IruSoft (Arabic: آيروسوفت) is an insurance regulatory platform designated for licensing, supervision and inspection of the insurance sector within a country. The platform introduced unique supervision-technology (suptech), insurance-technology (insurtech) and regulatory-technology (regtech) automated modules by which a regulator requires less resources to ensure fairness, transparency and competition and to prevent conflicts of interest in the sector. IruSoft was founded by Abdullah Al-Salloum and owned by the Insurance Regulatory Unit in Kuwait. The Insurance Regulatory Unit optimized processing insurance-sector's customer complaints by issuing Resolution No. (1) of 2022 that introduced IruSoft's complaints public module; an automated resolution center, by which the process of receiving submitted complaints, passing them on to the platforms of licensed insurance companies, tracking matter-related discussions and updates and getting them escalated if unresolved to be discussed by a committee assigned by the unit is integrally automated and analyzed for better key performance indicators.
Vulnerabilities Equities Process
The Vulnerabilities Equities Process (VEP) is a process used by the U.S. federal government to determine on a case-by-case basis how it should treat zero-day computer security vulnerabilities: whether to disclose them to the public to help improve general computer security, or to keep them secret for offensive use against the government's adversaries. The VEP was first developed during the period 2008–2009, but only became public in 2016, when the government released a redacted version of the VEP in response to a FOIA request by the Electronic Frontier Foundation. Following public pressure for greater transparency in the wake of the Shadow Brokers affair, the U.S. government made a more public disclosure of the VEP process in November 2017. == Participants == According to the VEP plan published in 2017, the Equities Review Board (ERB) is the primary forum for interagency deliberation and determinations concerning the VEP. The ERB meets monthly, but may also be convened sooner if an immediate need arises. The ERB consists of representatives from the following agencies: Office of Management and Budget Office of the Director of National Intelligence (including the Intelligence Community-Security Coordination Center) United States Department of the Treasury United States Department of State United States Department of Justice (including the Federal Bureau of Investigation and the National Cyber Investigative Joint Task Force) Department of Homeland Security (including the National Cybersecurity and Communications Integration Center and the United States Secret Service) United States Department of Energy United States Department of Defense (to include the National Security Agency, including Information Assurance and Signals Intelligence elements), United States Cyber Command, and DoD Cyber Crime Center) United States Department of Commerce Central Intelligence Agency The National Security Agency serves as the executive secretariat for the VEP. == Process == According to the November 2017 version of the VEP, the process is as follows: === Submission and notification === When an agency finds a vulnerability, it will notify the VEP secretariat as soon as is possible. The notification will include a description of the vulnerability and the vulnerable products or systems, together with the agency's recommendation to either disseminate or restrict the vulnerability information. The secretariat will then notify all participants of the submission within one business day, requesting them to respond if they have an relevant interest. === Equity and discussions === An agency expressing an interest must indicate whether it concurs with the original recommendation to disseminate or restrict within five business days. If it does not, it will hold discussions with the submitting agency and the VEP secretariat within seven business days to attempt to reach consensus. If no consensus is reached, the participants will suggest options for the Equities Review Board. === Determination to disseminate or restrict === Decisions whether to disclose or restrict a vulnerability should be made quickly, in full consultation with all concerned agencies, and in the overall best interest of the competing interests of the missions of the U.S. government. As far as possible, determinations should be based on rational, objective methodologies, taking into account factors such as prevalence, reliance, and severity. If the review board members cannot reach consensus, they will vote on a preliminary determination. If an agency with an equity disputes that decision, they may, by providing notice to the VEP secretariat, elect to contest the preliminary determination. If no agency contests a preliminary determination, it will be treated as a final decision. === Handling and follow-on actions === If vulnerability information is released, this will be done as quickly as possible, preferably within seven business days. Disclosure of vulnerabilities will be conducted according to guidelines agreed on by all members. The submitting agency is presumed to be most knowledgeable about the vulnerability and, as such, will be responsible for disseminating vulnerability information to the vendor. The submitting agency may elect to delegate dissemination responsibility to another agency on its behalf. The releasing agency will promptly provide a copy of the disclosed information to the VEP secretariat for record keeping. Additionally, the releasing agency is expected to follow up so the ERB can determine whether the vendor's action meets government requirements. If the vendor chooses not to address a vulnerability, or is not acting with urgency consistent with the risk of the vulnerability, the releasing agency will notify the secretariat, and the government may take other mitigation steps. == Criticism == The VEP process has been criticized for a number of deficiencies, including restriction by non-disclosure agreements, lack of risk ratings, special treatment for the NSA, and less than whole-hearted commitment to disclosure as the default option. == UK equivalent == British intelligence agencies—GCHQ in particular—follow a similar approach, also known as the Equities Process, to determine whether to disclose or retain security vulnerabilities. The Investigatory Powers Act 2016 was amended in 2022 to bring oversight of the operation of the process within the remit of the Investigatory Powers Commissioner. Details of the process were made public in 2018.
