From 2025 onwards, X (formerly Twitter)'s integrated chatbot, Grok, has allowed users to nonconsensually alter images of individuals, including minors, to show them in bikinis or transparent clothing, or in sexually suggestive contexts. The majority of these prompts were targeted at women and girls. Users were able to generate such images by responding to a photo with a request to Grok, such as "put her in a bikini", to which the chatbot would publicly reply with a generated image. The scandal drew significant criticism from lawmakers across the world, and there were calls for bans on X, as well as legal crackdowns on X and xAI for, amongst other reasons, the facilitation of sexual abuse, revenge porn, and child pornography. == Background == Deepfake pornography emerged in the late 2010s with the advent of machine learning. Originally, it was created on a small individual scale using a combination of machine learning algorithms, computer vision techniques, and AI software. However, the production process has significantly evolved since 2018, with the advent of several public apps that have largely automated the process. Since 2023, several AI apps available on Google Play and the Apple App Store are capable of "nudify-ing" user provided photos to generate non-consensual deepfake pornography. Grok would first be proposed by Elon Musk in 2023, when he expressed an intention to create his own AI chatbot to "combat bias". Grok version 2.0, released on August 14, 2024, would introduce image generation capabilities, ones which would be improved over successive updates. == Grok deepfake generation == Cases of Grok being used to remove the clothes from women in pictures, replacing them with bikinis or lingerie, began to surface in May 2025. By late December 2025, a trend of X users requesting such edits to women's photos without permission had taken root, and this received significant media attention in the first few days of January 2026. Some users prompted Grok to edit photos of women into sexualized poses, and others to add blood and bruising, with the chatbot publicly posting these graphic images in response. Grok's X account was restricted on January 9 from posting image generation responses to users who are not paid subscribers, providing a link to "subscribe to unlock these features". All users were still able to generate Grok-altered images using X's "Edit image" feature, and the standalone Grok website and app. However, by March 19, Grok’s Imagine feature was fully restricted to paid subscribers only (SuperGrok tier) for both the standalone Grok website and mobile app. == Analysis == An analysis of 20,000 images generated by Grok between December 25, 2025, and January 1, 2026, showed 2% appeared to be 18 or younger, including 30 of "young or very young" women or girls in bikinis or transparent clothes. A Reuters review of Grok requests over 10 minutes on January 2nd found 102 attempts to put women in bikinis. A separate analysis conducted over 24 hours from January 5 to 6 calculated that users had Grok create 6,700 sexually suggestive or nudified images per hour — 84 times more so than the top 5 deepfake websites combined. Wired reported that far more graphic AI-generated sexual imagery was being created by Grok on its website and app, which are separate to X, including female celebrities removing their clothes and engaging in sexual acts. An analysis of 800 pieces of recovered content by the Paris-based nonprofit AI Forensics found that almost 10% were "instances of photorealistic people, very young, doing sexual activities". AI-generated deepfakes have been described as sexual assault, and as a means to push women out of the public sphere. AI-generated sexually explicit or exploitative image claims are now being treated more like product safety or personal injury harms, not just privacy violations. Because harm may occur the moment an image is generated, some plaintiffs argue liability should focus on the system’s design and safety safeguards. == Reactions == On January 15, the Get Grok Gone campaign delivered letters to Apple and Google, demanding the removal of the app from Apple Store and Google Play Store respectively. The campaign accused both companies of profiting from nonconsensual intimate imagery and child sexual abuse imagery, which were also banned by the companies own policies. The Get Grok Gone campaign argues that the restrictions placed on Grok by xAI are not enough and that Apple and Google are enabling the distribution of harmful material by hosting the apps. === Elon Musk and xAI === xAI responded to requests for comment from media organizations with the automated reply, "Legacy Media Lies." On January 2, Elon Musk reacted "Not sure why, but I couldn’t stop laughing about this one 🤣🤣" to an image of a toaster dressed in a bikini by Grok. Later, on January 14, Elon Musk said that he was "not aware of any naked underage images generated by Grok. Literally zero." Later that same day, xAI announced that X users will no longer be able to use Grok to alter images of real people to portray them in revealing clothing. However, verified X users, as well as users of the standalone Grok app and website, were still able to generate such images. ==== Elon Musk's family ==== Ashley St. Clair, mother of one of Elon Musk's children, reported that Grok users were creating fake sexualized images from her photos, including a photo of her as a child. She considers the photos to be a form of revenge porn, and considered suing under the Take It Down Act. A spokesperson for X stated, "We take action against illegal content on X, including child sexual abuse material (CSAM), by removing it, permanently suspending accounts, and working with local governments and law enforcement as necessary. Anyone using or prompting Grok to make illegal content will suffer the same consequences as if they upload illegal content." However, Grok continued to post non-consensual sexual