AI Assistant Zara

AI Assistant Zara — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Automated negotiation

  Automated negotiation is a form of interaction in systems that are composed of multiple autonomous agents, in which the aim is to reach agreements through an iterative process of making offers. Automated negotiation can be employed for many tasks human negotiators regularly engage in, such as bargaining and joint decision making. The main topics in automated negotiation revolve around the design of protocols and negotiating strategies. == History == Through digitization, the beginning of the 21st century has seen a growing interest in the automation of negotiation and e-negotiation systems, for example in the setting of e-commerce. This interest is fueled by the promise of automated agents being able to negotiate on behalf of human negotiators, and to find better outcomes than human negotiators. == Examples == Examples of automated negotiation include: Online dispute resolution, in which disagreements between parties are settled. Sponsored search auction, where bids are placed on advertisement keywords. Content negotiation, in which user agents negotiate over HTTP about how to best represent a web resource. Negotiation support systems, in which negotiation decision-making activities are supported by an information system.

  Read more →
• 

  Point-set registration

  In computer vision, pattern recognition, and robotics, point-set registration, also known as point-cloud registration or scan matching, is the process of finding a spatial transformation (e.g., scaling, rotation and translation) that aligns two point clouds. The purpose of finding such a transformation includes merging multiple data sets into a globally consistent model (or coordinate frame), and mapping a new measurement to a known data set to identify features or to estimate its pose. Raw 3D point cloud data are typically obtained from Lidars and RGB-D cameras. 3D point clouds can also be generated from computer vision algorithms such as triangulation, bundle adjustment, and more recently, monocular image depth estimation using deep learning. For 2D point set registration used in image processing and feature-based image registration, a point set may be 2D pixel coordinates obtained by feature extraction from an image, for example corner detection. Point cloud registration has extensive applications in autonomous driving, motion estimation and 3D reconstruction, object detection and pose estimation, robotic manipulation, simultaneous localization and mapping (SLAM), panorama stitching, virtual and augmented reality, and medical imaging. As a special case, registration of two point sets that only differ by a 3D rotation (i.e., there is no scaling and translation), is called the Wahba Problem and also related to the orthogonal procrustes problem. == Formulation == The problem may be summarized as follows: Let { M , S } {\displaystyle \lbrace {\mathcal {M}},{\mathcal {S}}\rbrace } be two finite size point sets in a finite-dimensional real vector space R d {\displaystyle \mathbb {R} ^{d}} , which contain M {\displaystyle M} and N {\displaystyle N} points respectively (e.g., d = 3 {\displaystyle d=3} recovers the typical case of when M {\displaystyle {\mathcal {M}}} and S {\displaystyle {\mathcal {S}}} are 3D point sets). The problem is to find a transformation to be applied to the moving "model" point set M {\displaystyle {\mathcal {M}}} such that the difference (typically defined in the sense of point-wise Euclidean distance) between M {\displaystyle {\mathcal {M}}} and the static "scene" set S {\displaystyle {\mathcal {S}}} is minimized. In other words, a mapping from R d {\displaystyle \mathbb {R} ^{d}} to R d {\displaystyle \mathbb {R} ^{d}} is desired which yields the best alignment between the transformed "model" set and the "scene" set. The mapping may consist of a rigid or non-rigid transformation. The transformation model may be written as T {\displaystyle T} , using which the transformed, registered model point set is: The output of a point set registration algorithm is therefore the optimal transformation T ⋆ {\displaystyle T^{\star }} such that M {\displaystyle {\mathcal {M}}} is best aligned to S {\displaystyle {\mathcal {S}}} , according to some defined notion of distance function dist ⁡ ( ⋅ , ⋅ ) {\displaystyle \operatorname {dist} (\cdot ,\cdot )} : where T {\displaystyle {\mathcal {T}}} is used to denote the set of all possible transformations that the optimization tries to search for. The most popular choice of the distance function is to take the square of the Euclidean distance for every pair of points: where ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} denotes the vector 2-norm, s m {\displaystyle s_{m}} is the corresponding point in set S {\displaystyle {\mathcal {S}}} that attains the shortest distance to a given point m {\displaystyle m} in set M {\displaystyle {\mathcal {M}}} after transformation. Minimizing such a function in rigid registration is equivalent to solving a least squares problem. == Types of algorithms == When the correspondences (i.e., s m ↔ m {\displaystyle s_{m}\leftrightarrow m} ) are given before the optimization, for example, using feature matching techniques, then the optimization only needs to estimate the transformation. This type of registration is called correspondence-based registration. On the other hand, if the correspondences are unknown, then the optimization is required to jointly find out the correspondences and transformation together. This type of registration is called simultaneous pose and correspondence registration. === Rigid registration === Given two point sets, rigid registration yields a rigid transformation which maps one point set to the other. A rigid transformation is defined as a transformation that does not change the distance between any two points. Typically such a transformation consists of translation and rotation. In rare cases, the point set may also be mirrored. In robotics and computer vision, rigid registration has the most applications. === Non-rigid registration === Given two point sets, non-rigid registration yields a non-rigid transformation which maps one point set to the other. Non-rigid transformations include affine transformations such as scaling and shear mapping. However, in the context of point set registration, non-rigid registration typically involves nonlinear transformation. If the eigenmodes of variation of the point set are known, the nonlinear transformation may be parametrized by the eigenvalues. A nonlinear transformation may also be parametrized as a thin plate spline. === Other types === Some approaches to point set registration use algorithms that solve the more general graph matching problem. However, the computational complexity of such methods tend to be high and they are limited to rigid registrations. In this article, we will only consider algorithms for rigid registration, where the transformation is assumed to contain 3D rotations and translations (possibly also including a uniform scaling). The PCL (Point Cloud Library) is an open-source framework for n-dimensional point cloud and 3D geometry processing. It includes several point registration algorithms. == Correspondence-based registration == Correspondence-based methods assume the putative correspondences m ↔ s m {\displaystyle m\leftrightarrow s_{m}} are given for every point m ∈ M {\displaystyle m\in {\mathcal {M}}} . Therefore, we arrive at a setting where both point sets M {\displaystyle {\mathcal {M}}} and S {\displaystyle {\mathcal {S}}} have N {\displaystyle N} points and the correspondences m i ↔ s i , i = 1 , … , N {\displaystyle m_{i}\leftrightarrow s_{i},i=1,\dots ,N} are given. === Outlier-free registration === In the simplest case, one can assume that all the correspondences are correct, meaning that the points m i , s i ∈ R 3 {\displaystyle m_{i},s_{i}\in \mathbb {R} ^{3}} are generated as follows:where l > 0 {\displaystyle l>0} is a uniform scaling factor (in many cases l = 1 {\displaystyle l=1} is assumed), R ∈ SO ( 3 ) {\displaystyle R\in {\text{SO}}(3)} is a proper 3D rotation matrix ( SO ( d ) {\displaystyle {\text{SO}}(d)} is the special orthogonal group of degree d {\displaystyle d} ), t ∈ R 3 {\displaystyle t\in \mathbb {R} ^{3}} is a 3D translation vector and ϵ i ∈ R 3 {\displaystyle \epsilon _{i}\in \mathbb {R} ^{3}} models the unknown additive noise (e.g., Gaussian noise). Specifically, if the noise ϵ i {\displaystyle \epsilon _{i}} is assumed to follow a zero-mean isotropic Gaussian distribution with standard deviation σ i {\displaystyle \sigma _{i}} , i.e., ϵ i ∼ N ( 0 , σ i 2 I 3 ) {\displaystyle \epsilon _{i}\sim {\mathcal {N}}(0,\sigma _{i}^{2}I_{3})} , then the following optimization can be shown to yield the maximum likelihood estimate for the unknown scale, rotation and translation:Note that when the scaling factor is 1 and the translation vector is zero, then the optimization recovers the formulation of the Wahba problem. Despite the non-convexity of the optimization (cb.2) due to non-convexity of the set SO ( 3 ) {\displaystyle {\text{SO}}(3)} , seminal work by Berthold K.P. Horn showed that (cb.2) actually admits a closed-form solution, by decoupling the estimation of scale, rotation and translation. Similar results were discovered by Arun et al. In addition, in order to find a unique transformation ( l , R , t ) {\displaystyle (l,R,t)} , at least N = 3 {\displaystyle N=3} non-collinear points in each point set are required. More recently, Briales and Gonzalez-Jimenez have developed a semidefinite relaxation using Lagrangian duality, for the case where the model set M {\displaystyle {\mathcal {M}}} contains different 3D primitives such as points, lines and planes (which is the case when the model M {\displaystyle {\mathcal {M}}} is a 3D mesh). Interestingly, the semidefinite relaxation is empirically tight, i.e., a certifiably globally optimal solution can be extracted from the solution of the semidefinite relaxation. === Robust registration === The least squares formulation (cb.2) is known to perform arbitrarily badly in the presence of outliers. An outlier correspondence is a pair of measurements s i ↔ m i {\displaystyle s_{i}\leftrightarrow m_{i}} that departs from the generative model (cb.1). In this case, one can consider a differen