Cache language model
A cache language model is a type of statistical language model. These occur in the natural language processing subfield of computer science and assign probabilities to given sequences of words by means of a probability distribution. Statistical language models are key components of speech recognition systems and of many machine translation systems: they tell such systems which possible output word sequences are probable and which are improbable. The particular characteristic of a cache language model is that it contains a cache component and assigns relatively high probabilities to words or word sequences that occur elsewhere in a given text. The primary, but by no means sole, use of cache language models is in speech recognition systems. To understand why it is a good idea for a statistical language model to contain a cache component one might consider someone who is dictating a letter about elephants to a speech recognition system. Standard (non-cache) N-gram language models will assign a very low probability to the word "elephant" because it is a very rare word in English. If the speech recognition system does not contain a cache component, the person dictating the letter may be annoyed: each time the word "elephant" is spoken another sequence of words with a higher probability according to the N-gram language model may be recognized (e.g., "tell a plan"). These erroneous sequences will have to be deleted manually and replaced in the text by "elephant" each time "elephant" is spoken. If the system has a cache language model, "elephant" will still probably be misrecognized the first time it is spoken and will have to be entered into the text manually; however, from this point on the system is aware that "elephant" is likely to occur again – the estimated probability of occurrence of "elephant" has been increased, making it more likely that if it is spoken it will be recognized correctly. Once "elephant" has occurred several times, the system is likely to recognize it correctly every time it is spoken until the letter has been completely dictated. This increase in the probability assigned to the occurrence of "elephant" is an example of a consequence of machine learning and more specifically of pattern recognition. There exist variants of the cache language model in which not only single words but also multi-word sequences that have occurred previously are assigned higher probabilities (e.g., if "San Francisco" occurred near the beginning of the text subsequent instances of it would be assigned a higher probability). The cache language model was first proposed in a paper published in 1990, after which the IBM speech-recognition group experimented with the concept. The group found that implementation of a form of cache language model yielded a 24% drop in word-error rates once the first few hundred words of a document had been dictated. A detailed survey of language modeling techniques concluded that the cache language model was one of the few new language modeling techniques that yielded improvements over the standard N-gram approach: "Our caching results show that caching is by far the most useful technique for perplexity reduction at small and medium training data sizes". The development of the cache language model has generated considerable interest among those concerned with computational linguistics in general and statistical natural language processing in particular: recently, there has been interest in applying the cache language model in the field of statistical machine translation. The success of the cache language model in improving word prediction rests on the human tendency to use words in a "bursty" fashion: when one is discussing a certain topic in a certain context, the frequency with which one uses certain words will be quite different from their frequencies when one is discussing other topics in other contexts. The traditional N-gram language models, which rely entirely on information from a very small number (four, three, or two) of words preceding the word to which a probability is to be assigned, do not adequately model this "burstiness". Recently, the cache language model concept – originally conceived for the N-gram statistical language model paradigm – has been adapted for use in the neural paradigm. For instance, recent work on continuous cache language models in the recurrent neural network (RNN) setting has applied the cache concept to much larger contexts than before, yielding significant reductions in perplexity. Another recent line of research involves incorporating a cache component in a feed-forward neural language model (FN-LM) to achieve rapid domain adaptation.