images. On January 15, St. Clair filed a lawsuit against xAI in the New York Supreme Court. === Canada === In response to the Grok deepfake scandal, individuals have asked that the government of Canada boycott X. On January 10, 2026, Canadian MP and Minister of AI Evan Solomon declared that Canada "is not considering a ban on X". In April 2026, Bill C-16, An Act to amend certain Acts in relation to criminal and correctional matters (child protection, gender-based violence, delays and other measures), was amended following a proposal by Conservative MP Andrew Lawton to ensure that AI-generated images and "nearly nude" intimate images are criminalized. A further proposal by NDP MP Leah Gazan to encompass "sexualized or humiliating contexts, such transparent bathing suits or being covered in blood or bruises" was voted down. === France === On January 2, 2026, French ministers reported the AI tool to prosecutors, calling the content "manifestly illegal", and also asked regulators to check compliance with the Digital Services Act. On February 3, Paris prosecutors office, a cybercrime team employed by them and Europol searched the Paris offices of X. The investigation started as one into allegations of abuse of algorithms and fraudulent data extraction, but has expanded into spreading Holocaust denial and sexual deepfakes. Elon Musk and former CEO Linda Yaccarino have been summoned to a hearing on April 20, with other X staff as witnesses. On April 20, Musk did not turn up for the hearing. The Paris prosecutors office told the BBC on April 20 that it had "taken note of the absence of the people summoned", adding "the presence or absence (of the people summoned) is not an obstacle to continuing the investigation". === India === Indian Member of Parliament Priyanka Chaturvedi filed a complaint to India's IT ministry, demanding a review of Grok's safety mechanisms. === Indonesia === On January 10, Indonesia announced that Grok will be temporarily blocked, becoming the first country to do so. Meutya Hafid, the Minister of Communication and Digital Affairs, stated that "the government views the practice of non-consensual sexual deepfakes as a serious violation of human rights, dignity, and the security of citizens in the digital space." Access to Grok in the country was later restored on February 1. === Ireland === On January 6, Coimisiún na Meán, the Irish media commission, said they were consulting with the European Commission about concerns that Grok was generating sexualized images of women and children. The same day, Ofcom of the United Kingdom contacted X concerning complaints about these images. On January 13, Micheál Martin, Taoiseach of Ireland, announced he would talk with Rossa Fanning, the country's Attorney General, about the Grok chatbot being used to produce sexually explicit images of women and minors. On January 14, the Garda Síochána announced there are 200 investigations into child sex abuse images generated by Grok. The Garda National Cyber Crime Bureau has al
Anomaly detection
In data analysis, anomaly detection (also referred to as outlier detection and sometimes as novelty detection) is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority of the data and do not conform to a well defined notion of normal behavior. Such examples may arouse suspicions of being generated by a different mechanism, or appear inconsistent with the remainder of that set of data. Anomaly detection finds application in many domains including cybersecurity, medicine, machine vision, statistics, neuroscience, law enforcement and financial fraud to name only a few. Anomalies were initially searched for clear rejection or omission from the data to aid statistical analysis, for example to compute the mean or standard deviation. They were also removed to better predictions from models such as linear regression, and more recently their removal aids the performance of machine learning algorithms. However, in many applications anomalies themselves are of interest and are the observations most desirous in the entire data set, which need to be identified and separated from noise or irrelevant outliers. Three broad categories of anomaly detection techniques exist. Supervised anomaly detection techniques require a data set that has been labeled as "normal" and "abnormal" and involves training a classifier. However, this approach is rarely used in anomaly detection due to the general unavailability of labelled data and the inherent unbalanced nature of the classes. Semi-supervised anomaly detection techniques assume that some portion of the data is labelled. This may be any combination of the normal or anomalous data, but more often than not, the techniques construct a model representing normal behavior from a given normal training data set, and then test the likelihood of a test instance to be generated by the model. Unsupervised anomaly detection techniques assume the data is unlabelled and are by far the most commonly used due to their wider and relevant application. == Definition == Many attempts have been made in the statistical and computer science communities to define an anomaly. The most prevalent ones include the following, and can be categorised into three groups: those that are ambiguous, those that are specific to a method with pre-defined thresholds usually chosen empirically, and those that are formally defined: === Ill defined === An outlier is an observation which deviates so much from the other observations as to arouse suspicions that it was generated by a different mechanism. Anomalies are instances or collections of data that occur very rarely in the data set and whose features differ significantly from most of the data. An outlier is an observation (or subset of observations) which appears to be inconsistent with the remainder of that set of data. An anomaly is a point or collection of points that is relatively distant from other points in multi-dimensional space of features. Anomalies