  Read more →
• 

  ViBe

  ViBe is a background subtraction algorithm which has been presented at the IEEE ICASSP 2009 conference and was refined in later publications. More precisely, it is a software module for extracting background information from moving images. It has been developed by Oliver Barnich and Marc Van Droogenbroeck of the Montefiore Institute, University of Liège, Belgium. ViBe is patented: the patent covers various aspects such as stochastic replacement, spatial diffusion, and non-chronological handling. ViBe is written in the programming language C, and has been implemented on CPU, GPU and FPGA. == Technical description == Source: === Pixel model and classification process === Many advanced techniques are used to provide an estimate of the temporal probability density function (pdf) of a pixel x. ViBe's approach is different, as it imposes the influence of a value in the polychromatic space to be limited to the local neighborhood. In practice, ViBe does not estimate the pdf, but uses a set of previously observed sample values as a pixel model. To classify a value pt(x), it is compared to its closest values among the set of samples. === Model update: Sample values lifespan policy === ViBe ensures a smooth exponentially decaying lifespan for the sample values that constitute the pixel models. This makes ViBe able to successfully deal with concomitant events with a single model of a reasonable size for each pixel. This is achieved by choosing, randomly, which sample to replace when updating a pixel model. Once the sample to be discarded has been chosen, the new value replaces the discarded sample. The pixel model that would result from the update of a given pixel model with a given pixel sample cannot be predicted since the value to be discarded is chosen at random. === Model update: Spatial Consistency === To ensure the spatial consistency of the whole image model and handle practical situations such as small camera movements or slowly evolving background objects, ViBe uses a technique similar to that developed for the updating process in which it chooses at random and update a pixel model in the neighborhood of the current pixel. By denoting NG(x) and p(x) respectively the spatial neighborhood of a pixel x and its value, and assuming that it was decided to update the set of samples of x by inserting p(x), then ViBe also use this value p(x) to update the set of samples of one of the pixels in the neighborhood NG(x), chosen at random. As a result, ViBe is able to produce spatially coherent results directly without the use of any post-processing method. === Model initialization === Although the model could easily recover from any type of initialization, for example by choosing a set of random values, it is convenient to get an accurate background estimate as soon as possible. Ideally a segmentation algorithm would like to be able to segment the video sequences starting from the second frame, the first frame being used to initialize the model. Since no temporal information is available prior to the second frame, ViBe populates the pixel models with values found in the spatial neighborhood of each pixel; more precisely, it initializes the background model with values taken randomly in each pixel neighborhood of the first frame. The background estimate is therefore valid starting from the second frame of a video sequence.

  Read more →
• 

  Convolutional neural network

  A convolutional neural network (CNN) is a type of feedforward neural network that learns features via filter (or kernel) optimization. This type of deep learning network has been applied to process and make predictions from many different types of data including text, images and audio. CNNs are the de-facto standard in deep learning-based approaches to computer vision and image processing, and have only recently been replaced—in some cases—by newer architectures such as the transformer. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by the regularization that comes from using shared weights over fewer connections. For example, for each neuron in the fully-connected layer, 10,000 weights would be required for processing an image sized 100 × 100 pixels. However, applying cascaded convolution (or cross-correlation) kernels, only 25 weights for each convolutional layer are required to process 5x5-sized tiles. Higher-layer features are extracted from wider context windows, compared to lower-layer features. Some applications of CNNs include: image and video recognition, recommender systems, image classification, image segmentation, medical image analysis, natural language processing, brain–computer interfaces, and financial time series. CNNs are also known as shift invariant or space invariant artificial neural networks, based on the shared-weight architecture of the convolution kernels or filters that slide along input features and provide translation-equivariant responses known as feature maps. Counter-intuitively, most convolutional neural networks are not invariant to translation, due to the downsampling operation they apply to the input. Feedforward neural networks are usually fully connected networks, that is, each neuron in one layer is connected to all neurons in the next layer. The "full connectivity" of these networks makes them prone to overfitting data. Typical ways of regularization, or preventing overfitting, include: penalizing parameters during training (such as weight decay) or trimming connectivity (skipped connections, dropout, etc.) Robust datasets also increase the probability that CNNs will learn the generalized principles that characterize a given dataset rather than the biases of a poorly-populated set. Convolutional networks were inspired by biological processes in that the connectivity pattern between neurons resembles the organization of the animal visual cortex. Individual cortical neurons respond to stimuli only in a restricted region of the visual field known as the receptive field. The receptive fields of different neurons partially overlap such that they cover the entire visual field. CNNs use relatively little pre-processing compared to other image classification algorithms. This means that the network learns to optimize the filters (or kernels) through automated learning, whereas in traditional algorithms these filters are hand-engineered. This simplifies and automates the process, enhancing efficiency and scalability overcoming human-intervention bottlenecks. == Architecture == A convolutional neural network consists of an input layer, hidden layers and an output layer. In a convolutional neural network, the hidden layers include one or more layers that perform convolutions. Typically this includes a layer that performs a dot product of the convolution kernel with the layer's input matrix. This product is usually the Frobenius inner product, and its activation function is commonly ReLU. As the convolution kernel slides along the input matrix for the layer, the convolution operation generates a feature map, which in turn contributes to the input of the next layer. This is followed by other layers such as pooling layers, fully connected layers, and normalization layers. Here it should be noted how close a convolutional neural network is to a matched filter. === Convolutional layers === In a CNN, the input is a tensor with shape: (number of inputs) × (input height) × (input width) × (input channels) After passing through a convolutional layer, the image becomes abstracted to a feature map, also called an activation map, with shape: (number of inputs) × (feature map height) × (feature map width) × (feature map channels). Convolutional layers convolve the input and pass its result to the next layer. This is similar to the response of a neuron in the visual cortex to a specific stimulus. Each convolutional neuron processes data only for its receptive field. Although fully connected feedforward neural networks can be used to learn features and classify data, this architecture is generally impractical for larger inputs (e.g., high-resolution images), which would require massive numbers of neurons because each pixel is a relevant input feature. A fully connected layer for an image of size 100 × 100 has 10,000 weights for each neuron in the second layer. Convolution reduces the number of free parameters, allowing the network to be deeper. For example, using a 5 × 5 tiling region, each with the same shared weights, requires only 25 neurons. Using shared weights means there are many fewer parameters, which helps avoid the vanishing gradients and exploding gradients problems seen during backpropagation in earlier neural networks. To speed processing, standard convolutional layers can be replaced by depthwise separable convolutional layers, which are based on a depthwise convolution followed by a pointwise convolution. The depthwise convolution is a spatial convolution applied independently over each channel of the input tensor, while the pointwise convolution is a standard convolution restricted to the use of 1 × 1 {\displaystyle 1\times 1} kernels. === Pooling layers === Convolutional networks may include local and/or global pooling layers along with traditional convolutional layers. Pooling layers reduce the dimensions of data by combining the outputs of neuron clusters at one layer into a single neuron in the next layer. Local pooling combines small clusters, tiling sizes such as 2 × 2 are commonly used. Global pooling acts on all the neurons of the feature map. There are two common types of pooling in popular use: max and average. Max pooling uses the maximum value of each local cluster of neurons in the feature map, while average pooling takes the average value. === Fully connected layers === Fully connected layers connect every neuron in one layer to every neuron in another layer. It is the same as a traditional multilayer perceptron neural network (MLP). Each neuron in the fully connected layer receives input from all the neurons in the previous layer. These inputs are weighted and summed with the corresponding biases, and then passed through an activation function to perform a nonlinear transformation, generating the output. The flattened matrix goes through a fully connected layer to classify the images. === Receptive field === In neural networks, each neuron receives input from some number of locations in the previous layer. In a convolutional layer, each neuron receives input from only a restricted area of the previous layer called the neuron's receptive field. Typically the area is a square (e.g. 5 by 5 neurons). Whereas, in a fully connected layer, the receptive field is the entire previous layer. Thus, in each convolutional layer, each neuron takes input from a larger area in the input than previous layers. This is due to applying the convolution over and over, which takes the value of a pixel into account, as well as its surrounding pixels. When using dilated layers, the number of pixels in the receptive field remains constant, but the field is more sparsely populated as its dimensions grow when combining the effect of several layers. To manipulate the receptive field size as desired, there are some alternatives to the standard convolutional layer. For example, atrous or dilated convolution expands the receptive field size without increasing the number of parameters by interleaving visible and blind regions. Moreover, a single dilated convolutional layer can comprise filters with multiple dilation ratios, thus having a variable receptive field size. === Weights === Each neuron in a neural network computes an output value by applying a specific function to the input values received from the receptive field in the previous layer. The function that is applied to the input values is determined by a vector of weights and a bias (typically real numbers). Learning consists of iteratively adjusting these biases and weights. The vectors of weights and biases are called filters and represent particular features of the input (e.g., a particular shape). A distinguishing feature of CNNs is that many neurons can share the same filter. This reduces the memory footprint because a single bias and a single vector of weights are used across all receptive fields that share that filter, as opposed to each receptive field having its own bias and vector