Egocentric vision
Egocentric vision or first-person vision is a sub-field of computer vision that entails analyzing images and videos captured by a wearable camera, which is typically worn on the head or on the chest and naturally approximates the visual field of the camera wearer. Consequently, visual data capture the part of the scene on which the user focuses to carry out the task at hand and offer a valuable perspective to understand the user's activities and their context in a naturalistic setting. The wearable camera looking forwards is often supplemented with a camera looking inward at the user's eye and able to measure a user's eye gaze, which is useful to reveal attention and to better understand the user's activity and intentions. == History == The idea of using a wearable camera to gather visual data from a first-person perspective dates back to the 70s, when Steve Mann invented "Digital Eye Glass", a device that, when worn, causes the human eye itself to effectively become both an electronic camera and a television display. Subsequently, wearable cameras were used for health-related applications in the context of Humanistic Intelligence and Wearable AI. Egocentric vision is best done from the point-of-eye, but may also be done by way of a neck-worn camera when eyeglasses would be in-the-way. This neck-worn variant was popularized by way of the Microsoft SenseCam in 2006 for experimental health research works. The interest of the computer vision community into the egocentric paradigm has been arising slowly entering the 2010s and it is rapidly growing in recent years, boosted by both the impressive advances in the field of wearable technology and by the increasing number of potential applications. The prototypical first-person vision system described by Kanade and Hebert, in 2012 is composed by three basic components: a localization component able to estimate the surrounding, a recognition component able to identify object and people, and an activity recognition component, able to provide information about the current activity of the user. Together, these three components provide a complete situational awareness of the user, which in turn can be used to provide assistance to the user or to the caregiver. Following this idea, the first computational techniques for egocentric analysis focused on hand-related activity recognition and social interaction analysis. Also, given the unconstrained nature of the video and the huge amount of data generated, temporal segmentation and summarization were among the first problems addressed. After almost ten years of egocentric vision (2007–2017), the field is still undergoing diversification. Emerging research topics include: Social saliency estimation Multi-agent egocentric vision systems Privacy preserving techniques and applications Attention-based activity analysis Social interaction analysis Hand pose analysis Ego graphical User Interfaces (EUI) Understanding social dynamics and attention Revisiting robotic vision and machine vision as egocentric sensing Activity forecasting Gaze prediction == Technical challenges == Today's wearable cameras are small and lightweight digital recording devices that can acquire images and videos automatically, without the user intervention, with different resolutions and frame rates, and from a first-person point of view. Therefore, wearable cameras are naturally primed to gather visual information from our everyday interactions since they offer an intimate perspective of the visual field of the camera wearer. Depending on the frame rate, it is common to distinguish between photo-cameras (also called lifelogging cameras) and video-cameras. The former (e.g., Narrative Clip and Microsoft SenseCam), are commonly worn on the chest, and are characterized by a very low frame rate (up to 2fpm) that allows to capture images over a long period of time without the need of recharging the battery. Consequently, they offer considerable potential for inferring knowledge about e.g. behaviour patterns, habits or lifestyle of the user. However, due to the low frame-rate and the free motion of the camera, temporally adjacent images typically present abrupt appearance changes so that motion features cannot be reliably estimated. The latter (e.g., Google Glass, GoPro), are commonly mounted on the head, and capture conventional video (around 35fps) that allows to capture fine temporal details of interactions. Consequently, they offer potential for in-depth analysis of daily or special activities. However, since the camera is moving with the wearer head, it becomes more difficult to estimate the global motion of the wearer and in the case of abrupt movements, the images can result blurred. In both cases, since the camera is worn in a naturalistic setting, visual data present a huge variability in terms of illumination conditions and object appearance. Moreover, the camera wearer is not visible in the image and what he/she is doing has to be inferred from the information in the visual field of the camera, implying that important information about the wearer, such for instance as pose or facial expression estimation, is not available. == Applications == A collection of studies published in a special theme issue of the American Journal of Preventive Medicine has demonstrated the potential of lifelogs captured through wearable cameras from a number of viewpoints. In particular, it has been shown that used as a tool for understanding and tracking lifestyle behaviour, lifelogs would enable the prevention of noncommunicable diseases associated to unhealthy trends and risky profiles (such as obesity and depression). In addition, used as a tool of re-memory cognitive training, lifelogs would enable the prevention of cognitive and functional decline in elderly people. More recently, egocentric cameras have been used to study human and animal cognition, human-human social interaction, human-robot interaction, human expertise in complex tasks. Other applications include navigation/assistive technologies for the blind, monitoring and assistance of industrial workflows, and augmented reality interfaces.