are patterns in data that do not conform to a well-defined notion of normal behaviour. === Specific === Let T be observations from a univariate Gaussian distribution and O a point from T. Then the z-score for O is greater than a pre-selected threshold if and only if O is an outlier. == History == === Intrusion detection === The concept of intrusion detection, a critical component of anomaly detection, has evolved significantly over time. Initially, it was a manual process where system administrators would monitor for unusual activities, such as a vacationing user's account being accessed or unexpected printer activity. This approach was not scalable and was soon superseded by the analysis of audit logs and system logs for signs of malicious behavior. By the late 1970s and early 1980s, the analysis of these logs was primarily used retrospectively to investigate incidents, as the volume of data made it impractical for real-time monitoring. The affordability of digital storage eventually led to audit logs being analyzed online, with specialized programs being developed to sift through the data. These programs, however, were typically run during off-peak hours due to their computational intensity. The 1990s brought the advent of real-time intrusion detection systems capable of analyzing audit data as it was generated, allowing for immediate detection of and response to attacks. This marked a significant shift towards proactive intrusion detection. As the field has continued to develop, the focus has shifted to creating solutions that can be efficiently implemented across large and complex network environments, adapting to the ever-growing variety of security threats and the dynamic nature of modern computing infrastructures. == Applications == Anomaly detection is applicable in a very large number and variety of domains, and is an important subarea of unsupervised machine learning. As such it has applications in cyber-security, intrusion detection, fraud detection, fault detection, system health monitoring, event detection in sensor networks, detecting ecosystem disturbances, defect detection in images using machine vision, medical diagnosis and law enforcement. === Intrusion detection === Anomaly detection was proposed for intrusion detection systems (IDS) by Dorothy Denning in 1986. Anomaly detection for IDS is normally accomplished with thresholds and statistics, but can also be done with soft computing, and inductive learning. Types of features proposed by 1999 included profiles of users, workstations, networks, remote hosts, groups of users, and programs based on frequencies, means, variances, covariances, and standard deviations. The counterpart of anomaly detection in intrusion detection is misuse detection. === Fintech fraud detection === Anomaly detection is vital in fintech for fraud prevention. === Preprocessing === Preprocessing data to remove anomalies can be an important step in data analysis, and is done for a number of reasons. Statistics such as the mean and standard deviation are more accurate after the removal of anomalies, and the visualisation of data can also be improved. In supervised learning, removing the anomalous data from the dataset often results in a statistically significant increase in accuracy. === Video surveillance === Anomaly detection has become increasingly vital in video surveillance to enhance security and safety. With the advent of deep learning technologies, methods using Convolutional Neural Networks (CNNs) and Simple Recurrent Units (SRUs) have shown significant promise in identifying unusual activities or behaviors in video data. These models can process and analyze extensive video feeds in real-time, recognizing patterns that deviate from the norm, which may indicate potential security threats or safety violations. An important aspect for video surveillance is the development of scalable real-time frameworks. Such pipelines are required for processing multiple video streams with low computational resources. === IT infrastructure === In IT infrastructure management, anomaly detection is crucial for ensuring the smooth operation and reliability of services. These are complex systems, composed of many interactive elements and large data quantities, requiring methods to process and reduce this data into a human and machine interpretable format. Techniques like the IT Infrastructure Library (ITIL) and monitoring frameworks are employed to track and manage system performance and user experience. Detected anomalies can help identify and pre-empt potential performance degradations or system failures, thus maintaining productivity and business process effectiveness. === IoT systems === Anomaly detection is critical for the security and efficiency of Internet of Things (IoT) systems. It helps in identifying system failures and security breaches in complex networks of IoT devices. The methods must manage real-time data, diverse device types, and scale effectively. Garg et al. have introduced a multi-stage anomaly detection framework that improves upon traditional methods by incorporating spatial clustering, density-based clustering, and locality-sensitive hashing. This tailored approach is designed to better handle the vast and varied nature of IoT data, thereby enhancing security and operational reliability in smart infrastructure and industrial IoT systems. === Petroleum industry === Anomaly detection is crucial in the petroleum industry for monitoring critical machinery. A 2015 paper proposed a novel segmentation algorithm using support vector machines to analyze sensor data for real-time anomaly detection. === Oil and gas pipeline monitoring === In the oil and gas sector, anomaly detection is not just crucial for maintenance and safety, but also for environmental protection. Aljameel et al. propose an advanced machine learning-based model for detecting minor leaks in oil and gas pipelines, a task traditional methods may miss.
