pmatrix}}M{\begin{pmatrix}\Delta x\\\Delta y\end{pmatrix}},} where M is the structure tensor, M = ∑ ( x , y ) ∈ W [ I x 2 I x I y I x I y I y 2 ] = [ ∑ ( x , y ) ∈ W I x 2 ∑ ( x , y ) ∈ W I x I y ∑ ( x , y ) ∈ W I x I y ∑ ( x , y ) ∈ W I y 2 ] {\displaystyle M={\underset {(x,y)\in W}{\sum }}{\begin{bmatrix}I_{x}^{2}&I_{x}I_{y}\\I_{x}I_{y}&I_{y}^{2}\end{bmatrix}}={\begin{bmatrix}{\underset {(x,y)\in W}{\sum }}I_{x}^{2}&{\underset {(x,y)\in W}{\sum }}I_{x}I_{y}\\{\underset {(x,y)\in W}{\sum }}I_{x}I_{y}&{\underset {(x,y)\in W}{\sum }}I_{y}^{2}\end{bmatrix}}} == Process of Harris corner detection algorithm == Commonly, Harris corner detector algorithm can be divided into five steps. Color to grayscale Spatial derivative calculation Structure tensor setup Harris response calculation Non-maximum suppression === Color to grayscale === If we use Harris corner detector in a color image, the first step is to convert it into a grayscale image, which will enhance the processing speed. The value of the gray scale pixel can be computed as a weighted sums of the values R, B and G of the color image, ∑ C ∈ { R , G , B } w C ⋅ C {\displaystyle \sum _{C\,\in \,\{R,G,B\}}w_{C}\cdot C} , where, e.g., w R = 0.299 , w G = 0.587 , w B = 1 − ( w R + w G ) = 0.114. {\displaystyle w_{R}=0.299,\ w_{G}=0.587,\ w_{B}=1-(w_{R}+w_{G})=0.114.} === Spatial derivative calculation === Next, we are going to find the derivative with respect to x and the derivative with respect to y, I x ( x , y ) {\displaystyle I_{x}(x,y)} and I y ( x , y ) {\displaystyle I_{y}(x,y)} . This can be approximated by applying Sobel operators. === Structure tensor setup === With I x ( x , y ) {\displaystyle I_{x}(x,y)} , I y ( x , y ) {\displaystyle I_{y}(x,y)} , we can construct the structure tensor M {\displaystyle M} . === Harris response calculation === For x ≪ y {\displaystyle x\ll y} , one has x ⋅ y x + y = x 1 1 + x / y ≈ x . {\displaystyle {\tfrac {x\cdot y}{x+y}}=x{\tfrac {1}{1+x/y}}\approx x.} In this step, we compute the smallest eigenvalue of the structure tensor using that approximation: λ min ≈ λ 1 λ 2 ( λ 1 + λ 2 ) = det ( M ) tr ( M ) {\displaystyle \lambda _{\min }\approx {\frac {\lambda _{1}\lambda _{2}}{(\lambda _{1}+\lambda _{2})}}={\frac {\det(M)}{\operatorname {tr} (M)}}} with the trace t r ( M ) = m 11 + m 22 {\displaystyle \mathrm {tr} (M)=m_{11}+m_{22}} . Another commonly used Harris response calculation is shown as below, R = λ 1 λ 2 − k ( λ 1 + λ 2 ) 2 = det ( M ) − k tr ( M ) 2 {\displaystyle R=\lambda _{1}\lambda _{2}-k(\lambda _{1}+\lambda _{2})^{2}=\det(M)-k\operatorname {tr} (M)^{2}} where k {\displaystyle k} is an empirically determined constant; k ∈ [ 0.04 , 0.06 ] {\displaystyle k\in [0.04,0.06]} . === Non-maximum suppression === In order to pick up the optimal values to indicate corners, we find the local maxima as corners within the window which is a 3 by 3 filter. == Improvement == Sources: Harris-Laplace Corner Detector Differential Morphological Decomposition Based Corner Detector Multi-scale Bilateral Structure Tensor Based Corner Detector == Applications == Image Alignment, Stitching and Registration 2D Mosaics Creation 3D Scene Modeling and Reconstruction Motion Detection Object Recognition Image Indexing and Content-based Retrieval Video Tracking
ImageNet
The ImageNet project is a large visual database designed for use in visual object recognition software research. More than 14 million images have been hand-annotated by the project to indicate what objects are pictured and in at least one million of the images, bounding boxes are also provided. ImageNet contains more than 20,000 categories, with a typical category, such as "balloon" or "strawberry", consisting of several hundred images. The database of annotations of third-party image URLs is freely available directly from ImageNet, though the actual images are not owned by ImageNet. Since 2010, the ImageNet project runs an annual software contest, the ImageNet Large Scale Visual Recognition Challenge (ILSVRC), where software programs compete to correctly classify and detect objects and scenes. The challenge uses a "trimmed" list of one thousand non-overlapping classes. == History == AI researcher Fei-Fei Li began working on the idea for ImageNet in 2006. At a time when most AI research focused on models and algorithms, Li wanted to expand and improve the data available to train AI algorithms. In 2007, Li met with Princeton professor Christiane Fellbaum, one of the creators of WordNet, to discuss the project. As a result of this meeting, Li went on to build ImageNet starting from the roughly 22,000 nouns of WordNet and using many of its features. She was also inspired by a 1987 estimate that the average person recognizes roughly 30,000 different kinds of objects. As an assistant professor at Princeton, Li assembled a team of researchers to work on the ImageNet project. They used Amazon Mechanical Turk to help with the classification of images. Labeling started in July 2008 and ended in April 2010. It took 49K workers from 167 countries filtering and labeling over 160M candidate images. They had enough budget to have each of the 14 million images labelled three times. The original plan called for 10,000 images per category, for 40,000 categories at 400 million images, each verified 3 times. They found that humans can classify at most 2 images/sec. At this rate, it was estimated to take 19 human-years of labor (without rest). They presented their database for the first time as a poster at the 2009 Conference on Computer Vision and Pattern Recognition (CVPR) in Florida, titled "ImageNet: A Preview of a Large-scale Hierarchical Dataset". The poster was reused at Vision Sciences Society 2009. In 2009, Alex Berg suggested adding object localization as a task. Li approached PASCAL Visual Object Classes contest in 2009 for a collaboration. It resulted in the subsequent ImageNet Large Scale Visual Recognition Challenge starting in 2010, which has 1000 classes and object localization, as compared to PASCAL VOC which had just 20 classes and 19,737 images (in 2010). === Significance for deep learning === On 30 September 2012, a convolutional neural network (CNN) called AlexNet achieved a top-5 error of 15.3% in the ImageNet 2012 Challenge, more than 10.8 percentage points lower than that of the runner-up. Using convolutional neural networks was feasible due to the use of graphics processing units (GPUs) during training, an essential ingredient of the deep learning revolution. According to The Economist, "Suddenly people started to pay attention, not just within the AI community but across the technology industry as a whole." In 2015, AlexNet was outperformed by Microsoft's very deep CNN with over 100 layers, which won the ImageNet 2015 contest, having 3.57% error on the test set. Andrej Karpathy estimated in 2014 that with concentrated effort, he could reach 5.1% error rate, and ~10 people from his lab reached ~12-13% with less effort. It was estimated that with maximal effort, a human could reach 2.4%. == Dataset == ImageNet crowdsources its annotation process. Image-level annotations indicate the presence or absence of an object class in an image, such as "there are tigers in this image" or "there are no tigers in this image". Object-level annotations provide a bounding box around the (visible part of the) indicated object. ImageNet uses a variant of the broad WordNet schema to categorize objects, augmented with 120 categories of dog breeds to showcase fine-grained classification. In 2012, ImageNet was the world's largest academic user of Mechanical Turk. The average worker identified 50 images per minute. The original plan of the full ImageNet would have roughly 50M clean, diverse and full resolution images spread over approximately 50K synsets. This was not achieved. The summary statistics given on April 30, 2010: Total number of non-empty synsets: 21841 Total number of images: 14,197,122 Number of images with bounding box annotations: 1,034,908 Number of synsets with SIFT features: 1000 Number of images with SIFT features: 1.2 million === Categories === The categories of ImageNet were filtered from the WordNet concepts. Each concept, since it can contain multiple synonyms (for example, "kitty" and "young cat"), so each concept is called a "synonym set" or "synset". There were more than 100,000 synsets in WordNet 3.0, majority of them are nouns (80,000+). The ImageNet dataset filtered these to 21,841 synsets that are countable nouns that can be visually illustrated. Each synset in WordNet 3.0 has a "WordNet ID" (wnid), which is a concatenation of part of speech and an "offset" (a unique identifying number). Every wnid starts with "n" because ImageNet only includes nouns. For example, the wnid of synset "dog, domestic dog, Canis familiaris" is "n02084071". The categories in ImageNet fall into 9 levels, from level 1 (such as "mammal") to level 9 (such as "German shepherd"). === Image format === The images were scraped from online image search (Google, Picsearch, MSN, Yahoo, Flickr, etc) using synonyms in multiple languages. For example: German shepherd, German police dog, German shepherd dog, Alsatian, ovejero alemán, pastore tedesco, 德国牧羊犬. ImageNet consists of images in RGB format with varying resolutions. For example, in ImageNet 2012, "fish" category, the resolution ranges from 4288 x 2848 to 75 x 56. In machine learning, these are typically preprocessed into a standard constant resolution, and whitened, before further processing by neural networks. For example, in PyTorch, ImageNet images are by default normalized by dividing the pixel values so that they fall between 0 and 1, then subtracting by [0.485, 0.456, 0.406], then dividing by [0.229, 0.224, 0.225]. These are the mean and standard deviations for ImageNet, so this whitens the input data. === Labels and annotations === Each image is labelled with exactly one wnid. Dense SIFT features (raw SIFT descriptors, quantized codewords, and coordinates of each descriptor/codeword) for ImageNet-1K were available for download, designed for bag of visual words. The bounding boxes of objects were available for about 3000 popular synsets with on average 150 images in each synset. Furthermore, some images have attributes. They released 25 attributes for ~400 popular synsets: Color: black, blue, brown, gray, green, orange, pink, red, violet, white, yellow Pattern: spotted, striped Shape: long, round, rectangular, square Texture: furry, smooth, rough, shiny, metallic, vegetation, wooden, wet === ImageNet-21K === The full original dataset is referred to as ImageNet-21K. ImageNet-21k contains 14,197,122 images divided into 21,841 classes. Some papers round this up and name it ImageNet-22k. The full ImageNet-21k was released in Fall of 2011, as fall11_whole.tar. There is no official train-validation-test split for ImageNet-21k. Some classes contain only 1-10 samples, while others contain thousands. === ImageNet-1K === There are various subsets of the ImageNet dataset used in various context, sometimes referred to as "versions". One of the most highly used subsets of ImageNet is the "ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2012–2017 image classification and localization dataset". This is also referred to in the research literature as ImageNet-1K or ILSVRC2017, reflecting the original ILSVRC challenge that involved 1,000 classes. ImageNet-1K contains 1,281,167 training images, 50,000 validation images and 100,000 test images. Each category in ImageNet-1K is a leaf category, meaning that there are no child nodes below it, unlike ImageNet-21K. For example, in ImageNet-21K, there are some images categorized as simply "mammal", whereas in ImageNet-1K, there are only images categorized as things like "German shepherd", since there are no child-words below "German shepherd". === Later developments === In the WordNet they built ImageNet on, there were 2832 synsets in the "person" subtree. During 2018--2020 period, they removed the download of the ImageNet-21k as they went through extensive filtering in these person synsets. Out of these 2832 synsets, 1593 were deemed "potentially offensive". Out of the remaining 1239, 1081 were deemed not really "visual". The result was that only 158 syn
Stanza Living
Stanza Living is the common brand name for Dtwelve Spaces Private Limited. It provides fully-managed shared living accommodations to students and young professionals. Founded by Anindya Dutta and Sandeep Dalmia, the company is present across 23 cities including Delhi, NCR, Bangalore, Visakhapatnam, Hyderabad, Chennai, Coimbatore, Indore, Pune, Baroda, Vijayawada, and Dehradun, Kota in India, with a capacity of 70,000 beds. Stanza Living is a technology-enabled housing concept which provides fully-furnished residences with amenities like meals, internet, laundry services, housekeeping, security and community engagement programmes. The company has an asset-light business model under which it engages in long-term lease agreements with property owners/developers, who convert their assets into shared living residences as per company guidelines. These assets are subsequently operated by Stanza Living. == Industry background == A report by Cushman & Wakefield (C&W) titled 'Exploring the Student Housing Universe in India City Insights', estimates that there were over 9.08 million migrant student enrolments in India's higher educational institutions (HEIs) for the year 2018-19 who need quality accommodation facilities. According to the report, Delhi-NCR, Mumbai, and Pune are the three biggest markets for student housing in the country, and these cities require an additional 4.75 lakh beds from organized co-living operators to meet the current demand. == History == Stanza Living provides tech-enabled, fully managed community living facilities for students and working professionals. The company was launched as a student housing business in Delhi NCR with a capacity of 100 beds, and grew to 14 cities by 2019. By early 2020, the company began catering to working professionals as well. The company has a combined inventory of 70,000 beds under management for both students and working professionals. Stanza Living is currently valued at $300 million. It has raised a capital of about $70 million from leading global investors like Falcon Edge Capital, Sequoia Capital, Matrix Partners and Accel Partners. November 2017 – Seed funding, September 2018 – Series A, March 2019 – Debt financing, July 2019 – Series C round, December 2019 - Debt financing. The company has invested in building technology products for business efficiency and consumer experience, like the Stanza Resident App and Stanza Real Estate App. Stanza Living has close to 1,500 employees across India. It is recognized among Top Real Estate Tech Startups of 2020 across the globe by research and analysis company Tracxn. The company has been shortlisted among Top 25 Start-ups of India in 2019 by LinkedIn == Founders == Stanza Living was co-founded by Anindya Dutta and Sandeep Dalmia. Sandeep Dalmia is an alumnus of Delhi College of Engineering and IIM Ahmedabad. Prior to Stanza, he was a Principal at Boston Consulting Group, working across India, US and South East Asia markets. Anindya Dutta was previously a Real Estate investor with Oaktree Capital and prior to that, he worked at Goldman Sachs in London. He is an alumnus of IIT Kharagpur and IIM Ahmedabad.
Comparison of color models in computer graphics
This article provides introductory information about the RGB, HSV, and HSL color models from a computer graphics (web pages, images) perspective. An introduction to colors is also provided to support the main discussion. == Basics of color == === Primary colors and hue === First, "color" refers to the human brain's subjective interpretation of combinations of a narrow band of wavelengths of light. For this reason, the definition of "color" is not based on a strict set of physical phenomena. Therefore, even basic concepts like "primary colors" are not clearly defined. For example, traditional "Painter's Colors" use red, blue, and yellow as the primary colors, "Printer's Colors" use cyan, yellow, and magenta, and "Light Colors" use red, green, and blue. "Light colors", more formally known as additive colors, are formed by combining red, green, and blue light. This article refers to additive colors and refers to red, green, and blue as the primary colors. Hue is a term describing a pure color, that is, a color not modified by tinting or shading (see below). In additive colors, hues are formed by combining two primary colors. When two primary colors are combined in equal intensities, the result is a "secondary color". === Color wheel === A color wheel is a tool that provides a visual representation of the relationships between all possible hues. The primary colors are arranged around a circle at equal (120 degree) intervals. (Warning: Color wheels frequently depict "Painter's Colors" primary colors, which leads to a different set of hues than additive colors.) The illustration shows a simple color wheel based on the additive colors. Note that the position (top, right) of the starting color, typically red, is arbitrary, as is the order of green and blue (clockwise, counter-clockwise). The illustration also shows the secondary colors, yellow, cyan, and magenta, located halfway between (60 degrees) the primary colors. == Complementary color == The complement of a hue is the hue that is opposite it (180 degrees) on the color wheel. Using additive colors, mixing a hue and its complement in equal amounts produces white. === Tints and shades === The following discussion uses an illustration involving three projectors pointing to the same spot on a screen. Each projector is capable of generating one hue. The "intensities" of each projector are "matched" and can be equally adjusted from zero to full. (Note: "Intensity" is used here in the same sense as the RGB color model. The subject of matching, or "gamma correction", is beyond the level of this article.) A shade is produced by "dimming" a maximum chroma color. Painters refer to this as "adding black". In our illustration, one projector is set to full intensity, a second is set to some intensity between zero and full, and third is set to zero. "Dimming" is accomplished by decreasing each projector's intensity setting to the same fraction of its start setting. In the shade example, with any fully shaded hue, that all three projectors are set to zero intensity, resulting in black. A tint is produced by "lightening" a maximum chroma color. Painters refer to this as "adding white". In our illustration, one projector is set to full intensity, a second is set to some intensity between zero and full, and third is set to zero. "Lightening" is accomplished by increasing each projector's intensity setting by the same fraction from its start setting to full. In the tinting example, note that the third projector is now contributing. When the hue is fully lightened, all three projectors are each at full intensity, and the result is white. Note an attribute of the total intensity in the additive model. If full intensity for one projector is 1, then a primary color has a combined intensity of 1. A secondary color has a total intensity of 2. White has a total intensity of 3. Tinting, or "adding white", increases the total intensity of the hue. While this is simply a fact, the HSL model will take this fact into account in its design. === Tones === Tone is a general term, typically used by painters, to refer to the effects of reducing the "colorfulness" of a maximum chroma color; painters refer to it as "adding gray". Note that gray is not a color or even a single concept but refers to all the range of values between black and white where all three primary colors are equally represented. The general term is provided as more specific terms have conflicting definitions in different color models. Thus, shading takes a hue toward black, tinting takes a hue towards white, and tones cover the range between. == Choosing a color model == No one color model is necessarily "better" than another. Typically, the choice of a color model is dictated by external factors, such as a graphics tool or the need to specify colors according to the CSS2 or CSS3 standard. The following discussion only describes how the models function, centered on the concepts of hue, shade, tint, and tone. === RGB === The RGB model's approach to colors is important because: It directly reflects the physical properties of "Truecolor" displays As of 2011, most graphic cards define pixel values in terms of the colors red, green, and blue. The typical range of intensity values for each color, 0–255, is based on taking a binary number with 32 bits and breaking it up into four bytes of 8 bits each. 8 bits can hold a value from 0 to 255. The fourth byte is used to specify the "alpha", or the opacity, of the color. Opacity comes into play when layers with different colors are stacked. If the color in the top layer is less than fully opaque (alpha < 255), the color from underlying layers "shows through". In the RGB model, hues are represented by specifying one color as full intensity (255), a second color with a variable intensity, and the third color with no intensity (0). The following provides some examples using red as the full-intensity and green as the partial-intensity colors; blue is always zero: Shades are created by multiplying the intensity of each primary color by 1 minus the shade factor, in the range 0 to 1. A shade factor of 0 does nothing to the hue, a shade factor of 1 produces black: new intensity = current intensity (1 – shade factor) The following provides examples using orange: Tints are created by modifying each primary color as follows: the intensity is increased so that the difference between the intensity and full intensity (255) is decreased by the tint factor, in the range 0 to 1. A tint factor of 0 does nothing, a tint factor of 1 produces white: new intensity = current intensity + (255 – current intensity) tint factor The following provides examples using orange: Tones are created by applying both a shade and a tint. The order in which the two operations are performed does not matter, with the following restriction: when a tint operation is performed on a shade, the intensity of the dominant color becomes the "full intensity"; that is, the intensity value of the dominant color must be used in place of 255. The following provides examples using orange: === HSV === The HSV, or HSB, model describes colors in terms of hue, saturation, and value (brightness). Note that the range of values for each attribute is arbitrarily defined by various tools or standards. Be sure to determine the value ranges before attempting to interpret a value. Hue corresponds directly to the concept of hue in the Color Basics section. The advantages of using hue are The angular relationship between tones around the color circle is easily identified Shades, tints, and tones can be generated easily without affecting the hue Saturation corresponds directly to the concept of tint in the Color Basics section, except that full saturation produces no tint, while zero saturation produces white, a shade of gray, or black. Value corresponds directly to the concept of intensity in the Color Basics section. Pure colors are produced by specifying a hue with full saturation and value Shades are produced by specifying a hue with full saturation and less than full value Tints are produced by specifying a hue with less than full saturation and full value Tones are produced by specifying a hue and both less than full saturation and value White is produced by specifying zero saturation and full value, regardless of hue Black is produced by specifying zero value, regardless of hue or saturation Shades of gray are produced by specifying zero saturation and between zero and full value The advantage of HSV is that each of its attributes corresponds directly to the basic color concepts, which makes it conceptually simple. The perceived disadvantage of HSV is that the saturation attribute corresponds to tinting, so desaturated colors have increasing total intensity. For this reason, the CSS3 standard plans to support RGB and HSL but not HSV. === HSL === The HSL model describes colors in terms of hue, saturation, and lightness (also called luminance). (Note: the definition of sa
JBoss Tools
JBoss Tools is a set of Eclipse plugins and features designed to help JBoss and JavaEE developers develop applications. It is an umbrella project for the JBoss developed plugins that will make it into JBoss Developer Studio. == Modules == JBoss Tools includes the following modules: Visual Page Editor (VPE). The visual editor contributed by Exadel supports visual editing of HTML and JSF (JSP and Facelets) pages. VPE also includes visual support for JSF component libraries including JBoss RichFaces. Seam Tools. Includes support for (for example) seam-gen, RichFaces VE integration, Seam related code completion and refactoring. Hibernate Tools. Supporting mapping files, annotations and JPA with reverse engineering, code completion, project wizards, refactoring, interactive HQL/JPA-QL/Criteria execution and more. In short a merger of Hibernate Tools and Exadel ORM features. JBoss AS Tools. Easy start, stop and debug of JBoss AS 4+ servers from within Eclipse. Also includes features for packaging and deployment of any type of Eclipse project. Drools IDE. Rules file editing, Rete View, working memory debugging/inspection and more. jBPM Tools. jBPM workflow editing, deployment, etc. JBossWS Tools. Inspecting, invoking, developing and functional/load/compliance testing of web services over HTTP, base tooling provided by soapUI with the addition of JBossWS specific features/support. JBoss ESB Tools. The structured xml editor for the jboss-esb.xml file used in JBoss ESB. Birt Tools. Hibernate and Seam extensions for Eclipse BIRT. Portal Tools. JBoss Tools supports the JSR-168 Portlet Specification (Portlet 1.0), JSR-286 Portlet Specification (Portlet 2.0) and works with PortletBridge for supporting Portlets in JSF/Seam applications. To enable these features, add the JBoss Portlet facet to a new or an existing web project. Core/General Tools. To reduce the UI clutter, most of the "configure project" menu items move into the Configure menu introduced in Eclipse 3.5 instead of always having a static JBoss Tools menu entry show up even in projects unrelated to JBoss Tools. Smooks Tools. The editor for Smooks configuration files. JBoss ESB Tools. The ESB project Wizard, which creates a project that can be deployed as an .esb archive to a JBoss AS-based server with JBoss ESB installed. JMX Tools. JMX Tools allows establishing multiple JMX connections and provides views for exploring the JMX tree and execute operations directly from Eclipse. The JMX Tools replaces the JMX node previously available in the JBoss Server View. JST/JSF Tools. RichFaces Support, Code Assists, Web XML/JSP/XHTML Editors, CSS Style Editing, web.xml validation, Faceleted taglib in taglib.xml is supported with XSD schema location. Project Examples. The experimental feature called Project Example wizard aims to allow users to download example projects from a remote site and have them working out-of-the-box. AS/Project Archives Tools. To deploy projects compressed, configurable in the server editor. If enabled, all projects deployed to that server will be compressed instead of in an exploded folder. Maven Tools. The optional integration with m2eclipse to provide Maven support for projects created by JBoss Tools and to some extent core WTP projects. BPEL Tools. A BPEL Editor based on the Eclipse BPEL project has been added to JBoss Tools. This means that users can create, edit and deploy BPEL artifacts for the Riftsaw BPEL Runtime. CDI (JSR-299) Tools. Support of the Contexts and Dependency Injection annotations; it works on any Eclipse Java project (via the Configure menu with CDI enabled).
Mozilla VPN
Mozilla VPN is an open-source virtual private network developed by Mozilla. It launched in beta as Firefox Private Network on September 10, 2019, and officially launched on July 15, 2020, as Mozilla VPN. Mozilla VPN should not be confused with the built-in VPN in Firefox since version 149 released in March 2026, which is free with a monthly data limit of 50 GB but only masks traffic that originates in Firefox unlike Mozilla VPN that protects the entire device. == History == The Firefox Private Network web browser extension beta version was released on September 10, 2019, as part of the relaunch of Mozilla's Test Pilot Program, a program that allowed Firefox users to test experimental new features which had been shuttered in January 2019. The beta of the subscription-based standalone virtual private network for Android, Microsoft Windows, and Chromebook launched on February 19, 2020, with the iOS version following soon after. Firefox Private Network was rebranded as "Mozilla VPN" on June 18, 2020, and officially launched as Mozilla VPN on July 15, 2020. At launch, Mozilla VPN was available in six countries (the United States, Canada, the United Kingdom, Singapore, Malaysia, and New Zealand) for Windows 10, Android, and iOS (beta). Over time, the service also launched in Germany, France, Italy, Spain, Switzerland, Austria, Belgium, Netherlands, Ireland, Finland, Sweden, Poland, Czechia, Hungary, Romania, Bulgaria, Slovakia, Portugal, Denmark, Croatia, Lithuania, Slovenia, Latvia, Luxembourg, Estonia, Cyprus, and Malta. == Audits history == Cybersecurity firm Cure53 conducted a security audit for Mozilla VPN in August 2020 and identified multiple vulnerabilities, including one critical-severity vulnerability. In March 2021, Cure53 conducted a second security audit, which noted significant improvements since the 2020 audit. The second audit identified multiple issues, including two medium-severity and one high-severity vulnerability, but concluded that by the time of publication, only one vulnerability remained unresolved, and that it would require "a strong state-funded attacker-model" to be exploitable. Mozilla disclosed most of the vulnerabilities in July 2021 and released the full report by Cure53 in August 2021. In April 2023, Cure53 conducted a third security audit, the results of which Mozilla disclosed in December that year, along with the full report by Cure53. == Features == Mozilla VPN masks the user's IP address, hiding the user's location data from the websites accessed by the user, and encrypts all network activity. The service allows for up to 5 simultaneous connections, to any of more than 500 servers in 30+ countries, and is available on the mobile operating systems iOS and Android and the desktop operating systems Microsoft Windows, macOS and Linux. Mozilla VPN's infrastructure is provided by the Swedish Mullvad VPN service, which uses the WireGuard VPN protocol. The VPN software comes with additional features, like recommended server locations, the ability to block ads, block ad trackers and malware, the ability to exclude certain applications from protection, the ability to set multi-hop connections, and to set custom DNS servers. When used with Firefox and the official extension, Mozilla VPN allows the use of different settings per container as well as bypassing the VPN for specific websites.