Flok (company)
Flok (formerly Loyalblocks) was an American tech startup based in New York City that provides marketing services such as chatbots/AI, customer loyalty programs, mobile apps and CRM services to local businesses. In January 2017, the company was acquired by Wix.com. Around March 2017, Flok ceased regular communication. At some point in 2019 Flok communicated to its customers that it would shut down in March 2020. == Background == Flok was founded in 2011 by Ido Gaver and Eran Kirshenboim and has offices in Tel Aviv, Israel. In May 2013, Flok secured a $9 million Series A Round from General Catalyst Partners with participation from Founder Collective and existing investor Gemini Israel Ventures. In total, Flok has raised over $18 million in venture capital in three rounds. In May 2014, Flok announced a self-service loyalty platform for SMBs to build their own programs with beacon integration. At that time, approximately 40,000 businesses were using the service. In 2016, Flok released a turnkey chatbot service for local businesses, and was featured in AdWeek for developing the first weed bot chatbot for a California cannabis business. == Services == Flok offered an eponymous customer-facing app, that consumers use to receive rewards and deals from partner businesses, and a Flok business app for merchants to manage the platform.
PenTile matrix family
PenTile matrix is a family of patented subpixel matrix schemes used in electronic device displays. PenTile is a trademark of Samsung. PenTile matrices are used in AMOLED and LCD displays. These subpixel layouts are specifically designed to operate with proprietary algorithms for subpixel rendering embedded in the display driver, allowing plug and play compatibility with conventional RGB (Red-Green-Blue) stripe panels. == Overview == "PenTile Matrix" (a neologism from penta-, meaning "five" in Greek and tile) describes the geometric layout of the prototypical subpixel arrangement developed in the early 1990s. The layout consists of a quincunx comprising two red subpixels, two green subpixels, and one central blue subpixel in each unit cell. It was inspired by biomimicry of the human retina, which has nearly equal numbers of L and M type cone cells, but significantly fewer S cones. As the S cones are primarily responsible for perceiving blue colors, which do not appreciably affect the perception of luminance, reducing the number of blue subpixels with respect to the red and green subpixels in a display does not reduce the image quality. However, the layout may cause color leakage image distortion, which can be reduced by filters. In some cases the layout causes reduced moiré and blockiness compared to conventional RGB layouts. The PenTile layout is specifically designed to work with and be dependent upon subpixel rendering that uses only one and a quarter subpixel per pixel, on average, to render an image. That is, that any given input pixel is mapped to either a red-centered logical pixel, or a green-centered logical pixel. === History === PenTile was invented by Candice H. Brown Elliott, for which she was awarded the Society for Information Display's Otto Schade Prize in 2014. The technology was licensed by the company Clairvoyante from 2000 until 2008, during which time several prototype PenTile displays were developed by a number of Asian liquid crystal display (LCD) manufacturers. In March 2008, Samsung Electronics acquired Clairvoyante's PenTile IP assets. Samsung then funded a new company, Nouvoyance, Inc. to continue development of the PenTile technology. == PenTile RGBG == PenTile RGBG layout used in AMOLED and plasma displays uses green pixels interleaved with alternating red and blue pixels. The human eye is most sensitive to green, especially for high resolution luminance information. The green subpixels are mapped to input pixels on a one-to-one basis. The red and blue subpixels are subsampled, reconstructing the chroma signal at a lower resolution. The luminance signal is processed using adaptive subpixel rendering filters to optimize reconstruction of high spatial frequencies from the input image, wherein the green subpixels provide the majority of the reconstruction. The red and blue subpixels are capable of reconstructing the horizontal and vertical spatial frequencies, but not the highest of the diagonal. Diagonal high spatial frequency information in the red and blue channels of the input image are transferred to the green subpixels for image reconstruction. Thus the RG-BG scheme creates a color display with one third fewer subpixels than a traditional RGB-RGB scheme but with the same measured luminance display resolution. This is similar to the Bayer filter commonly used in digital cameras. === Devices === As of 2021, "almost all" OLED screens in portable consumer devices use some form of Pentile subpixel layout. == PenTile RGBW == PenTile RGBW technology, used in LCD, adds an extra subpixel to the traditional red, green and blue subpixels that is a clear area without color filtering material and with the only purpose of letting backlight come through, hence W for white. This makes it possible to produce a brighter image compared to an RGB-matrix while using the same amount of power, or produce an equally bright image while using less power. The PenTile RGBW layout uses each red, green, blue and white subpixel to present