Affinity (software)
Affinity is a graphics editor developed by Serif, a subsidiary of Canva. It is simultaneously a vector graphics editor, a raster graphics editor and a desktop publishing application. It was first released in 2025 as a successor to Serif's Affinity Designer, Affinity Photo and Affinity Publisher, uniting the three editors into one application. While the previous versions competed individually against Adobe's Illustrator, Photoshop, and InDesign, Affinity 3.0 integrates their functionality into a single application. It uses a freemium model monetized by AI features exclusive to Canva Pro subscribers. == Functionality == Affinity is divided into a number of workspaces ("studios"), which are equivalent to the previous suite of Affinity applications: "vector" for vector graphics (Designer), "pixel" for raster editing (Photo), and "layout" for desktop publishing (Publisher). Additionally, it introduces the ability to create custom workspaces. The application supports real-time previews and non-destructive editing, which are based on GPU acceleration. Supported file formats include Adobe Photoshop, InDesign and Illustrator files, PDF, SVG, and TIFF, as well as a custom .af file format. === Vector editing === === Raster editing === Affinity includes photo editing tools including adjustments, masks, blend modes, batch processing, and retouching facilities. Additionally, the application can develop RAW files, similar to Adobe Lightroom. === Desktop publishing === Publishing features include master pages, text styles, and advanced typography. === AI features === The application supports Canva's existing AI features, such as background removal and generative fill. This requires a Canva subscription. == Development == === Background and acquisition (2014–2024) === Serif launched the original Affinity suite starting with Affinity Designer in 2014, followed by Photo (2015) and Publisher (2019). The software gained popularity for its one-time purchase model, contrasting with Adobe's subscription-based Creative Cloud. In November 2022, Serif released Version 2 of the suite, introducing a "Universal License" that covered all three apps across all platforms. In March 2024, Canva acquired Serif for approximately A$580 million (£300 million). Following user backlash regarding a potential shift to subscriptions, Canva and Serif issued a joint "Pledge" committing to four key principles: fair pricing, no mandatory subscriptions, perpetual licenses for existing products, and continued development of Affinity as a standalone suite. === Unified release (2025) === In September 2025, Serif pulled all existing versions of Affinity Designer, Affinity Photo and Affinity Publisher from sale ahead an upcoming announcement on 30 October; also ahead of the announcement, the iPadOS versions of the Affinity suite became free on App Store. During a "Creative Freedom" keynote on 30 October 2025, Canva released a new version now simply branded as "Affinity" (also known as "Affinity by Canva"), and referred to internally as version 3.0. Version 3 drops the separate applications and integrates their functionality into a singular application, and adds the ability to export directly to the Canva platform. It also adds a Canva AI studio, including background removal, "Expand & Edit", and generative fill. As of version 3, Affinity has switched to a freemium model; it is now available at no charge to users, although access to Canva AI features are locked behind the existing Canva Pro subscription service. Serif stated that the perpetually-licensed version 2 will remain available to existing owners, although it will no longer be actively maintained. The new version is currently available for macOS and Windows only, with an iPadOS version to be released soon. == Reception == The change in business model by Canva in 2025 was met with mixed reception, including concerns about its incorporation of AI features. Some users were concerned that their projects would be used for machine learning purposes, or that future versions would suffer from a lack of maintenance or become adware. Additionally, some felt it turned Affinity into fundamentally subscription-based software, given the prevalence of these features in professional contexts. Affinity publicly stated on social media that it would remain "free forever", users' projects would not be used to train AI models, and that "Canva has built a sustainable business model that allows this kind of generosity. And when more professionals use Affinity, Canva can sell more seats into businesses."