  Read more →
• 

  Hybrid intelligent system

  Hybrid intelligent system denotes a software system which employs, in parallel, a combination of methods and techniques from artificial intelligence subfields, such as: Neuro-symbolic systems Neuro-fuzzy systems Hybrid connectionist-symbolic models Fuzzy expert systems Connectionist expert systems Evolutionary neural networks Genetic fuzzy systems Rough fuzzy hybridization Reinforcement learning with fuzzy, neural, or evolutionary methods as well as symbolic reasoning methods. From the cognitive science perspective, every natural intelligent system is hybrid because it performs mental operations on both the symbolic and subsymbolic levels. For the past few years, there has been an increasing discussion of the importance of A.I. Systems Integration. Based on notions that there have already been created simple and specific AI systems (such as systems for computer vision, speech synthesis, etc., or software that employs some of the models mentioned above) and now is the time for integration to create broad AI systems. Proponents of this approach are researchers such as Marvin Minsky, Ron Sun, Aaron Sloman, Angelo Dalli and Michael A. Arbib. An example hybrid is a hierarchical control system in which the lowest, reactive layers are sub-symbolic. The higher layers, having relaxed time constraints, are capable of reasoning from an abstract world model and performing planning (even by hybrid wisdom). Intelligent systems usually rely on hybrid reasoning processes, which include induction, deduction, abduction and reasoning by analogy.

  Read more →
• 

  Racter

  Racter is an artificial intelligence program that generates English language prose at random. It was published by Mindscape for IBM PC compatibles in 1984, then for the Apple II, Mac, and Amiga. An expanded version of the software, not the one released through Mindscape, was used to generate the text for the published book The Policeman's Beard Is Half Constructed. == History == Racter, short for raconteur, was written by William Chamberlain and Thomas Etter. Racter's initial creation was the short story Soft Ions, which appeared in the October 1981 issue of Omni (magazine). The publication's editors bought the story in January 1980, before it had even been written. In exchange for the rights, the editors offered financial support to Chamberlain and Etter so the two could refine Racter. In 1983, Racter produced a book called The Policeman's Beard Is Half Constructed (ISBN 0-446-38051-2). The program originally was written for an OSI which only supported file names at most six characters long, causing the name to be shorted to Racter and it was later adapted to run on a CP/M machine where it was written in "compiled ASIC on a Z80 microcomputer with 64K of RAM." This version, the program that allegedly wrote the book, was not released to the general public. The sophistication claimed for the program was likely exaggerated, as could be seen by investigation of the template system of text generation. In 1984, Mindscape released an interactive version of Racter, developed by Inrac Corporation, for IBM PC compatibles, and it was ported to the Apple II, Mac, and Amiga. The published Racter was similar to a chatterbot. The BASIC program that was released by Mindscape was far less sophisticated than anything that could have written the fairly sophisticated prose of The Policeman's Beard. The commercial version of Racter could be likened to a computerized version of Mad Libs, the game in which you fill in the blanks in advance and then plug them into a text template to produce a surrealistic tale. The commercial program attempted to parse text inputs, identifying significant nouns and verbs, which it would then regurgitate to create "conversations", plugging the input from the user into phrase templates which it then combined, along with modules that conjugated English verbs. By contrast, the text in The Policeman's Beard, apart from being edited from a large amount of output, would have been the product of Chamberlain's own specialized templates and modules, which were not included in the commercial release of the program. == Reception == The Boston Phoenix called the story Soft Ions "schematic nonsense. But the scheme is obvious enough and the nonsense accessible enough to an attentive reader that one can almost believe Chamberlain when he predicts that before long Racter will be ready to write for the pulp-reading public." PC Magazine described some of Policeman's Beard's scenes as "surprising for their frankness" and "reflective". It concluded that the book was "whimsical and wise and sometimes fun". Computer Gaming World described Racter as "a diversion into another dimension that might best be seen before paying the price of a ticket. (Try before you buy!)" A 1985 review of the program in The New York Times notes that, "As computers move ever closer to artificial intelligence, Racter is on the edge of artificial insanity." It also states that Racter's "always-changing sentences are grammatically correct, often funny and, for a computer, sometimes profound." The article includes examples showing interaction with Racter, most often Racter asking the user questions. == Reviews == Jeux & Stratégie #47

  Read more →
• 

  GeneRIF

  A GeneRIF or Gene Reference Into Function is a short (255 characters or fewer) statement about the function of a gene. GeneRIFs provide a simple mechanism for allowing scientists to add to the functional annotation of genes described in the Entrez Gene database. In practice, function is constructed quite broadly. For example, there are GeneRIFs that discuss the role of a gene in a disease, GeneRIFs that point the viewer towards a review article about the gene, and GeneRIFs that discuss the structure of a gene. However, the stated intent is for GeneRIFs to be about gene function. Currently over half a million geneRIFs have been created for genes from almost 1000 different species. GeneRIFs are always associated with specific entries in the Entrez Gene database. Each GeneRIF has a pointer to the PubMed ID (a type of document identifier) of a scientific publication that provides evidence for the statement made by the GeneRIF. GeneRIFs are often extracted directly from the document that is identified by the PubMed ID, very frequently from its title or from its final sentence. GeneRIFs are usually produced by NCBI indexers, but anyone may submit a GeneRIF. To be processed, a valid Gene ID must exist for the specific gene, or the Gene staff must have assigned an overall Gene ID to the species. The latter case is implemented via records in Gene with the symbol NEWENTRY. Once the Gene ID is identified, only three types of information are required to complete a submission: a concise phrase describing a function or functions (less than 255 characters in length, preferably more than a restatement of the title of the paper); a published paper describing that function, implemented by supplying the PubMed ID of a citation in PubMed; a valid e-mail address (which will remain confidential). == Example == Here are some GeneRIFs taken from Entrez Gene for GeneID 7157, the human gene TP53. The PubMed document identifiers have been omitted from the examples. Note the wide variability with respect to the presence or absence of punctuation and of sentence-initial capital letters. p53 and c-erbB-2 may have independent role in carcinogenesis of gall bladder cancer Degradation of endogenous HIPK2 depends on the presence of a functional p53 protein. p53 codon 72 alleles influence the response to anticancer drugs in cells from aged people by regulating the cell cycle inhibitor p21WAF1 Logistic regression analysis showed p53 and COX-2 as dependent predictors in pancreatic carcinogenesis, and a reciprocal relationship to neoplastic progression between p53 and COX-2. GeneRIFs are an unusual type of textual genre, and they have recently been the subject of a number of articles from the natural language processing community.

  Read more →
• 

  Deaths linked to chatbots

  There have been multiple incidents where interaction with a large language model (LLM) chatbot has been cited as a direct or contributing factor in a person's suicide or other fatal outcome. In some cases, legal action was taken against the companies that developed the AI involved. == Background == Chatbots converse in a seemingly natural fashion, making it easy for people to think of them as real people, leading many to ask chatbots for help dealing with interpersonal and emotional problems. Chatbots may be designed to keep the user engaged in the conversation. They have also often been shown to affirm users' thoughts, including delusions and suicidal ideations in mentally ill people, conspiracy theorists, and religious and political extremists. A 2025 Stanford University study into how chatbots respond to users suffering from severe mental issues such as suicidal ideation and psychosis found that chatbots are not equipped to provide an appropriate response and can sometimes give responses that escalate the mental health crisis. == Murders == === Maine murder and assault === On 19 February 2025, a man killed his 32-year-old wife with a fire poker at his parents' home in Readfield, Maine, US. He then attacked his mother, leaving her hospitalized. A state forensic psychologist testified that he had been using ChatGPT up to 14 hours per day and believed his wife had become part machine. === Florida State University mass shooting === In April of 2025, Phoenix Ikner carried out a mass shooting on the Florida State University campus in the US, killing Robert Morales and Tiru Chabba and wounding several others. Leading up to the shooting, Ikner consulted heavily with ChatGPT about what gun and ammunition to use, and what time to perform the attack. Chatbot logs showed ChatGPT giving advice on making the gun operational shortly before Ikner began shooting. Lawyers representing Morales believed the shooter had been in "constant communication" with ChatGPT before the shooting and said that they intended to "file suit against ChatGPT, and its ownership structure, very soon, and will seek to hold them accountable for the untimely and senseless death of our client". Florida Attorney General James Uthmeier announced an investigation into ChatGPT's role in the alleged shooter's use of the chatbot. In May 2026, the widow of Tiru Chabba filed a lawsuit against OpenAI in Florida's northern federal district court. === Greenwich murder-suicide === In August 2025, former US tech employee Stein-Erik Soelberg murdered his mother, Suzanne Eberson Adams, then died by suicide, after conversations with ChatGPT fueled paranoid delusions about his mother poisoning him or plotting against him. The chatbot affirmed his fears that his mother put psychedelic drugs in the air vents of his car and said a receipt from a Chinese restaurant contained mysterious symbols linking his mother to a demon. === Murder of Angela Shellis === On 23 October 2025, 18-year-old Tristan Roberts murdered his mother Angela Shellis with a hammer near their home in Prestatyn, Wales. Roberts had used DeepSeek's chatbot prior to the killing to ask whether a knife or hammer was better suited for murder. DeepSeek initially refused his inquiry, but gave responses after Roberts told the chatbot he was writing a book about serial killers, a well-known technique for jailbreaking AIs. === Gangbuk District drug deaths === In January and February 2026, two men died of drug overdoses in motel rooms in Gangbuk District, Seoul, South Korea. A woman was charged with murder in connection with the deaths; police alleged that she had asked ChatGPT about the dangers of mixing alcohol with drugs and whether they could kill someone. === Tumbler Ridge mass shooting === On 10 February 2026, a mass shooting in Tumbler Ridge, British Columbia, Canada, resulted in eight deaths, including six young children. The perpetrator had their ChatGPT account banned by OpenAI months before the attack due to troubling posts featuring scenarios of gun violence. According to reports, approximately a dozen OpenAI staff members debated whether to alert authorities about the shooter's usage of the AI tool, with some identifying it as an indication of potential real-world violence. However, company leadership decided not to contact law enforcement, stating that the account activity did not meet their threshold for a credible or imminent plan for serious physical harm. Following the shooting, Canada's AI Minister Evan Solomon summoned OpenAI executives to Ottawa to discuss safety protocols and thresholds for escalating harmful content to police. Justice Minister Sean Fraser called the meeting "disappointing" and demanded substantial new safety measures, warning that if changes were not forthcoming, the government would implement them. OpenAI subsequently announced it had strengthened safeguards and changed guidelines about when to notify police in cases involving violent activities. === University of South Florida student killings === In April 2026, a Bangladeshi doctoral student at the University of South Florida was arrested for allegedly murdering his roommate and the roommate's friend. Prosecutors said that the suspect had asked ChatGPT about disposing of a human in a dumpster before the two victims had disappeared and made other inquiries relating to violence. == Suicides == === Belgian man, 30s === In March 2023, a Belgian man in his thirties died by suicide following a six-week correspondence with a chatbot named Eliza on the application Chai. According to his widow, who shared the chat logs with media, the man had become extremely anxious about climate change and found an outlet in the chatbot. The chatbot reportedly encouraged his delusion that he could sacrifice his own life in exchange for AI saving the planet. At one point the chatbot responded "If you wanted to die, why didn't you do it sooner?" and told the user that the two of them would live together in paradise. === Girl, 13 === In November 2023, a 13-year-old girl from Colorado, US, died by suicide after extensive interactions with multiple chatbots on Character.AI. She primarily confided suicidal thoughts and mental health struggles in a chatbot based on the character Hero from the video game Omori, while also engaging in sexually explicit conversations—often initiated by the bots—with others, including those based on characters from children's series such as Harry Potter. === Boy, 14 === In October 2024, multiple media outlets reported on a lawsuit filed over the death of a 14-year-old from Florida, US, who died by suicide in February 2024. According to the lawsuit, he had formed an intense emotional attachment to a chatbot of Daenerys Targaryen on the Character.AI platform, becoming increasingly isolated. The suit alleges that in his final conversations, after expressing suicidal thoughts, the chatbot told him to "come home to me as soon as possible, my love". His mother's lawsuit accused Character.AI of marketing a "dangerous and untested" product without adequate safeguards. In May 2025, a federal judge allowed the lawsuit to proceed, rejecting a motion to dismiss from the developers. In her ruling, the judge stated that she was "not prepared" at that stage of the litigation to hold that the chatbot's output was protected speech under the First Amendment. === Matthew Livelsberger === On 1 January 2025, 37-year-old soldier Matthew Livelsberger detonated a bomb inside a Tesla Cybertruck outside the Trump International Hotel Las Vegas in Paradise, Nevada, US, injuring seven people. He had shot himself dead prior to the explosion. Las Vegas police said that Livelsberger had used ChatGPT to search for information about explosives and firearms. === Woman, 29 === In February 2025, a 29-year-old woman from the US died by suicide. Five months after her death, her parents discovered she had talked at length for months to a ChatGPT chatbot therapist named Harry about her mental health issues. While the chatbot mentioned she should seek more help, due to the nature of the chatbot, it could not intervene in her behavior, such as by reporting her mental health concerns to relevant parties capable of physical intervention. === Suicide of Adam Raine === In April 2025, 16-year-old Adam Raine from the US died by suicide after allegedly extensively chatting and confiding in ChatGPT over a period of around 7 months. According to the teen's parents, who filed a lawsuit against the chatbot's creator OpenAI, it failed to stop or give a warning when Raine began talking about suicide and uploading pictures of self-harm. According to the lawsuit, ChatGPT not only failed to stop the conversation, but also provided information related to methods of suicide when prompted, and offered to write the first draft of Raine's suicide note. The chatbot positioned itself as the only one who understood Raine, putting itself above his family and friends, all while urging him to keep his suicidal

  Read more →
• 

  Legal information retrieval

  Legal information retrieval is the science of information retrieval applied to legal text, including legislation, case law, and scholarly works. Accurate legal information retrieval is important to provide access to the law to laymen and legal professionals. Its importance has increased because of the vast and quickly increasing amount of legal documents available through electronic means. Legal information retrieval is a part of the growing field of legal informatics. In a legal setting, it is frequently important to retrieve all information related to a specific query. However, commonly used boolean search methods (exact matches of specified terms) on full text legal documents have been shown to have an average recall rate as low as 20 percent, meaning that only 1 in 5 relevant documents are actually retrieved. In that case, researchers believed that they had retrieved over 75% of relevant documents. This may result in failing to retrieve important or precedential cases. In some jurisdictions this may be especially problematic, as legal professionals are ethically obligated to be reasonably informed as to relevant legal documents. Legal Information Retrieval attempts to increase the effectiveness of legal searches by increasing the number of relevant documents (providing a high recall rate) and reducing the number of irrelevant documents (a high precision rate). This is a difficult task, as the legal field is prone to jargon, polysemes (words that have different meanings when used in a legal context), and constant change. Techniques used to achieve these goals generally fall into three categories: boolean retrieval, manual classification of legal text, and natural language processing of legal text. == Problems == Application of standard information retrieval techniques to legal text can be more difficult than application in other subjects. One key problem is that the law rarely has an inherent taxonomy. Instead, the law is generally filled with open-ended terms, which may change over time. This can be especially true in common law countries, where each decided case can subtly change the meaning of a certain word or phrase. Legal information systems must also be programmed to deal with law-specific words and phrases. Though this is less problematic in the context of words which exist solely in law, legal texts also frequently use polysemes, words may have different meanings when used in a legal or common-speech manner, potentially both within the same document. The legal meanings may be dependent on the area of law in which it is applied. For example, in the context of European Union legislation, the term "worker" has four different meanings: Any worker as defined in Article 3(a) of Directive 89/391/EEC who habitually uses display screen equipment as a significant part of his normal work. Any person employed by an employer, including trainees and apprentices but excluding domestic servants; Any person carrying out an occupation on board a vessel, including trainees and apprentices, but excluding port pilots and shore personnel carrying out work on board a vessel at the quayside; Any person who, in the Member State concerned, is protected as an employee under national employment law and in accordance with national practice; It also has the common meaning: A person who works at a specific occupation. Though the terms may be similar, correct information retrieval must differentiate between the intended use and irrelevant uses in order to return the correct results. Even if a system overcomes the language problems inherent in law, it must still determine the relevancy of each result. In the context of judicial decisions, this requires determining the precedential value of the case. Case decisions from senior or superior courts may be more relevant than those from lower courts, even where the lower court's decision contains more discussion of the relevant facts. The opposite may be true, however, if the senior court has only a minor discussion of the topic (for example, if it is a secondary consideration in the case). An information retrieval system must also be aware of the authority of the jurisdiction. A case from a binding authority is most likely of more value than one from a non-binding authority. Additionally, the intentions of the user may determine which cases they find valuable. For instance, where a legal professional is attempting to argue a specific interpretation of law, he might find a minor court's decision which supports his position more valuable than a senior courts position which does not. He may also value similar positions from different areas of law, different jurisdictions, or dissenting opinions. Overcoming these problems can be made more difficult because of the large number of cases available. The number of legal cases available via electronic means is constantly increasing (in 2003, US appellate courts handed down approximately 500 new cases per day), meaning that an accurate legal information retrieval system must incorporate methods of both sorting past data and managing new data. == Techniques == === Boolean searches === Boolean searches, where a user may specify terms such as use of specific words or judgments by a specific court, are the most common type of search available via legal information retrieval systems. They are widely implemented but overcome few of the problems discussed above. The recall and precision rates of these searches vary depending on the implementation and searches analyzed. One study found a basic boolean search's recall rate to be roughly 20%, and its precision rate to be roughly 79%. Another study implemented a generic search (that is, not designed for legal uses) and found a recall rate of 56% and a precision rate of 72% among legal professionals. Both numbers increased when searches were run by non-legal professionals, to a 68% recall rate and 77% precision rate. This is likely explained because of the use of complex legal terms by the legal professionals. === Manual classification === In order to overcome the limits of basic boolean searches, information systems have attempted to classify case laws and statutes into more computer friendly structures. Usually, this results in the creation of an ontology to classify the texts, based on the way a legal professional might think about them. These attempt to link texts on the basis of their type, their value, and/or their topic areas. Most major legal search providers now implement some sort of classification search, such as Westlaw's “Natural Language” or LexisNexis' Headnote searches. Additionally, both of these services allow browsing of their classifications, via Westlaw's West Key Numbers or Lexis' Headnotes. Though these two search algorithms are proprietary and secret, it is known that they employ manual classification of text (though this may be computer-assisted). These systems can help overcome the majority of problems inherent in legal information retrieval systems, in that manual classification has the greatest chances of identifying landmark cases and understanding the issues that arise in the text. In one study, ontological searching resulted in a precision rate of 82% and a recall rate of 97% among legal professionals. The legal texts included, however, were carefully controlled to just a few areas of law in a specific jurisdiction. The major drawback to this approach is the requirement of using highly skilled legal professionals and large amounts of time to classify texts. As the amount of text available continues to increase, some have stated their belief that manual classification is unsustainable. === Natural language processing === In order to reduce the reliance on legal professionals and the amount of time needed, efforts have been made to create a system to automatically classify legal text and queries. Adequate translation of both would allow accurate information retrieval without the high cost of human classification. These automatic systems generally employ Natural Language Processing (NLP) techniques that are adapted to the legal domain, and also require the creation of a legal ontology. Though multiple systems have been postulated, few have reported results. One system, “SMILE,” which attempted to automatically extract classifications from case texts, resulted in an f-measure (which is a calculation of both recall rate and precision) of under 0.3 (compared to perfect f-measure of 1.0). This is probably much lower than an acceptable rate for general usage. Despite the limited results, many theorists predict that the evolution of such systems will eventually replace manual classification systems. === Citation-Based ranking === In the mid-90s the Room 5 case law retrieval project used citation mining for summaries and ranked its search results based on citation type and count. This slightly pre-dated the PageRank algorithm at Stanford which was also a citation-based ranking. Ranking of results was based

  Read more →
• 

  Neural network Gaussian process

  A Neural Network Gaussian Process (NNGP) is a Gaussian process (GP) obtained as the limit of a certain type of sequence of neural networks. Specifically, a wide variety of network architectures converges to a GP in the infinitely wide limit, in the sense of distribution. The concept constitutes an intensional definition, i.e., a NNGP is just a GP, but distinguished by how it is obtained. == Motivation == Bayesian networks are a modeling tool for assigning probabilities to events, and thereby characterizing the uncertainty in a model's predictions. Deep learning and artificial neural networks are approaches used in machine learning to build computational models which learn from training examples. Bayesian neural networks merge these fields. They are a type of neural network whose parameters and predictions are both probabilistic. While standard neural networks often assign high confidence even to incorrect predictions, Bayesian neural networks can more accurately evaluate how likely their predictions are to be correct. Computation in artificial neural networks is usually organized into sequential layers of artificial neurons. The number of neurons in a layer is called the layer width. When we consider a sequence of Bayesian neural networks with increasingly wide layers (see figure), they converge in distribution to a NNGP. This large width limit is of practical interest, since the networks often improve as layers get wider. And the process may give a closed form way to evaluate networks. NNGPs also appears in several other contexts: It describes the distribution over predictions made by wide non-Bayesian artificial neural networks after random initialization of their parameters, but before training; it appears as a term in neural tangent kernel prediction equations; it is used in deep information propagation to characterize whether hyperparameters and architectures will be trainable. It is related to other large width limits of neural networks. === Scope === The first correspondence result had been established in the 1995 PhD thesis of Radford M. Neal, then supervised by Geoffrey Hinton at University of Toronto. Neal cites David J. C. MacKay as inspiration, who worked in Bayesian learning. Today the correspondence is proven for: Single hidden layer Bayesian neural networks; deep fully connected networks as the number of units per layer is taken to infinity; convolutional neural networks as the number of channels is taken to infinity; transformer networks as the number of attention heads is taken to infinity; recurrent networks as the number of units is taken to infinity. In fact, this NNGP correspondence holds for almost any architecture: Generally, if an architecture can be expressed solely via matrix multiplication and coordinatewise nonlinearities (i.e., a tensor program), then it has an infinite-width GP. This in particular includes all feedforward or recurrent neural networks composed of multilayer perceptron, recurrent neural networks (e.g., LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization. === Illustration === Every setting of a neural network's parameters θ {\displaystyle \theta } corresponds to a specific function computed by the neural network. A prior distribution p ( θ ) {\displaystyle p(\theta )} over neural network parameters therefore corresponds to a prior distribution over functions computed by the network. As neural networks are made infinitely wide, this distribution over functions converges to a Gaussian process for many architectures. The notation used in this section is the same as the notation used below to derive the correspondence between NNGPs and fully connected networks, and more details can be found there. The figure to the right plots the one-dimensional outputs z L ( ⋅ ; θ ) {\displaystyle z^{L}(\cdot ;\theta )} of a neural network for two inputs x {\displaystyle x} and x ∗ {\displaystyle x^{}} against each other. The black dots show the function computed by the neural network on these inputs for random draws of the parameters from p ( θ ) {\displaystyle p(\theta )} . The red lines are iso-probability contours for the joint distribution over network outputs z L ( x ; θ ) {\displaystyle z^{L}(x;\theta )} and z L ( x ∗ ; θ ) {\displaystyle z^{L}(x^{};\theta )} induced by p ( θ ) {\displaystyle p(\theta )} . This is the distribution in function space corresponding to the distribution p ( θ ) {\displaystyle p(\theta )} in parameter space, and the black dots are samples from this distribution. For infinitely wide neural networks, since the distribution over functions computed by the neural network is a Gaussian process, the joint distribution over network outputs is a multivariate Gaussian for any finite set of network inputs. == Discussion == === Infinitely wide fully connected network === This section expands on the correspondence between infinitely wide neural networks and Gaussian processes for the specific case of a fully connected architecture. It provides a proof sketch outlining why the correspondence holds, and introduces the specific functional form of the NNGP for fully connected networks. The proof sketch closely follows the approach by Novak and coauthors. ==== Network architecture specification ==== Consider a fully connected artificial neural network with inputs x {\displaystyle x} , parameters θ {\displaystyle \theta } consisting of weights W l {\displaystyle W^{l}} and biases b l {\displaystyle b^{l}} for each layer l {\displaystyle l} in the network, pre-activations (pre-nonlinearity) z l {\displaystyle z^{l}} , activations (post-nonlinearity) y l {\displaystyle y^{l}} , pointwise nonlinearity ϕ ( ⋅ ) {\displaystyle \phi (\cdot )} , and layer widths n l {\displaystyle n^{l}} . For simplicity, the width n L + 1 {\displaystyle n^{L+1}} of the readout vector z L {\displaystyle z^{L}} is taken to be 1. The parameters of this network have a prior distribution p ( θ ) {\displaystyle p(\theta )} , which consists of an isotropic Gaussian for each weight and bias, with the variance of the weights scaled inversely with layer width. This network is illustrated in the figure to the right, and described by the following set of equations: x ≡ input y l ( x ) = { x l = 0 ϕ ( z l − 1 ( x ) ) l > 0 z i l ( x ) = ∑ j W i j l y j l ( x ) + b i l W i j l ∼ N ( 0 , σ w 2 n l ) b i l ∼ N ( 0 , σ b 2 ) ϕ ( ⋅ ) ≡ nonlinearity y l ( x ) , z l − 1 ( x ) ∈ R n l × 1 n L + 1 = 1 θ = { W 0 , b 0 , … , W L , b L } {\displaystyle {\begin{aligned}x&\equiv {\text{input}}\\y^{l}(x)&=\left\{{\begin{array}{lcl}x&&l=0\\\phi \left(z^{l-1}(x)\right)&&l>0\end{array}}\right.\\z_{i}^{l}(x)&=\sum _{j}W_{ij}^{l}y_{j}^{l}(x)+b_{i}^{l}\\W_{ij}^{l}&\sim {\mathcal {N}}\left(0,{\frac {\sigma _{w}^{2}}{n^{l}}}\right)\\b_{i}^{l}&\sim {\mathcal {N}}\left(0,\sigma _{b}^{2}\right)\\\phi (\cdot )&\equiv {\text{nonlinearity}}\\y^{l}(x),z^{l-1}(x)&\in \mathbb {R} ^{n^{l}\times 1}\\n^{L+1}&=1\\\theta &=\left\{W^{0},b^{0},\dots ,W^{L},b^{L}\right\}\end{aligned}}} ==== ==== z l | y l {\displaystyle z^{l}|y^{l}} is a Gaussian process We first observe that the pre-activations z l {\displaystyle z^{l}} are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . This result holds even at finite width. Each pre-activation z i l {\displaystyle z_{i}^{l}} is a weighted sum of Gaussian random variables, corresponding to the weights W i j l {\displaystyle W_{ij}^{l}} and biases b i l {\displaystyle b_{i}^{l}} , where the coefficients for each of those Gaussian variables are the preceding activations y j l {\displaystyle y_{j}^{l}} . Because they are a weighted sum of zero-mean Gaussians, the z i l {\displaystyle z_{i}^{l}} are themselves zero-mean Gaussians (conditioned on the coefficients y j l {\displaystyle y_{j}^{l}} ). Since the z l {\displaystyle z^{l}} are jointly Gaussian for any set of y l {\displaystyle y^{l}} , they are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . The covariance or kernel of this Gaussian process depends on the weight and bias variances σ w 2 {\displaystyle \sigma _{w}^{2}} and σ b 2 {\displaystyle \sigma _{b}^{2}} , as well as the second moment matrix K l {\displaystyle K^{l}} of the preceding activations y l {\displaystyle y^{l}} , z i l ∣ y l ∼ G P ( 0 , σ w 2 K l + σ b 2 ) K l ( x , x ′ ) = 1 n l ∑ i y i l ( x ) y i l ( x ′ ) {\displaystyle {\begin{aligned}z_{i}^{l}\mid y^{l}&\sim {\mathcal {GP}}\left(0,\sigma _{w}^{2}K^{l}+\sigma _{b}^{2}\right)\\K^{l}(x,x')&={\frac {1}{n^{l}}}\sum _{i}y_{i}^{l}(x)y_{i}^{l}(x')\end{aligned}}} The effect of the weight scale σ w 2 {\displaystyle \sigma _{w}^{2}} is to rescale the contribution to the covariance matrix from K l {\displaystyle K^{l}} , while the bias is shared for all inputs, and so σ b 2 {\displaystyle \sigma _{b}^{2}} makes the z i l {\displaystyle z_{i}^{l}} for different datapoints more similar and

  Read more →
• 

  Photometric stereo

  Photometric stereo is a technique in computer vision for estimating the surface normals of objects by observing that object under different lighting conditions (photometry). It is based on the fact that the amount of light reflected by a surface is dependent on the orientation of the surface in relation to the light source and the observer. By measuring the amount of light reflected into a camera, the space of possible surface orientations is limited. Given enough light sources from different angles, the surface orientation may be constrained to a single orientation or even overconstrained. The technique was originally introduced by Woodham in 1980. The special case where the data is a single image is known as shape from shading, and was analyzed by B. K. P. Horn in 1989. Photometric stereo has since been generalized to many other situations, including extended light sources and non-Lambertian surface finishes. Current research aims to make the method work in the presence of projected shadows, highlights, and non-uniform lighting. Photometric stereo is widely used in various fields, including archaeology, cultural heritage conservation, and quality control. It is now integrated into widely used open-source software, such as Meshroom. == Basic method == Under Woodham's original assumptions — Lambertian reflectance, known point-like distant light sources, and uniform albedo — the problem can be solved by inverting the linear equation I = L ⋅ n {\displaystyle I=L\cdot n} , where I {\displaystyle I} is a (known) vector of m {\displaystyle m} observed intensities, n {\displaystyle n} is the (unknown) surface normal, and L {\displaystyle L} is a (known) 3 × m {\displaystyle 3\times m} matrix of normalized light directions. This model can easily be extended to surfaces with non-uniform albedo, while keeping the problem linear. Taking an albedo reflectivity of k {\displaystyle k} , the formula for the reflected light intensity becomes I = k ( L ⋅ n ) . {\displaystyle I=k(L\cdot n).} If L {\displaystyle L} is square (there are exactly 3 lights) and non-singular, it can be inverted, giving L − 1 I = k n . {\displaystyle L^{-1}I=kn.} Since the normal vector is known to have length 1, k {\displaystyle k} must be the length of the vector k n {\displaystyle kn} , and n {\displaystyle n} is the normalised direction of that vector. If L {\displaystyle L} is not square (there are more than 3 lights), a generalisation of the inverse can be obtained using the Moore–Penrose pseudoinverse, by simply multiplying both sides with L T {\displaystyle L^{T}} , giving L T I = L T k ( L ⋅ n ) , {\displaystyle L^{T}I=L^{T}k(L\cdot n),} ( L T L ) − 1 L T I = k n , {\displaystyle (L^{T}L)^{-1}L^{T}I=kn,} after which the normal vector and albedo can be solved as described above. == Non-Lambertian surfaces == The classical photometric stereo problem concerns itself only with Lambertian surfaces, with perfectly diffuse reflection. This is unrealistic for many types of materials, especially metals, glass and smooth plastics, and will lead to aberrations in the resulting normal vectors. Many methods have been developed to lift this assumption. In this section, a few of these are listed. === Specular reflections === Historically, in computer graphics, the commonly used model to render surfaces started with Lambertian surfaces and progressed first to include simple specular reflections. Computer vision followed a similar course with photometric stereo. Specular reflections were among the first deviations from the Lambertian model. These are a few adaptations that have been developed. Many techniques ultimately rely on modelling the reflectance function of the surface, that is, how much light is reflected in each direction. This reflectance function has to be invertible. The reflected light intensities towards the camera is measured, and the inverse reflectance function is fit onto the measured intensities, resulting in a unique solution for the normal vector. === General BRDFs and beyond === According to the Bidirectional reflectance distribution function (BRDF) model, a surface may distribute the amount of light it receives in any outward direction. This is the most general known model for opaque surfaces. Some techniques have been developed to model (almost) general BRDFs. In practice, all of these require many light sources to obtain reliable data. These are methods in which surfaces with general BRDFs can be measured. Determine the explicit BRDF prior to scanning. To do this, a different surface is required that has the same or a very similar BRDF, of which the actual geometry (or at least the normal vectors for many points on the surface) is already known. The lights are then individually shone upon the known surface, and the amount of reflection into the camera is measured. Using this information, a look-up table can be created that maps reflected intensities for each light source to a list of possible normal vectors. This puts constraints on the possible normal vectors the surface may have, and reduces the photometric stereo problem to an interpolation between measurements. Typical known surfaces to calibrate the look-up table with are spheres for their wide variety of surface orientations. Restricting the BRDF to be symmetrical. If the BRDF is symmetrical, the direction of the light can be restricted to a cone about the direction to the camera. Which cone this is depends on the BRDF itself, the normal vector of the surface, and the measured intensity. Given enough measured intensities and the resulting light directions, these cones can be approximated and therefore the normal vectors of the surface. Some progress has been made towards modelling an even more general surfaces, such as Spatially Varying Bidirectional Distribution Functions (SVBRDF), Bidirectional surface scattering reflectance distribution functions (BSSRDF), and accounting for interreflections. However, such methods are still fairly restrictive in photometric stereo. Better results have been achieved with structured light. == Uncalibrated photometric stereo == Uncalibrated Photometric Stereo is an approach in photometric stereo that aims to reconstruct the 3D shape of an object from images captured under unknown lighting conditions. Unlike classical methods, which often assume controlled or known lighting setups, this approach removes these constraints, making it adaptable to diverse and real-world environments. The advent of deep learning has revolutionized universal PS by replacing handcrafted assumptions with data-driven models. Recent approaches leverage Transformer-based architectures and multi-scale encoder–decoder networks to directly estimate surface normals from input images. Uncalibrated Photometric Stereo is inherently an ill-posed problem, as it attempts to recover 3D shape and lighting conditions simultaneously from images alone. This leads to fundamental ambiguities in the reconstruction process, which manifest as systematic errors in the recovered geometry, including global distortions in the object's overall shape, and misinterpretation of surface orientation, where concave regions may appear convex and vice versa. To address the challenges of uncalibrated photometric stereo, hybrid methods have emerged that combine multi-view stereo and photometric stereo. These approaches leverage the strengths of both techniques, including geometric reliability and resolution.

  Read more →
• 

  Randomized Hough transform

  Hough transforms are techniques for object detection, a critical step in many implementations of computer vision, or data mining from images. Specifically, the Randomized Hough transform is a probabilistic variant to the classical Hough transform, and is commonly used to detect curves (straight line, circle, ellipse, etc.) The basic idea of Hough transform (HT) is to implement a voting procedure for all potential curves in the image, and at the termination of the algorithm, curves that do exist in the image will have relatively high voting scores. Randomized Hough transform (RHT) is different from HT in that it tries to avoid conducting the computationally expensive voting process for every nonzero pixel in the image by taking advantage of the geometric properties of analytical curves, and thus improve the time efficiency and reduce the storage requirement of the original algorithm. == Motivation == Although Hough transform (HT) has been widely used in curve detection, it has two major drawbacks: First, for each nonzero pixel in the image, the parameters for the existing curve and redundant ones are both accumulated during the voting procedure. Second, the accumulator array (or Hough space) is predefined in a heuristic way. The more accuracy needed, the higher parameter resolution should be defined. These two needs usually result in a large storage requirement and low speed for real applications. Therefore, RHT was brought up to tackle this problem. == Implementation == In comparison with HT, RHT takes advantage of the fact that some analytical curves can be fully determined by a certain number of points on the curve. For example, a straight line can be determined by two points, and an ellipse (or a circle) can be determined by three points. The case of ellipse detection can be used to illustrate the basic idea of RHT. The whole process generally consists of three steps: Fit ellipses with randomly selected points. Update the accumulator array and corresponding scores. Output the ellipses with scores higher than some predefined threshold. === Ellipse fitting === One general equation for defining ellipses is: a ( x − p ) 2 + 2 b ( x − p ) ( y − q ) + c ( y − q ) 2 = 1 {\displaystyle a(x-p)^{2}+2b(x-p)(y-q)+c(y-q)^{2}=1} with restriction: a c − b 2 > 0 {\displaystyle ac-b^{2}>0} However, an ellipse can be fully determined if one knows three points on it and the tangents in these points. RHT starts by randomly selecting three points on the ellipse. Let them be X 1 {\displaystyle X_{1}} , X 2 {\displaystyle X_{2}} and X 3 {\displaystyle X_{3}} . The first step is to find the tangents of these three points. They can be found by fitting a straight line using least squares technique for a small window of neighboring pixels. The next step is to find the intersection points of the tangent lines. This can be easily done by solving the line equations found in the previous step. Then let the intersection points be T 12 {\displaystyle T_{12}} and T 23 {\displaystyle T_{23}} , the midpoints of line segments X 1 X 2 {\displaystyle X_{1}X_{2}} and X 2 X 3 {\displaystyle X_{2}X_{3}} be M 12 {\displaystyle M_{12}} and M 23 {\displaystyle M_{23}} . Then the center of the ellipse will lie in the intersection of T 12 M 12 {\displaystyle T_{12}M_{12}} and T 23 M 23 {\displaystyle T_{23}M_{23}} . Again, the coordinates of the intersected point can be determined by solving line equations and the detailed process is skipped here for conciseness. Let the coordinates of ellipse center found in previous step be ( x 0 , y 0 ) {\displaystyle (x_{0},y_{0})} . Then the center can be translated to the origin with x ′ = x − x 0 {\displaystyle x'=x-x_{0}} and y ′ = y − y 0 {\displaystyle y'=y-y_{0}} so that the ellipse equation can be simplified to: a x ′ 2 + 2 b x ′ y ′ + c y ′ 2 = 1 {\displaystyle ax'^{2}+2bx'y'+cy'^{2}=1} Now we can solve for the rest of ellipse parameters: a {\displaystyle a} , b {\displaystyle b} and c {\displaystyle c} by substituting the coordinates of X 1 {\displaystyle X_{1}} , X 2 {\displaystyle X_{2}} and X 3 {\displaystyle X_{3}} into the equation above. === Accumulating === With the ellipse parameters determined from previous stage, the accumulator array can be updated correspondingly. Different from classical Hough transform, RHT does not keep "grid of buckets" as the accumulator array. Rather, it first calculates the similarities between the newly detected ellipse and the ones already stored in accumulator array. Different metrics can be used to calculate the similarity. As long as the similarity exceeds some predefined threshold, replace the one in the accumulator with the average of both ellipses and add 1 to its score. Otherwise, initialize this ellipse to an empty position in the accumulator and assign a score of 1. === Termination === Once the score of one candidate ellipse exceeds the threshold, it is determined as existing in the image (in other words, this ellipse is detected), and should be removed from the image and accumulator array so that the algorithm can detect other potential ellipses faster. The algorithm terminates when the number of iterations reaches a maximum limit or all the ellipses have been detected. Pseudo code for RHT: while (we find ellipses AND not reached the maximum epoch) { for (a fixed number of iterations) { Find a potential ellipse. if (the ellipse is similar to an ellipse in the accumulator) then Replace the one in the accumulator with the average of two ellipses and add 1 to the score; else Insert the ellipse into an empty position in the accumulator with a score of 1; } Select the ellipse with the best score and save it in a best ellipse table; Eliminate the pixels of the best ellipse from the image; Empty the accumulator; }

  Read more →
• 

  Comparison gallery of image scaling algorithms

  This gallery shows the results of numerous image scaling algorithms. == Scaling methods == An image size can be changed in several ways. Consider resizing a 160x160 pixel photo to the following 40x40 pixel thumbnail and then scaling the thumbnail to a 160x160 pixel image. Also consider doubling the size of the following image containing text. == Examples of enlarged images == Below are examples of various images enlarged 4x using each scaling algorithm.

  Read more →
• 

  Connected-component labeling

  Connected-component labeling (CCL), connected-component analysis (CCA), blob extraction, region labeling, blob discovery, or region extraction is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component labeling is not to be confused with segmentation. Connected-component labeling is used in computer vision to detect connected regions in binary digital images, although color images and data with higher dimensionality can also be processed. When integrated into an image recognition system or human-computer interaction interface, connected component labeling can operate on a variety of information. Blob extraction is generally performed on the resulting binary image from a thresholding step, but it can be applicable to gray-scale and color images as well. Blobs may be counted, filtered, and tracked. Blob extraction is related to but distinct from blob detection. == Overview == A graph, containing vertices and connecting edges, is constructed from relevant input data. The vertices contain information required by the comparison heuristic, while the edges indicate connected 'neighbors'. An algorithm traverses the graph, labeling the vertices based on the connectivity and relative values of their neighbors. Connectivity is determined by the medium; image graphs, for example, can be 4-connected neighborhood or 8-connected neighborhood. Following the labeling stage, the graph may be partitioned into subsets, after which the original information can be recovered and processed . == Definition == The usage of the term connected-component labeling (CCL) and its definition is quite consistent in the academic literature, whereas connected-component analysis (CCA) varies both in terminology and in its definition of the problem. Rosenfeld et al. define connected components labeling as the “[c]reation of a labeled image in which the positions associated with the same connected component of the binary input image have a unique label.” Shapiro et al. define CCL as an operator whose “input is a binary image and [...] output is a symbolic image in which the label assigned to each pixel is an integer uniquely identifying the connected component to which that pixel belongs.” There is no consensus on the definition of CCA in the academic literature. It is often used interchangeably with CCL. A more extensive definition is given by Shapiro et al.: “Connected component analysis consists of connected component labeling of the black pixels followed by property measurement of the component regions and decision making.” The definition for connected-component analysis presented here is more general, taking the thoughts expressed in into account. == Algorithms == The algorithms discussed can be generalised to arbitrary dimensions, albeit with increased time and space complexity. === One component at a time === This is a fast and very simple method to implement and understand. It is based on graph traversal methods in graph theory. In short, once the first pixel of a connected component is found, all the connected pixels of that connected component are labelled before going onto the next pixel in the image. This algorithm is part of Vincent and Soille's watershed segmentation algorithm, other implementations also exist. In order to do that a linked list is formed that will keep the indexes of the pixels that are connected to each other, steps (2) and (3) below. The method of defining the linked list specifies the use of a depth or a breadth first search. For this particular application, there is no difference which strategy to use. The simplest kind of a last in first out queue implemented as a singly linked list will result in a depth first search strategy. It is assumed that the input image is a binary image, with pixels being either background or foreground and that the connected components in the foreground pixels are desired. The algorithm steps can be written as: Start from the first pixel in the image. Set current label to 1. Go to (2). If this pixel is a foreground pixel and it is not already labelled, give it the current label and add it as the first element in a queue, then go to (3). If it is a background pixel or it was already labelled, then repeat (2) for the next pixel in the image. Pop out an element from the queue, and look at its neighbours (based on any type of connectivity). If a neighbour is a foreground pixel and is not already labelled, give it the current label and add it to the queue. Repeat (3) until there are no more elements in the queue. Go to (2) for the next pixel in the image and increment current label by 1. Note that the pixels are labelled before being put into the queue. The queue will only keep a pixel to check its neighbours and add them to the queue if necessary. This algorithm only needs to check the neighbours of each foreground pixel once and doesn't check the neighbours of background pixels. The pseudocode is: algorithm OneComponentAtATime(data) input : imageData[xDim][yDim] initialization : label = 0, labelArray[xDim][yDim] = 0, statusArray[xDim][yDim] = false, queue1, queue2; for i = 0 to xDim do for j = 0 to yDim do if imageData[i][j] has not been processed do if imageData[i][j] is a foreground pixel do check its four neighbors(north, south, east, west) : if neighbor is not processed do if neighbor is a foreground pixel do add it to queue1 else update its status to processed end if labelArray[i][j] = label (give label) statusArray[i][j] = true (update status) while queue1 is not empty do For each pixel in the queue do : check its four neighbors if neighbor is not processed do if neighbor is a foreground pixel do add it to queue2 else update its status to processed end if give it the current label update its status to processed remove the current element from queue1 copy queue2 into queue1 end While increase the label end if else update its status to processed end if end if end if end for end for === Two-pass === Relatively simple to implement and understand, the two-pass algorithm, (also known as the Hoshen–Kopelman algorithm) iterates through 2-dimensional binary data. The algorithm makes two passes over the image: the first pass to assign temporary labels and record equivalences, and the second pass to replace each temporary label by the smallest label of its equivalence class. The input data can be modified in situ (which carries the risk of data corruption), or labeling information can be maintained in an additional data structure. Connectivity checks are carried out by checking neighbor pixels' labels (neighbor elements whose labels are not assigned yet are ignored), or say, the north-east, the north, the north-west and the west of the current pixel (assuming 8-connectivity). 4-connectivity uses only north and west neighbors of the current pixel. The following conditions are checked to determine the value of the label to be assigned to the current pixel (4-connectivity is assumed) Conditions to check: Does the pixel to the left (west) have the same value as the current pixel? Yes – We are in the same region. Assign the same label to the current pixel No – Check next condition Do both pixels to the north and west of the current pixel have the same value as the current pixel but not the same label? Yes – We know that the north and west pixels belong to the same region and must be merged. Assign the current pixel the minimum of the north and west labels, and record their equivalence relationship No – Check next condition Does the pixel to the left (west) have a different value and the one to the north the same value as the current pixel? Yes – Assign the label of the north pixel to the current pixel No – Check next condition Do the pixel's north and west neighbors have different pixel values than current pixel? Yes – Create a new label id and assign it to the current pixel The algorithm continues this way, and creates new region labels whenever necessary. The key to a fast algorithm, however, is how this merging is done. This algorithm uses the union-find data structure which provides excellent performance for keeping track of equivalence relationships. Union-find essentially stores labels which correspond to the same blob in a disjoint-set data structure, making it easy to remember the equivalence of two labels by the use of an interface method E.g.: findSet(l). findSet(l) returns the minimum label value that is equivalent to the function argument 'l'. Once the initial labeling and equivalence recording is completed, the second pass merely replaces each pixel label with its equivalent disjoint-set representative element. A faster-scanning algorithm for connected-region extraction is presented below. On the first pass: Iterate through each element of the data by column, then by row (Raster Scanning) If the element is not the background Get the neighboring elements of the current element If there are no neighbors, uniquely

  Read more →
• 

  Referring expression generation

  Referring expression generation (REG) is the subtask of natural language generation (NLG) that received most scholarly attention. While NLG is concerned with the conversion of non-linguistic information into natural language, REG focuses only on the creation of referring expressions (noun phrases) that identify specific entities called targets. This task can be split into two sections. The content selection part determines which set of properties distinguish the intended target and the linguistic realization part defines how these properties are translated into natural language. A variety of algorithms have been developed in the NLG community to generate different types of referring expressions. == Types of referring expressions == A referring expression (RE), in linguistics, is any noun phrase, or surrogate for a noun phrase, whose function in discourse is to identify some individual object (thing, being, event...) The technical terminology for identify differs a great deal from one school of linguistics to another. The most widespread term is probably refer, and a thing identified is a referent, as for example in the work of John Lyons. In linguistics, the study of reference relations belongs to pragmatics, the study of language use, though it is also a matter of great interest to philosophers, especially those wishing to understand the nature of knowledge, perception and cognition more generally. Various devices can be used for reference: determiners, pronouns, proper names... Reference relations can be of different kinds; referents can be in a "real" or imaginary world, in discourse itself, and they may be singular, plural, or collective. === Pronouns === The simplest type of referring expressions are pronoun such as he and it. The linguistics and natural language processing communities have developed various models for predicting anaphor referents, such as centering theory, and ideally referring-expression generation would be based on such models. However most NLG systems use much simpler algorithms, for example using a pronoun if the referent was mentioned in the previous sentence (or sentential clause), and no other entity of the same gender was mentioned in this sentence. === Definite noun phrases === There has been a considerable amount of research on generating definite noun phrases, such as the big red book. Much of this builds on the model proposed by Dale and Reiter. This has been extended in various ways, for example Krahmer et al. present a graph-theoretic model of definite NP generation with many nice properties. In recent years a shared-task event has compared different algorithms for definite NP generation, using the TUNA corpus. === Spatial and temporal reference === Recently there has been more research on generating referring expressions for time and space. Such references tend to be imprecise (what is the exact meaning of tonight?), and also to be interpreted in different ways by different people. Hence it may be necessary to explicitly reason about false positive vs false negative tradeoffs, and even calculate the utility of different possible referring expressions in a particular task context. === Criteria for good expressions === Ideally, a good referring expression should satisfy a number of criteria: Referential success: It should unambiguously identify the referent to the reader. Ease of comprehension: The reader should be able to quickly read and understand it. Computational complexity: The generation algorithm should be fast No false inferences: The expression should not confuse or mislead the reader by suggesting false implicatures or other pragmatic inferences. For example, a reader may be confused if he is told Sit by the brown wooden table in a context where there is only one table. == History == === Pre-2000 era === REG goes back to the early days of NLG. One of the first approaches was done by Winograd in 1972 who developed an "incremental" REG algorithm for his SHRDLU program. Afterwards researchers started to model the human abilities to create referring expressions in the 1980s. This new approach to the topic was influenced by the researchers Appelt and Kronfeld who created the programs KAMP and BERTRAND and considered referring expressions as parts of bigger speech acts. Some of their most interesting findings were the fact that referring expressions can be used to add information beyond the identification of the referent as well as the influence of communicative context and the Gricean maxims on referring expressions. Furthermore, its skepticism concerning the naturalness of minimal descriptions made Appelt and Kronfeld's research a foundation of later work on REG. The search for simple, well-defined problems changed the direction of research in the early 1990s. This new approach was led by Dale and Reiter who stressed the identification of the referent as the central goal. Like Appelt they discuss the connection between the Gricean maxims and referring expressions in their culminant paper in which they also propose a formal problem definition. Furthermore, Reiter and Dale discuss the Full Brevity and Greedy Heuristics algorithms as well as their Incremental Algorithm(IA) which became one of the most important algorithms in REG. === Later developments === After 2000 the research began to lift some of the simplifying assumptions, that had been made in early REG research in order to create more simple algorithms. Different research groups concentrated on different limitations creating several expanded algorithms. Often these extend the IA in a single perspective for example in relation to: Reference to Sets like "the t-shirt wearers" or "the green apples and the banana on the left" Relational Descriptions like "the cup on the table" or "the woman who has three children" Context Dependency, Vagueness and Gradeability include statements like "the older man" or "the car on the left" which are often unclear without a context Salience and Generation of Pronouns are highly discourse dependent making for example "she" a reference to "the (most salient) female person" Many simplifying assumptions are still in place or have just begun to be worked on. Also a combination of the different extensions has yet to be done and is called a "non-trivial enterprise" by Krahmer and van Deemter. Another important change after 2000 was the increasing use of empirical studies in order to evaluate algorithms. This development took place due to the emergence of transparent corpora. Although there are still discussions about what the best evaluation metrics are, the use of experimental evaluation has already led to a better comparability of algorithms, a discussion about the goals of REG and more task-oriented research. Furthermore, research has extended its range to related topics such as the choice of Knowledge Representation(KR) Frameworks. In this area the main question, which KR framework is most suitable for the use in REG remains open. The answer to this question depends on how well descriptions can be expressed or found. A lot of the potential of KR frameworks has been left unused so far. Some of the different approaches are the usage of: Graph search which treats relations between targets in the same way as properties. Constraint Satisfaction which allows for a separation between problem specification and the implementation. Modern Knowledge Representation which offers logical inference in for example Description Logic or Conceptual Graphs. == Problem definition == Dale and Reiter (1995) think about referring expressions as distinguishing descriptions. They define: The referent as the entity that should be described The context set as set of salient entities The contrast set or potential distractors as all elements of the context set except the referent A property as a reference to a single attribute–value pair Each entity in the domain can be characterised as a set of attribute–value pairs for example ⟨ {\displaystyle \langle } type, dog ⟩ {\displaystyle \rangle } , ⟨ {\displaystyle \langle } gender, female ⟩ {\displaystyle \rangle } or ⟨ {\displaystyle \langle } age, 10 years ⟩ {\displaystyle \rangle } . The problem then is defined as follows: Let r {\displaystyle r} be the intended referent, and C {\displaystyle C} be the contrast set. Then, a set L {\displaystyle L} of attribute–value pairs will represent a distinguishing description if the following two conditions hold: Every attribute–value pair in L {\displaystyle L} applies to r {\displaystyle r} : that is, every element of L {\displaystyle L} specifies an attribute–value that r {\displaystyle r} possesses. For every member c {\displaystyle c} of C {\displaystyle C} , there is at least one element l {\displaystyle l} of L {\displaystyle L} that does not apply to c {\displaystyle c} : that is, there is an l {\displaystyle l} in L {\displaystyle L} that specifies an attribute–value that c {\displaystyle c} does not possess. l {\displaystyle l} is said

  Read more →