high-resolution luminance information to the human eyes' red-sensing and green-sensing cone cells, while using the combined effect of all the color subpixels to present lower-resolution chroma (color) information to all three cone cell types. Combined, this optimizes the match of display technology to the biological mechanisms of human vision. The layout uses one third fewer subpixels for the same resolution as the RGB stripe (RGB-RGB) layout, in spite of having four color primaries instead of the conventional three, using subpixel rendering combined with metamer rendering. Metamer rendering optimizes the energy distribution between the white subpixel and the combined red, green, and blue subpixels: W <> RGB, to improve image sharpness. The display driver chip has an RGB to RGBW color vector space converter and gamut mapping algorithm, followed by metamer and subpixel rendering algorithms. In order to maintain saturated color quality, to avoid simultaneous contrast error between saturated colors and peak white brightness, while simultaneously reducing backlight power requirements, the display backlight brightness is under control of the PenTile driver engine. When the image is mostly desaturated colors, those near white or grey, the backlight brightness is significantly reduced, often to less than 50% peak, while the LCD levels are increased to compensate. When the image has very bright saturated colors, the backlight brightness is maintained at higher levels. The PenTile RGBW also has an optional high-brightness mode that doubles the brightness of the desaturated color image areas, such as black-and-white text, for improved outdoor viewability. === Devices === Motorola MC65 Motorola ES55 Motorola ES400 Motorola Atrix 4G Samsung Galaxy Note 10.1 2014 version Lenovo Yoga 2 Pro Lenovo Yoga 3 Pro HP ENVY TouchSmart 14-k022tx Sleekbook MSI GS60 Ghost Pro 4K Lenovo IdeaPad Y50 4K Asus ZenBook UX303LN 4K Asus ZenBook Pro UX501JW LG UH7500/6500/6100 LG ThinQ G7/G7+ Oculus Quest 1 == Controversy == An ongoing controversy regarding the definition or measurement of resolution of color subpixelated flat panel displays led many people to question the resolution claims of PenTile display products. Journalists have noted that in "just about every flat-panel TV in existence, each pixel is composed of one red, one green, and one blue subpixel (RGB), all of uniform size". In traditional flat-panel screens, the resolution is defined by the number of red, green, and blue subpixels, in groups of three, in an array in each axis. As a result, each pixel or group of subpixels can render any colour on the screen, regardless of neighbouring pixels. This is not the case with PenTile screens. The Video Electronics Standards Association (VESA) method of measuring and defining resolution in color displays is to measure the contrast of line pairs, requiring a minimum of 50% Michelson contrast for displays intended for rendering text. The developers of PenTile displays use this VESA criterion for contrast of line pairs to calculate the resolutions specified. In the RGBG layout the alternate red and blue subpixels are 'shared' or sub-sampled with neighboring pixels. Due to the one third lower subpixel density on PenTile displays the pixel structure may be more visible when compared to RGB stripe displays with the same pixel density. The loss of subpixels for a given resolution specification has led some journalists to describe the use of PenTile as "shady practice" and "sort of cheating". For a given size and resolution specification, the PenTile screen can appear grainy, pixelated, speckled, with blurred text on some saturated colors and backgrounds when compared to RGB stripe color. This effect is understood to be caused by the restriction of the number of subpixels that may participate in the image reconstruction when colors are highly saturated to primaries. In the RGBW case, this is caused as the W subpixel will not be available in order to maintain the saturated color. In the RGBG case, this effect will occur when the color boundary is primarily red or blue, as the fully populated (one green per pixel) sub-pixel cannot contribute. For all other cases, text and especially full color images are effectively reconstructed. == Advantages and disadvantages == The PenTile layout reduces the number of subpixels needed to create a specified resolution. Consequently it is possible to achieve an HD resolution on a PenTile AMOLED screen at lower cost than other technologies, and most reviewers note that "300 ppi" (as per VESA - not full pixels) resolution displays (such as Samsung Galaxy S III) make the PenTile effect less obvious than lower resolution PenTile displays (Droid Razr). The second advantage is lower power consumption: the HTC One S's use of a PenTile display makes it more energy efficient and thinner than equivalent LCD screens, giving it better battery life than the HTC One X's IPS LCD. A PenTile AMOLED screen is also
Geometric hashing