Polynomial texture mapping
Polynomial texture mapping (PTM), also known as Reflectance Transformation Imaging (RTI), is a technique of imaging and interactively displaying objects under varying lighting conditions to reveal surface phenomena. The data acquisition method is single camera multi light (SCML). == Origins == The method was originally developed by Tom Malzbender of HP Labs in order to generate enhanced 3D computer graphics and it has since been adopted for cultural heritage applications. == Methodology == A series of images is captured in a darkened environment with the camera in a fixed position and the object lit from different angles (Single Camera Multi Light). Interactive software processes and combines the set of images to enable the user inspecting the object to control a virtual light source. The virtual light source may be manipulated to simulate light from different angles and of different intensity or wavelengths to illuminate the surface of artefacts and reveal details. Open-source tools for processing the captured images and publishing the resulting relightable images on the web are freely available. == Applications == Polynomial texture mapping may be used for detailed recording and documentation, 3D modeling, edge detection, and to aid the study of inscriptions, rock art and other artefacts. It has been applied to hundreds of the Vindolanda tablets by the Centre for the Study of Ancient Documents at the University of Oxford in conjunction with the British Museum. It has also been deployed, by Ben Altshuler of the Institute for Digital Archaeology, to scan the Philae obelisk at Kingston Lacy and the Parian Chronicle at the Ashmolean Museum; in both cases scans revealed significant, previously illegible text. Method was also used for identifying microscopic worked antler from Star Carr and recording ancient rock art in Armenia. A 'dome' supporting twenty-four lights has been used to image paintings in the National Gallery and produce polynomial texture maps, providing information on condition phenomena for conservation purposes. Studies of the technique at the National Gallery and Tate concluded that it is an effective tool for documenting changes in the condition of paintings, more easily repeatable than raking light photography, and therefore could be used to assess paintings during structural treatment and before and after loan. Twelve dome-based systems built by the University of Southampton have been used to capture thousands of cuneiform tablets at various museums. The technique is now also finding uses in the field of forensic science, for example in imaging footprints, tyre marks, and indented writing.
Reconstruction from projections
The problem of reconstructing a multidimensional signal from its projection is uniquely multidimensional, having no 1-D counterpart. It has applications that range from computer-aided tomography to geophysical signal processing. It is a problem which can be explored from several points of view—as a deconvolution problem, a modeling problem, an estimation problem, or an interpolation problem. == Motivation and applications == Many fields in science and engineering use reconstruction from projections, especially in imaging. It is widely applied geophysical tomography, medical imaging and industrial radiography. For example, in a CT scanner, the 3D structure of the patient’s body being scanned is measured with beams going through the tissue and hitting a detector, giving a flat projection of the body from that angle. Multiple projections are put together to get an image of the position and shape of structures inside in 3D. == Problem statement and basics == A projection is a linear mapping of an M {\displaystyle M} dimensional signal into an N {\displaystyle N} dimensional one, where N ≤ M {\displaystyle N\leq M} . And the objective of reconstruction is to restore the M {\displaystyle M} dimensional signal based on the N {\displaystyle N} dimensional signal. The following case is a 2-D signal projected into 1D signal. The signal in the original coordinate is denoted as d ( u , v ) {\displaystyle d(u,v)} . Now consider a collimated beam of radiation coming from the opposite orientation of v ^ {\displaystyle {\hat {v}}} , producing a projection along u ^ {\displaystyle {\hat {u}}} . v ^ {\displaystyle {\hat {v}}} and u ^ {\displaystyle {\hat {u}}} are normal to each other, and the angle between u {\displaystyle u} and u ^ {\displaystyle {\hat {u}}} is theta. The signal obtained along u ^ {\displaystyle {\hat {u}}} axis is defined to be p θ ( u ^ ) {\displaystyle p_{\theta }({\hat {u}})} . The relationship between the original coordinate and the rotated coordinate is given by [ u ^ v ^ ] = [ cos θ sin θ − sin θ cos θ ] [ u v ] {\displaystyle {\begin{bmatrix}{\hat {u}}\\{\hat {v}}\end{bmatrix}}={\begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}u\\v\end{bmatrix}}} or inversely, [ u v ] = [ cos θ − sin θ sin θ cos θ ] [ u ^ v ^ ] {\displaystyle {\begin{bmatrix}u\\v\end{bmatrix}}={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}{\hat {u}}\\{\hat {v}}\end{bmatrix}}} Then we have p θ ( u ^ ) = ∫ − ∞ ∞ d ( u , v ) d v ^ = ∫ − ∞ ∞ d ( u ^ cos ( θ ) − v ^ sin ( θ ) , u ^ sin ( θ ) + v ^ cos ( θ ) ) d v ^ {\displaystyle p_{\theta }({\hat {u}})=\int _{-\infty }^{\infty }d(u,v)\,\mathrm {d} {\hat {v}}=\int _{-\infty }^{\infty }d({\hat {u}}\cos(\theta )-{\hat {v}}\sin(\theta ),{\hat {u}}\sin(\theta )+{\hat {v}}\cos(\theta ))\,\mathrm {d} {\hat {v}}} By varying theta, a large number of projections can be obtained. Given the projection-slice theorem, D ( Ω , θ ) {\displaystyle D(\Omega ,\theta )} ,the slice of the Fourier transform of d ( u , v ) {\displaystyle d(u,v)} at angle theta, is equivalent to P θ ( Ω ) {\displaystyle P_{\theta }(\Omega )} , the Fourier Transform of the projection p θ ( u ^ ) {\displaystyle p_{\theta }({\hat {u}})} . Therefore, the unknown d ( u , v ) {\displaystyle d(u,v)} can be obtained from its Fourier transform by means of the Fourier transform inversion integral d ( u , v ) = 1 4 π 2 ∫ − ∞ ∞ ∫ − ∞ ∞ D ( Ω 1 , Ω 2 ) e j Ω 1 u e j Ω 2 v d Ω 1 , Ω 2 {\displaystyle \mathrm {d} (u,v)={\frac {1}{4\pi ^{2}}}\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }D(\Omega _{1},\Omega _{2})e^{j\Omega _{1}u}e^{j\Omega _{2}v}\,\mathrm {d} \Omega _{1},\Omega _{2}} = 1 4 π 2 ∫ 0 ∞ ∫ − π π D ( Ω , θ ) e j Ω u cos ( θ ) e j Ω v s i n θ | Ω | d Ω d θ {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{0}^{\infty }\int _{-\pi }^{\pi }D(\Omega ,\theta )e^{j\Omega u\cos(\theta )}e^{j\Omega vsin\theta }{\begin{vmatrix}\Omega \end{vmatrix}}\,\mathrm {d} \Omega \mathrm {d} \theta } = 1 4 π 2 ∫ − π π ∫ 0 ∞ P θ ( Ω ) e j Ω ( u cos θ + v sin θ ) | Ω | d Ω d θ {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{-\pi }^{\pi }\int _{0}^{\infty }P_{\theta }(\Omega )e^{j}\Omega (u\cos \theta +v\sin \theta ){\begin{vmatrix}\Omega \end{vmatrix}}\,\mathrm {d} \Omega \mathrm {d} \theta } = 1 4 π 2 ∫ 0 π ( ∫ − ∞ ∞ P θ ( Ω ) | Ω | {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{0}^{\pi }(\int _{-\infty }^{\infty }P_{\theta }(\Omega ){\begin{vmatrix}\Omega \end{vmatrix}}} e j Ω u ^ d Ω ) d θ {\displaystyle e^{j\Omega {\hat {u}}}\mathrm {d} \Omega )\mathrm {d} \theta } By taking the inverse Fourier Transform and assuming g ( u ^ ) = F − 1 ( | Ω | 2 ) {\displaystyle g({\hat {u}})={\mathcal {F}}^{-1}({{\begin{vmatrix}\Omega \end{vmatrix}}^{2}})} , we get d ( u , v ) = ∑ i △ θ i [ p θ ( u ^ ) ∗ g θ i ( u ^ ) ] {\displaystyle d(u,v)=\sum _{i}\vartriangle \theta _{i}[p_{\theta }({\hat {u}})g_{\theta i}({\hat {u}})]} == Approaches == In practice, there are a wide variety of methods that are utilized, most of which are reconstruct 3-D information (volume) from 2-D signals (image). Typically used methods are CT, MRI, PET and SPECT. And the filtered back projection based on the principles introduced above are commonly applied. === Computed Tomography (CT) === In CT, a volume is formed by stacking the axial slices. The software cuts the volume in a different plane (usually orthogonal). Commonly, slice data is generated using an X-ray source that rotates around the object. X-ray sensors are positioned on the opposite side of the circle from the X-ray source. === Magnetic resonance imaging (MRI) === In MRI, energy from an oscillating magnetic field is temporarily applied to the patient at the appropriate resonance frequency. The protons (hydrogen atoms) emit a radio frequency signal which is measured by a receiving coil. The radio signal can be made to encode position information by varying the main magnetic field using gradient coils. === Positron emission tomography (PET) === The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule. Three-dimensional images of tracer concentration within the body are then constructed by computer analysis. In modern PET-CT scanners, three dimensional imaging is often accomplished with the aid of a CT X-ray scan performed on the patient during the same session, in the same machine. === Single-photon emission computed tomography (SPECT) === SPECT imaging is performed by using a gamma camera to acquire multiple 2-D images (projections) from multiple angles. Multiple projections are used to yield a 3-D data set. This data set may then be manipulated to show thin slices along any chosen axis of the body. SPECT is similar to PET in its use of radioactive tracer material and detection of gamma rays, while the tracers used in SPECT emit gamma radiation that is measured more directly.
