Floyd–Steinberg dithering is an image dithering algorithm first published in 1976 by Robert W. Floyd and Louis Steinberg. It is commonly used by image manipulation software, for example, when converting an image from a Truecolor 24-bit PNG format into a GIF format, which is restricted to a maximum of 256 colors. == Implementation == The algorithm achieves dithering using error diffusion, meaning it pushes (adds) the residual quantization error of a pixel onto its neighboring pixels, to be quantized after. It spreads the debt out according to the distribution (shown as a map of the neighboring pixels): [ ∗ 7 16 … … 3 16 5 16 1 16 … ] {\displaystyle {\begin{bmatrix}&&&{\frac {\displaystyle 7}{\displaystyle 16}}&\ldots \\\ldots &{\frac {\displaystyle 3}{\displaystyle 16}}&{\frac {\displaystyle 5}{\displaystyle 16}}&{\frac {\displaystyle 1}{\displaystyle 16}}&\ldots \\\end{bmatrix}}} The pixel indicated with a star () indicates the pixel currently being scanned, and the blank pixels are the previously scanned pixels. The specific values (7/16, 3/16, 5/16, 1/16) were originally found by trial-and-error, "guided by the desire to have a region of desired density 0.5 come out as a checkerboard pattern". The algorithm scans the image from left to right, top to bottom, quantizing pixel values one by one. Each time, the quantization error is transferred to the neighboring pixels, while not affecting the pixels that already have been quantized. Hence, if a number of pixels have been rounded downwards, it becomes more likely that the next pixel is rounded upwards, such that on average, the quantization error is close to zero. The diffusion coefficients have the property that if the original pixel values are exactly halfway in between the nearest available colors, the dithered result is a checkerboard pattern. For example, 50% grey data could be dithered as a black-and-white checkerboard pattern. For optimal dithering, the counting of quantization errors should be in sufficient accuracy to prevent rounding errors from affecting the result. For correct results, all values should be linearized first, rather than operating directly on sRGB values as is common for images stored on computers. In some implementations, the horizontal direction of scan alternates between lines; this is called "serpentine scanning" or boustrophedon transform dithering. The algorithm described above is in the following pseudocode. This works for any approximately linear encoding of pixel values, such as 8-bit integers, 16-bit integers or real numbers in the range [0, 1]. for each y from top to bottom do for each x from left to right do oldpixel := pixels[x][y] newpixel := find_closest_palette_color(oldpixel) pixels[x][y] := newpixel quant_error := oldpixel - newpixel pixels[x + 1][y ] := pixels[x + 1][y ] + quant_error × 7 / 16 pixels[x - 1][y + 1] := pixels[x - 1][y + 1] + quant_error × 3 / 16 pixels[x ][y + 1] := pixels[x ][y + 1] + quant_error × 5 / 16 pixels[x + 1][y + 1] := pixels[x + 1][y + 1] + quant_error × 1 / 16 When converting grayscale pixel values from a high to a low bit depth (e.g. 8-bit grayscale to 1-bit black-and-white), find_closest_palette_color() may perform just a simple rounding, for example: find_closest_palette_color(oldpixel) = round(oldpixel / 255) The pseudocode can result in pixel values exceeding the valid values (such as greater than 255 in 8-bit grayscale images). Such values should ideally be handled by the find_closest_palette_color() function, rather than clipping the intermediate values, since a subsequent error may bring the value back into range. However, if fixed-width integers are used, wrapping of intermediate values would cause inversion of black and white, and so should be avoided. The find_closest_palette_color() implementation is nontrivial for a palette that is not evenly distributed, however small inaccuracies in selecting the correct palette color have minimal visual impact due to error being propagated to future pixels. A nearest neighbor search in 3D is frequently used.
Google Messages
Google Messages (formerly known as Messenger, Android Messages, and Messages by Google) is a text messaging software application developed by Google for its Android and Wear OS mobile operating systems. It is also available as a web app. Google's official universal messaging platform for the Android ecosystem, Messages employs SMS, MMS, and Rich Communication Services (RCS). Starting in 2023, Google has RCS activated by default on participating Android devices, similar to the implementation of iMessage on Apple devices. Samsung Messages will be discontinued on July 6th 2026, with Samsung transitioning users to Google Messages as the default messaging application. == History == The original code for Android SMS messaging was released in 2009 integrated into the operating system. It was released as a standalone application independent of Android with the release of Android 5.0 Lollipop in 2014, replacing Google Hangouts as the default SMS app on Google's Nexus line of phones. In 2018, Messages adopted RCS messages and evolved to send larger data files, sync with other apps, and even create mass messages. This was in preparation for when Google launched Messages for web. In December 2019, Google began to introduce support for Rich Communication Services (RCS) messaging via an RCS service hosted by Google, referred to in the user interface as "chat features". This was followed by a wider global rollout throughout 2020. The app surpassed 1 billion installs in April 2020, doubling its number of installs in less than a year. Initially, RCS did not support end-to-end encryption. In June 2021, Google introduced end-to-end encryption in Messages by default using the Signal Protocol, for all one-to-one RCS-based conversations, for all RCS group chats in December 2022 for beta users, and for all RCS users by August 2023, as well as enabling RCS for all users by default to encourage encryption. In July 2023, Google announced it would build the Message Layer Security (MLS) end-to-end encryption protocol into Google Messages. Beginning with the Samsung Galaxy S21, Messages replaces Samsung's in-house Messages app as the default text messaging app for One UI for some regions and carriers. In April 2021, the app began to receive UI modifications on Samsung devices to follow aspects of One UI, including pushing the top of the message list towards the middle of the screen to improve ergonomics. In February 2023, Google began to replace references to "chat features" in the Messages user interface with "RCS". In August 2023, Google announced that Messages will use RCS by default for all users unless they opt out, to allow them to benefit from secure messaging. In December 2023, with the arrival of several new features, the app was renamed "Google Messages". In July 2024, Samsung announced it would no longer pre-install Samsung Messages on its Galaxy devices in some regions, starting with the Galaxy Z Fold 6 and Flip, favoring Google Messages instead. In April 2026, Samsung announced that Samsung Messages would be discontinued in July 2026. It encouraged users to switch to Google Messages. == Features == Some of the most important features in Google Messages are: Send instant text and voice messages in 1:1 or group chat conversations over mobile data and Wi-Fi, via Android, Wear OS or the web. End-to-end encryption for RCS chats. Typing, sent, delivered and read status Reply and react to specific messages Share files and high-resolution photos Voice message transcriptions Schedule messages In-app reminders for birthdays and messages you didn't respond to after some time with Nudges Tight integration with the Google ecosystem, e.g. Google Calendar, Meet, Maps, YouTube, Photos, Contacts, Assistant, Search, Safe Browsing etc. Web interface: Users can visit https://messages.google.com/web and either sign in with their Google account or scan the QR code that is shown with their smartphone to access a limited web version of the app that allows them to send and receive messages, provided the smartphone remains connected. Phone number recognition: The app shows the country and province of the caller. Additionally, it can show the company's name or a warning for spam calls if the number is registered in a data base. Access to the Gemini chatbot on select Pixel, Galaxy and Android devices.
Egocentric vision
Egocentric vision or first-person vision is a sub-field of computer vision that entails analyzing images and videos captured by a wearable camera, which is typically worn on the head or on the chest and naturally approximates the visual field of the camera wearer. Consequently, visual data capture the part of the scene on which the user focuses to carry out the task at hand and offer a valuable perspective to understand the user's activities and their context in a naturalistic setting. The wearable camera looking forwards is often supplemented with a camera looking inward at the user's eye and able to measure a user's eye gaze, which is useful to reveal attention and to better understand the user's activity and intentions. == History == The idea of using a wearable camera to gather visual data from a first-person perspective dates back to the 70s, when Steve Mann invented "Digital Eye Glass", a device that, when worn, causes the human eye itself to effectively become both an electronic camera and a television display. Subsequently, wearable cameras were used for health-related applications in the context of Humanistic Intelligence and Wearable AI. Egocentric vision is best done from the point-of-eye, but may also be done by way of a neck-worn camera when eyeglasses would be in-the-way. This neck-worn variant was popularized by way of the Microsoft SenseCam in 2006 for experimental health research works. The interest of the computer vision community into the egocentric paradigm has been arising slowly entering the 2010s and it is rapidly growing in recent years, boosted by both the impressive advances in the field of wearable technology and by the increasing number of potential applications. The prototypical first-person vision system described by Kanade and Hebert, in 2012 is composed by three basic components: a localization component able to estimate the surrounding, a recognition component able to identify object and people, and an activity recognition component, able to provide information about the current activity of the user. Together, these three components provide a complete situational awareness of the user, which in turn can be used to provide assistance to the user or to the caregiver. Following this idea, the first computational techniques for egocentric analysis focused on hand-related activity recognition and social interaction analysis. Also, given the unconstrained nature of the video and the huge amount of data generated, temporal segmentation and summarization were among the first problems addressed. After almost ten years of egocentric vision (2007–2017), the field is still undergoing diversification. Emerging research topics include: Social saliency estimation Multi-agent egocentric vision systems Privacy preserving techniques and applications Attention-based activity analysis Social interaction analysis Hand pose analysis Ego graphical User Interfaces (EUI) Understanding social dynamics and attention Revisiting robotic vision and machine vision as egocentric sensing Activity forecasting Gaze prediction == Technical challenges == Today's wearable cameras are small and lightweight digital recording devices that can acquire images and videos automatically, without the user intervention, with different resolutions and frame rates, and from a first-person point of view. Therefore, wearable cameras are naturally primed to gather visual information from our everyday interactions since they offer an intimate perspective of the visual field of the camera wearer. Depending on the frame rate, it is common to distinguish between photo-cameras (also called lifelogging cameras) and video-cameras. The former (e.g., Narrative Clip and Microsoft SenseCam), are commonly worn on the chest, and are characterized by a very low frame rate (up to 2fpm) that allows to capture images over a long period of time without the need of recharging the battery. Consequently, they offer considerable potential for inferring knowledge about e.g. behaviour patterns, habits or lifestyle of the user. However, due to the low frame-rate and the free motion of the camera, temporally adjacent images typically present abrupt appearance changes so that motion features cannot be reliably estimated. The latter (e.g., Google Glass, GoPro), are commonly mounted on the head, and capture conventional video (around 35fps) that allows to capture fine temporal details of interactions. Consequently, they offer potential for in-depth analysis of daily or special activities. However, since the camera is moving with the wearer head, it becomes more difficult to estimate the global motion of the wearer and in the case of abrupt movements, the images can result blurred. In both cases, since the camera is worn in a naturalistic setting, visual data present a huge variability in terms of illumination conditions and object appearance. Moreover, the camera wearer is not visible in the image and what he/she is doing has to be inferred from the information in the visual field of the camera, implying that important information about the wearer, such for instance as pose or facial expression estimation, is not available. == Applications == A collection of studies published in a special theme issue of the American Journal of Preventive Medicine has demonstrated the potential of lifelogs captured through wearable cameras from a number of viewpoints. In particular, it has been shown that used as a tool for understanding and tracking lifestyle behaviour, lifelogs would enable the prevention of noncommunicable diseases associated to unhealthy trends and risky profiles (such as obesity and depression). In addition, used as a tool of re-memory cognitive training, lifelogs would enable the prevention of cognitive and functional decline in elderly people. More recently, egocentric cameras have been used to study human and animal cognition, human-human social interaction, human-robot interaction, human expertise in complex tasks. Other applications include navigation/assistive technologies for the blind, monitoring and assistance of industrial workflows, and augmented reality interfaces.
Phase correlation
Phase correlation is an approach to estimate the relative translative offset between two similar images (digital image correlation) or other data sets. It is commonly used in image registration and relies on a frequency-domain representation of the data, usually calculated by fast Fourier transforms. The term is applied particularly to a subset of cross-correlation techniques that isolate the phase information from the Fourier-space representation of the cross-correlogram. == Example == The following image demonstrates the usage of phase correlation to determine relative translative movement between two images corrupted by independent Gaussian noise. The image was translated by (20,23) pixels. Accordingly, one can clearly see a peak in the phase-correlation representation at approximately (20,23). == Method == Given two input images g a {\displaystyle \ g_{a}} and g b {\displaystyle \ g_{b}} : Apply a window function (e.g., a Hamming window) on both images to reduce edge effects (this may be optional depending on the image characteristics). Then, calculate the discrete 2D Fourier transform of both images. G a = F { g a } , G b = F { g b } {\displaystyle \ \mathbf {G} _{a}={\mathcal {F}}\{g_{a}\},\;\mathbf {G} _{b}={\mathcal {F}}\{g_{b}\}} Calculate the cross-power spectrum by taking the complex conjugate of the second result, multiplying the Fourier transforms together elementwise, and normalizing this product elementwise. R = G a ∘ G b ∗ | G a ∘ G b ∗ | {\displaystyle \ R={\frac {\mathbf {G} _{a}\circ \mathbf {G} _{b}^{}}{|\mathbf {G} _{a}\circ \mathbf {G} _{b}^{}|}}} Where ∘ {\displaystyle \circ } is the Hadamard product (entry-wise product) and the absolute values are taken entry-wise as well. Written out entry-wise for element index ( j , k ) {\displaystyle (j,k)} : R j k = G a , j k ⋅ G b , j k ∗ | G a , j k ⋅ G b , j k ∗ | {\displaystyle \ R_{jk}={\frac {G_{a,jk}\cdot G_{b,jk}^{}}{|G_{a,jk}\cdot G_{b,jk}^{}|}}} Obtain the normalized cross-correlation by applying the inverse Fourier transform. r = F − 1 { R } {\displaystyle \ r={\mathcal {F}}^{-1}\{R\}} Determine the location of the peak in r {\displaystyle \ r} . ( Δ x , Δ y ) = arg max ( x , y ) { r } {\displaystyle \ (\Delta x,\Delta y)=\arg \max _{(x,y)}\{r\}} === Subpixel registration === Commonly, interpolation methods are used to estimate the peak location in the cross-correlogram to non-integer values, despite the fact that the data are discrete, and this procedure is often termed 'subpixel registration'. A large variety of subpixel interpolation methods are given in the technical literature. Common peak interpolation methods such as parabolic interpolation have been used, and the OpenCV computer vision package uses a centroid-based method, though these generally have inferior accuracy compared to more sophisticated methods. Because the Fourier representation of the data has already been computed, it is especially convenient to use the Fourier shift theorem with real-valued (sub-integer) shifts for this purpose, which essentially interpolates using the sinusoidal basis functions of the Fourier transform. An especially popular FT-based estimator is given by Foroosh et al. In this method, the subpixel peak location is approximated by a simple formula involving peak pixel value and the values of its nearest neighbors, where r ( 0 , 0 ) {\displaystyle r_{(0,0)}} is the peak value and r ( 1 , 0 ) {\displaystyle r_{(1,0)}} is the nearest neighbor in the x direction (assuming, as in most approaches, that the integer shift has already been found and the comparand images differ only by a subpixel shift). Δ x = r ( 1 , 0 ) r ( 1 , 0 ) ± r ( 0 , 0 ) {\displaystyle \ \Delta x={\frac {r_{(1,0)}}{r_{(1,0)}\pm r_{(0,0)}}}} The Foroosh et al. method is quite fast compared to most methods, though it is not always the most accurate. Some methods shift the peak in Fourier space and apply non-linear optimization to maximize the correlogram peak, but these tend to be very slow since they must apply an inverse Fourier transform or its equivalent in the objective function. It is also possible to infer the peak location from phase characteristics in Fourier space without the inverse transformation, as noted by Stone. These methods usually use a linear least squares (LLS) fit of the phase angles to a planar model. The long latency of the phase angle computation in these methods is a disadvantage, but the speed can sometimes be comparable to the Foroosh et al. method depending on the image size. They often compare favorably in speed to the multiple iterations of extremely slow objective functions in iterative non-linear methods. Since all subpixel shift computation methods are fundamentally interpolative, the performance of a particular method depends on how well the underlying data conform to the assumptions in the interpolator. This fact also may limit the usefulness of high numerical accuracy in an algorithm, since the uncertainty due to interpolation method choice may be larger than any numerical or approximation error in the particular method. Subpixel methods are also particularly sensitive to noise in the images, and the utility of a particular algorithm is distinguished not only by its speed and accuracy but its resilience to the particular types of noise in the application. == Rationale == The method is based on the Fourier shift theorem. Let the two images g a {\displaystyle \ g_{a}} and g b {\displaystyle \ g_{b}} be circularly-shifted versions of each other: g b ( x , y ) = d e f g a ( ( x − Δ x ) mod M , ( y − Δ y ) mod N ) {\displaystyle \ g_{b}(x,y)\ {\stackrel {\mathrm {def} }{=}}\ g_{a}((x-\Delta x){\bmod {M}},(y-\Delta y){\bmod {N}})} (where the images are M × N {\displaystyle \ M\times N} in size). Then, the discrete Fourier transforms of the images will be shifted relatively in phase: G b ( u , v ) = G a ( u , v ) e − 2 π i ( u Δ x M + v Δ y N ) {\displaystyle \mathbf {G} _{b}(u,v)=\mathbf {G} _{a}(u,v)e^{-2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}} One can then calculate the normalized cross-power spectrum to factor out the phase difference: R ( u , v ) = G a G b ∗ | G a G b ∗ | = G a G a ∗ e 2 π i ( u Δ x M + v Δ y N ) | G a G a ∗ e 2 π i ( u Δ x M + v Δ y N ) | = G a G a ∗ e 2 π i ( u Δ x M + v Δ y N ) | G a G a ∗ | = e 2 π i ( u Δ x M + v Δ y N ) {\displaystyle {\begin{aligned}R(u,v)&={\frac {\mathbf {G} _{a}\mathbf {G} _{b}^{}}{|\mathbf {G} _{a}\mathbf {G} _{b}^{}|}}\\&={\frac {\mathbf {G} _{a}\mathbf {G} _{a}^{}e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}}{|\mathbf {G} _{a}\mathbf {G} _{a}^{}e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}|}}\\&={\frac {\mathbf {G} _{a}\mathbf {G} _{a}^{}e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}}{|\mathbf {G} _{a}\mathbf {G} _{a}^{}|}}\\&=e^{2\pi i({\frac {u\Delta x}{M}}+{\frac {v\Delta y}{N}})}\end{aligned}}} since the magnitude of an imaginary exponential always is one, and the phase of G a G a ∗ {\displaystyle \ \mathbf {G} _{a}\mathbf {G} _{a}^{}} always is zero. The inverse Fourier transform of a complex exponential is a Dirac delta function, i.e. a single peak: r ( x , y ) = δ ( x + Δ x , y + Δ y ) {\displaystyle \ r(x,y)=\delta (x+\Delta x,y+\Delta y)} This result could have been obtained by calculating the cross correlation directly. The advantage of this method is that the discrete Fourier transform and its inverse can be performed using the fast Fourier transform, which is much faster than correlation for large images. === Benefits === Unlike many spatial-domain algorithms, the phase correlation method is resilient to noise, occlusions, and other defects typical of medical or satellite images. The method can be extended to determine rotation and scaling differences between two images by first converting the images to log-polar coordinates. Due to properties of the Fourier transform, the rotation and scaling parameters can be determined in a manner invariant to translation. === Limitations === In practice, it is more likely that g b {\displaystyle \ g_{b}} will be a simple linear shift of g a {\displaystyle \ g_{a}} , rather than a circular shift as required by the explanation above. In such cases, r {\displaystyle \ r} will not be a simple delta function, which will reduce the performance of the method. In such cases, a window function (such as a Gaussian or Tukey window) should be employed during the Fourier transform to reduce edge effects, or the images should be zero padded so that the edge effects can be ignored. If the images consist of a flat background, with all detail situated away from the edges, then a linear shift will be equivalent to a circular shift, and the above derivation will hold exactly. The peak can be sharpened by using edge or vector correlation. For periodic images (such as a chessboard or picket fence), phase correlation may yield ambiguous results with several peaks in the resulting output. == Applications == Phase correlation is the preferred m
Image destriping
Image destriping is the process of removing stripes or streaks from images and videos without disrupting the original image/video. These artifacts plague a range of fields in scientific imaging including atomic force microscopy, light sheet fluorescence microscopy, and planetary satellite imaging. The most common image processing techniques to reduce stripe artifacts is with Fourier filtering. Unfortunately, filtering methods risk altering or suppressing useful image data. Methods developed for multiple-sensor imaging systems in planetary satellites use statistical-based methods to match signal distribution across multiple sensors. More recently, a new class of approaches leverage compressed sensing, to regularize an optimization problem, and recover stripe free images. In many cases, these destriped images have little to no artifacts, even at low signal to noise ratios.
National Parking Platform
The National Parking Platform is a digital platform in the United Kingdom providing interoperability between car park operators, parking apps, and other service providers. It enables all parking apps that support the system: RingGo, JustPark, PayByPhone, Apcoa Connect, AppyParking, and Caura to work at all participating car parks. It has been rolled out in 13 local authorities so far. It was first developed by the Department for Transport starting in 2019, and since May 2025 is controlled by the British Parking Association on a not-for-profit basis. == Participating local authorities == Buckinghamshire Cheshire West and Chester Coventry City East Hertfordshire East Suffolk Liverpool City Manchester City Oxfordshire County Peterborough City Stevenage Sutton Walsall Welwyn Hatfield
Kruti
Kruti is a multilingual AI agent and chatbot developed by the Indian company Ola Krutrim. It is designed to perform real-world tasks for users, such as booking taxis and ordering food, by integrating directly with various online services. It is notable for its ability to understand and respond in multiple Indian languages. Developed by a team founded by Bhavish Aggarwal, Kruti functions as an "agentic" AI, meaning it can reason, plan, and execute multi-step tasks to fulfill a user's request. The backend technology combines several open-source large language models with Ola's proprietary Krutrim V2 model. The system was developed to work primarily on smartphones, addressing the Indian market's specific needs, including language diversity and potential bandwidth constraints. Kruti was officially released in June 2025, replacing an earlier chatbot from the company that was also named Krutrim. Initially supporting 13 languages, the company plans to expand its capabilities to 22 Indian languages. == Background == Kruti is an improved version of Ola's Krutrim chatbot, which was first launched in 2023 and was intended to be replaced by Kruti. It was officially released on 12 June 2025 as an upgrade to passive chatbots, with support for text and voice in 13 Indian languages. As an agentic AI, it can execute tasks with customization and reasoning, providing adaptive answers based on user preferences and past interactions. Kruti is optimized for smartphone usage and designed to accommodate bandwidth constraints and usage patterns in India. To ensure scalability and cost-effective performance, it combines various open-source large language models with Ola's own Krutrim V2, which has 12 billion parameters. Its speech recognition is built to identify regional Indian languages, dialects, and accents. Due to its integration with numerous apps and services, Kruti is context-aware and can proactively complete tasks. Initially connected only with Ola ecosystem services, Krutrim intends to expand and incorporate various Indian services into Kruti, with the goal of adding services from Blinkit, Swiggy, and Uber with respective voice command support. On 20 June 2025, Krutrim acquired the AI platform BharatSah‘AI’yak to increase its involvement in government, education, and agriculture projects. This acquisition will allow Kruti to assist in broadening the scope of BharatSah'AI'yak's work on India-centric, vernacular retrieval-augmented generation AI bots. == Development == Kruti is designed to perform tasks with minimal user input, accepting documents, images, and text, without requiring users to switch between applications. Its agentic framework breaks queries into sub-tasks executed by multiple agents working sequentially or concurrently, with reported accuracy exceeding 90%. Kruti connects to company databases and APIs via the Model Context Protocol and presents responses as summaries, tables, or narratives adapted to user behaviour. The system supports payments via credit/debit cards and UPI. The underlying stack, which includes foundation models and AI training and inference systems, is intended to support adaptation across sectors such as healthcare, education, and finance. Ola Cabs and the Open Network for Digital Commerce have begun integrating Kruti into their platforms pending broader reliability testing.