In computer science, geometric hashing is a method for efficiently finding two-dimensional objects represented by discrete points that have undergone an affine transformation, though extensions exist to other object representations and transformations. In an off-line step, the objects are encoded by treating each pair of points as a geometric basis. The remaining points can be represented in an invariant fashion with respect to this basis using two parameters. For each point, its quantized transformed coordinates are stored in the hash table as a key, and indices of the basis points as a value. Then a new pair of basis points is selected, and the process is repeated. In the on-line (recognition) step, randomly selected pairs of data points are considered as candidate bases. For each candidate basis, the remaining data points are encoded according to the basis and possible correspondences from the object are found in the previously constructed table. The candidate basis is accepted if a sufficiently large number of the data points index a consistent object basis. Geometric hashing was originally suggested in computer vision for object recognition in 2D and 3D, but later was applied to different problems such as structural alignment of proteins. == Geometric hashing in computer vision == Geometric hashing is a method used for object recognition. Let’s say that we want to check if a model image can be seen in an input image. This can be accomplished with geometric hashing. The method could be used to recognize one of the multiple objects in a base, in this case the hash table should store not only the pose information but also the index of object model in the base. === Example === For simplicity, this example will not use too many point features and assume that their descriptors are given by their coordinates only (in practice local descriptors such as SIFT could be used for indexing). ==== Training Phase ==== Find the model's feature points. Assume that 5 feature points are found in the model image with the coordinates ( 12 , 17 ) ; {\displaystyle (12,17);} ( 45 , 13 ) ; {\displaystyle (45,13);} ( 40 , 46 ) ; {\displaystyle (40,46);} ( 20 , 35 ) ; {\displaystyle (20,35);} ( 35 , 25 ) {\displaystyle (35,25)} , see the picture. Introduce a basis to describe the locations of the feature points. For 2D space and similarity transformation the basis is defined by a pair of points. The point of origin is placed in the middle of the segment connecting the two points (P2, P4 in our example), the x ′ {\displaystyle x'} axis is directed towards one of them, the y ′ {\displaystyle y'} is orthogonal and goes through the origin. The scale is selected such that absolute value of x ′ {\displaystyle x'} for both basis points is 1. Describe feature locations with respect to that basis, i.e. compute the projections to the new coordinate axes. The coordinates should be discretised to make recognition robust to noise, we take the bin size 0.25. We thus get the coordinates ( − 0.75 , − 1.25 ) ; {\displaystyle (-0.75,-1.25);} ( 1.00 , 0.00 ) ; {\displaystyle (1.00,0.00);} ( − 0.50 , 1.25 ) ; {\displaystyle (-0.50,1.25);} ( − 1.00 , 0.00 ) ; {\displaystyle (-1.00,0.00);} ( 0.00 , 0.25 ) {\displaystyle (0.00,0.25)} Store the basis in a hash table indexed by the features (only transformed coordinates in this case). If there were more objects to match with, we should also store the object number along with the basis pair. Repeat the process for a different basis pair (Step 2). It is needed to handle occlusions. Ideally, all the non-colinear pairs should be enumerated. We provide the hash table after two iterations, the pair (P1, P3) is selected for the second one. Hash Table: Most hash tables cannot have identical keys mapped to different values. So in real life one won’t encode basis keys (1.0, 0.0) and (-1.0, 0.0) in a hash table. ==== Recognition Phase ==== Find interesting feature points in the input image. Choose an arbitrary basis. If there isn't a suitable arbitrary basis, then it is likely that the input image does not contain the target object. Describe coordinates of the feature points in the new basis. Quantize obtained coordinates as it was done before. Compare all the transformed point features in the input image with the hash table. If the point features are identical or similar, then increase the count for the corresponding basis (and the type of object, if any). For each basis such that the count exceeds a certain threshold, verify the hypothesis that it corresponds to an image basis chosen in Step 2. Transfer the image coordinate system to the model one (for the supposed object) and try to match them. If successful, the object is found. Otherwise, go back to Step 2. === Finding mirrored pattern === It seems that this method is only capable of handling scaling, translation, and rotation. However, the input image may contain the object in mirror transform. Therefore, geometric hashing should be able to find the object, too. There are two ways to detect mirrored objects. For the vector graph, make the left side positive, and the right side negative. Multiplying the x position by -1 will give the same result. Use 3 points for the basis. This allows detecting mirror images (or objects). Actually, using 3 points for the basis is another approach for geometric hashing. === Geometric hashing in higher-dimensions === Similar to the example above, hashing applies to higher-dimensional data. For three-dimensional data points, three points are also needed for the basis. The first two points define the x-axis, and the third point defines the y-axis (with the first point). The z-axis is perpendicular to the created axis using the right-hand rule. Notice that the order of the points affects the resulting basis