Visual analytics
Visual analytics is a multidisciplinary science and technology field that emerged from information visualization and scientific visualization. It focuses on how analytical reasoning can be facilitated by interactive visual interfaces. == Overview == Visual analytics is "the science of analytical reasoning facilitated by interactive visual interfaces." It can address problems whose size, complexity, and need for closely coupled human and machine analysis may make them otherwise intractable. Visual analytics advances scientific and technological development across multiple domains, including analytical reasoning, human–computer interaction, data transformations, visual representation for computation and analysis, analytic reporting, and the transition of new technologies into practice. As a research agenda, visual analytics brings together several scientific and technical communities from computer science, information visualization, cognitive and perceptual sciences, interactive design, graphic design, and social sciences. Visual analytics integrates new computational and theory-based tools with innovative interactive techniques and visual representations to enable human-information discourse. The design of the tools and techniques is based on cognitive, design, and perceptual principles. This science of analytical reasoning provides the reasoning framework upon which one can build both strategic and tactical visual analytics technologies for threat analysis, prevention, and response. Analytical reasoning is central to the analyst's task of applying human judgments to reach conclusions from a combination of evidence and assumptions. Visual analytics has some overlapping goals and techniques with information visualization and scientific visualization. There is currently no clear consensus on the boundaries between these fields, but broadly speaking the three areas can be distinguished as follows: Scientific visualization deals with data that has a natural geometric structure (e.g., MRI data, wind flows). Information visualization handles abstract data structures such as trees or graphs. Visual analytics is especially concerned with coupling interactive visual representations with underlying analytical processes (e.g., statistical procedures, data mining techniques) such that high-level, complex activities can be effectively performed (e.g., sense making, reasoning, decision making). Visual analytics seeks to marry techniques from information visualization with techniques from computational transformation and analysis of data. Information visualization forms part of the direct interface between user and machine, amplifying human cognitive capabilities in six basic ways: by increasing cognitive resources, such as by using a visual resource to expand human working memory, by reducing search, such as by representing a large amount of data in a small space, by enhancing the recognition of patterns, such as when information is organized in space by its time relationships, by supporting the easy perceptual inference of relationships that are otherwise more difficult to induce, by perceptual monitoring of a large number of potential events, and by providing a manipulable medium that, unlike static diagrams, enables the exploration of a space of parameter values These capabilities of information visualization, combined with computational data analysis, can be applied to analytic reasoning to support the sense-making process. == History == As an interdisciplinary approach, visual analytics has its roots in information visualization, cognitive sciences, and computer science. The term and scope of the field was defined in the early 2000s through researchers such as Jim Thomas, Kristin A. Cook, John Stasko, Pak Chung Wong, Daniel A. Keim and David S. Ebert. As a reaction to the September 11, 2001 attacks the United States Department of Homeland Security was established in late 2002, combining dozens of previously separated government agencies. Building upon earlier work on visual data mining by Daniel A. Keim starting in the late 1990s, this simultaneously lead to the development of a research agenda for visual analytics. As part of these efforts the National Visualization and Analytics Center (NVAC) at Pacific Northwest National Laboratory was established in 2004, whose charter was to develop system to mitigate information overload after the September 11, 2001 attacks in the intelligence community. Their research work determined core challenges, posed open research questions, and positioned visual analytics as a new research domain, in particular through the 2005 research agenda Illuminating the Path. In 2006, the IEEE VIS community led by Pak Chung Wong and Daniel A. Keim launched the annual IEEE Conference on Visual Analytics Science and Technology (VAST), providing a dedicated venue for research into visual analytics, which in 2020 merged to form the IEEE Visualization conference. In 2008, scope and challenges of visual analytics were conceptually defined by Daniel A. Keim and Jim Thomas in their influential book about visual data mining. The domain was further refined as part of the European Commissions FP7 VisMaster program in the late 2000s. == Topics == === Scope === Visual analytics is a multidisciplinary field that includes the following focus areas: Analytical reasoning techniques that enable users to obtain deep insights that directly support assessment, planning, and decision making Data representations and transformations that convert all types of conflicting and dynamic data in ways that support visualization and analysis Techniques to support production, presentation, and dissemination of the results of an analysis to communicate information in the appropriate context to a variety of audiences. Visual representations and interaction techniques that take advantage of the human eye's broad bandwidth pathway into the mind to allow users to see, explore, and understand large amounts of information at once. === Analytical reasoning techniques === Analytical reasoning techniques are the method by which users obtain deep insights that directly support situation assessment, planning, and decision making. Visual analytics must facilitate high-quality human judgment with a limited investment of the analysts’ time. Visual analytics tools must enable diverse analytical tasks such as: Understanding past and present situations quickly, as well as the trends and events that have produced current conditions Identifying possible alternative futures and their warning signs Monitoring current events for emergence of warning signs as well as unexpected events Determining indicators of the intent of an action or an individual Supporting the decision maker in times of crisis. These tasks will be conducted through a combination of individual and collaborative analysis, often under extreme time pressure. Visual analytics must enable hypothesis-based and scenario-based analytical techniques, providing support for the analyst to reason based on the available evidence. === Data representations === Data representations are structured forms suitable for computer-based transformations. These structures must exist in the original data or be derivable from the data themselves. They must retain the information and knowledge content and the related context within the original data to the greatest degree possible. The structures of underlying data representations are generally neither accessible nor intuitive to the user of the visual analytics tool. They are frequently more complex in nature than the original data and are not necessarily smaller in size than the original data. The structures of the data representations may contain hundreds or thousands of dimensions and be unintelligible to a person, but they must be transformable into lower-dimensional representations for visualization and analysis. === Theories of visualization === Theories of visualization include: Jacques Bertin's Semiology of Graphics (1967) Nelson Goodman's Languages of Art (1977) Jock D. Mackinlay's Automated design of optimal visualization (APT) (1986) Leland Wilkinson's Grammar of Graphics (1998) Hadley Wickham's Layered Grammar of Graphics (2010) === Visual representations === Visual representations translate data into a visible form that highlights important features, including commonalities and anomalies. These visual representations make it easy for users to perceive salient aspects of their data quickly. Augmenting the cognitive reasoning process with perceptual reasoning through visual representations permits the analytical reasoning process to become faster and more focused. == Process == The input for the data sets used in the visual analytics process are heterogeneous data sources (i.e., the internet, newspapers, books, scientific experiments, expert systems). From these rich sources, the data sets S = S1, ..., Sm are chosen, whereas each Si , i ∈ (1, ..., m) consists of attrib
Parasolid
Parasolid is a geometric modeling kernel originally developed by Shape Data Limited, now owned and developed by Siemens Digital Industries Software. It can be licensed by other companies for use in their 3D computer graphics software products. Parasolid's abilities include model creation and editing utilities such as Boolean modeling operators, feature modeling support, advanced surfacing, thickening and hollowing, blending and filleting, and sheet modeling. It also incorporates modeling with mesh surfaces and lattices. Parasolid also includes tools for direct model editing, including tapering, offsetting, geometry replacement and removing feature details with automated regeneration of surrounding data. Parasolid also provides wide-ranging graphical and rendering support, including hidden-line, wireframe and drafting, tessellation, and model data inquiries. To use Parasolid effectively, software developers need knowledge of CAD in general, computational geometry, and topology. Parasolid is available for Windows (32-bit, 64-bit and AArch64), Linux (64-bit and AArch64), macOS (Apple silicon and Intel), iOS, and Android. == Parasolid XT format == Parasolid parts are normally saved in XT format, which usually has the file extension .X_T. The format is documented and open. There is also a binary version of the format, usually with an .X_B extension, which is somewhat more compact. Both .X_T and .X_B are used for parts files. == Applications == It is used in many computer-aided design (CAD), computer-aided manufacturing (CAM), computer-aided engineering (CAE), product visualization, and CAD data exchange packages. Notable uses include: