Comparing the best AI art generator? An AI art generator is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI art generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
Lenny (chatbot)
Lenny is a chatbot designed to scam bait telemarketers, scammers, and other unwanted incoming calls using messages. == Background == Telemarketers may be perceived by some as annoying and wasting people's time, and some deliberately attempt to scam or defraud people. In April 2018, stats published by YouMail estimated the United States received over three billion robocalls that month. Attempts to block the callers have been hindered by Caller ID spoofing. == Features == The bot was written in 2011, and development taken over by an Alberta-based programmer known as "Mango" two years later. It is driven by sixteen pre-recorded audio clips, spoken in a soft and slow Australian accent in the manner of an elderly man. The bot's original creator stated on Reddit that in building the character he asked himself the question "What would be a telemarketer's worst nightmare?" He answered with this being a lonely old man who is up for a chat, proud of his family and can't focus on the telemarketer's goal. There is no speech recognition or artificial intelligence, and the bot's software is simple and straightforward. The first four clips are played sequentially in order to grab the telemarketer's interest and begin their sales pitch to Lenny, then the remaining twelve are played sequentially on loop until the telemarketer hangs up. The program waits for a gap of 1.5 seconds of silence before playing the next audio clip, to simulate natural breaks in the conversation. The messages are purposefully vague and open-ended so they can be applied to as many conversations as possible. They include references to Lenny's children, the state of the economy, and being interrupted by some ducks outside. According to research into the bot, around 75% of callers realise they are talking to a computer program within two minutes; however, some calls have lasted around an hour. == Distribution == Though other chatbots had been developed earlier, Lenny was the first one to be released for free on a public server and could be accessed by anyone. Recordings of conversations with the bot are widely shared online on websites such as Reddit and YouTube. Though "Mango" only intended Lenny to be used against dishonest telemarketers, such as scammers, he does not mind it being used against callers who are merely annoying. The bot has also been used against political campaigners, such as a supporter of Pierre Poilievre in the 2015 Canadian federal election.
Desktop video
Desktop video refers to a phenomenon lasting from the mid-1980s to the early 1990s when the graphics capabilities of personal computers such as the Amiga, Macintosh II, and specially-upgraded IBM PC compatibles had advanced to the point where individuals and local broadcasters could use them for analog non-linear editing and vision mixing in video production. Despite the use of computers, desktop video should not be confused with digital video since the video data remained analog, and it uses items like a VCR and a camcorder to record the video. Full-screen, full-motion video's vast storage requirements meant that the promise of digital encoding would not be realized on desktop computers for at least another decade. == Description == There were multiple models of genlock cards available to synchronize the content; the Newtek Video Toaster was commonly used in Amiga in countries that used NTSC (PAL-M in Brazil), while PCs had Truevision and Matrox Illuminator cards and Mac systems had the SuperMac Video Spigot and Radius VideoVision cards. Apple later introduced the Macintosh Quadra 840AV and Centris 660AV systems to specifically address this market. Desktop video was a parallel development to desktop publishing and enabled many small production houses and local TV stations to produce their own original content for the first time. Along with the advent of public-access cable channels, desktop video meant that television advertising became affordable for local businesses such as retailers, restaurants, real estate agents, contractors and auto dealers. As with the phrase desktop publishing, use of the term died out as the technologies to which it referred become the norm for any kind of video production.
Companion robot
A companion robot is a robot created to create real or apparent companionship for human beings. Target markets for companion robots include the elderly and single children. Companions robots are expected to communicate with non-experts in a natural and intuitive way. They offer a variety of functions, such as monitoring the home remotely, communicating with people, or waking people up in the morning. Their aim is to perform a wide array of tasks including educational functions, home security, diary duties, entertainment and message delivery services, etc. The idea of companionship with robots has already existed on science fictions of 1970s, like R2-D2. Starting from the late 20th century, companion robots became a reality, mostly as robotic pets. Besides entertainment purposes, interactive robots were also introduced as a personal service robot for elderly care around 2000. == Characteristics == Companion robots try to interact with users. They gather information about users based on their interactions and yield feedback. This procedure varies slightly based on their specific roles. For example, social-companion robots make simple conversations, while pet-companion robots mimic being real pets. == Types == Companion robots can perform a variety of tasks and they are produced in a specialized manner according to their purpose or target audience in order to increase convenience and end user satisfaction. === Social companion robots === Social companion robots are designed to provide companionship and be a solution for unwanted solitude. They often mimic adult human, child or pet behaviours appealing to the user base. Robots which are specifically devised for simple conversations, conveying emotions and respond to user feelings fall under this category. === Assistive companion robots === Assistive companion robots are aimed at people who require constant care because of age, disability or rehabilitation purposes. Such robots can help disadvantaged users with their daily tasks, act as reminders (e.g., for regular medication) and facilitate mobility in everyday actions. Assistive companion robots reduce the intensity of labour that should be performed by caretakers, nurses and legal guardians. === Educational companion robots === Educational companion robots perform tutorship for students, regardless of their ages, and can teach desired subjects with activities tailored for the user such as interactive assignments and games. Rather than replacing teachers and instructors, educational companion robots are aides to them. === Therapeutic companion robots === Designed for individuals coping with stress (PTSD in severe cases), anxiety and loneliness; therapeutic companion robots support users' emotional and mental wellbeing. Such robots can be utilized in hospitals and care facilities as well as dwellings where the distressed user may need the most help. Therapeutic companion robots bear a vast resemblance to assistive companion robots to the extent of being a branch of them; the nuance between these two types of companion robots is that the former is for long-term/lifetime usage while the latter is mostly for the duration of the therapy received by the user. === Pet companion robots === Pet companion robots are for individuals who seek an alternative to live pets as live animals demand a considerable amount of care and may not be eligible for people with allergies. These robots aim to be perfect imitations of a pet while diminishing the chore aspect of having one. === Entertainment companion robots === Entertainment companion robots are designed solely for entertainment and can provide numerous ways of entertainment, ranging from dancing to playing games with the user. People who would appreciate an individual to have fun with are the main audience of such products. === Personal assistant robots === Personal assistant robots help people with daily tasks, management, scheduling, reminding etc. Their area of activity can be offices as well as homes and public spaces. === Sex robots === Sex robots are anthropomorphic robotic sex dolls that have human-like movement or behavior, and some degree of artificial intelligence. As of 2026, although elaborately instrumented sex dolls have been created by a number of inventors, no fully animated sex robots yet exist. Simple devices have been created which can speak, make facial expressions, or respond to touch. There is controversy as to whether developing them would be morally justifiable. In 2015, robot ethicist Kathleen Richardson called for a ban on the creation of anthropomorphic sex robots with concerns about normalizing relationships with machines and reinforcing female dehumanization. Questions about their ethics, effects, and possible legal regulations have been discussed since then. == Examples == There are several companion robot prototypes, and these include Paro, CompanionAble, and EmotiRob, among others. === Paro === Paro is a pet-type robot system developed by Japan's National Institute of Advanced Industrial Science and Technology (AIST). The robot, which looked like a small harp seal, was designed as a therapeutic tool for use in hospitals and nursing homes. The robot is programmed to cry for attention and respond to its name. Experiments showed that Paro facilitated elderly residents to communicate with each other, which led to psychological improvements. === CompanionAble === This robot is classified as an FP 7 EU project. It is built to "cooperate with Ambient Assistive Living environment". The autonomous device, which is also built to support the elderly, helps its owner interact with smart home environment as well as caregivers. The robot functions as a mobile friend, by which natural interaction is possible via speech and the touchscreen to detect and track people at home. === EmotiRob === EmotiRob is developed in a robotics project which is the continuity of the MAPH (Active Media For the Handicap) project in emotion synthesis. The aim of the project was to maintain emotional interaction with children. EmotiRob designed in a way that a child can hold it in a his/her arms and with which he/she could interact by talking to it, and then the robot would express itself through body postures or facial expressions. It has cognitive capabilities, which are further extended so that the robot can have a natural linguistic interaction with its owner through the DRAGON speech-recognition software developed by a company called NUANCE. Such interaction is expected to facilitate a child's cognitive development and develop new learning patterns. === LOVOT === Lovot is a Japanese company robot whose only purpose is "to make you happy". It features over 50 sensors that mimic the behavior of a human baby or small pet, a 360° camera with a microphone, the ability to distinguish humans from objects, neoteny eyes, and an internal warmth of 30° celsius. An interactive Lovot Café was opened in Japan October 3, 2020. === NICOBO === Nicobo was developed by Panasonic and was influenced by the loneliness of lockdowns created as a measure of the COVID-19 pandemic. It was designed to appear vulnerable, which creates empathy in its owners. Nicobo's name derives from the Japanese word for "smile". It wags its tail, engages in baby talk, and stays as a housemate. === Hyodol === Hyodol is an advanced care robot designed to support the elderly by reminding them to take their medications and monitoring their movements to keep their guardians informed. Additionally, this innovative robot can detect and respond to the emotional states of its elderly users, adding a layer of personalized care. Hyodol is designed with the appearance and speech style of a 7-year-old Korean grandchild, featuring a soft fabric exterior and user interaction methods such as striking the head or patting the back. It is equipped with various sensors and wireless communication technologies to collect and process data, supporting mobile apps and PC web monitoring systems for remote monitoring from anywhere. In South Korea, approximately 10,000 Hyodol robots are deployed to the homes of elderly individuals living alone, providing essential support and companionship. Local governments, including provincial and county offices, have embraced Hyodol as a solution to address social challenges stemming from the country's rapidly aging society.Furthermore, the robot is widely utilized in the treatment of dementia patients at a university hospital in Gangwon province. Hyodol was honored with the Mobile World Congress (MWC) Global Mobile Awards (GLOMO) in the "Best Mobile Innovation for Connected Health and Wellbeing" category on February 29, 2024. === Moxie === Moxie was a companion robot for autistic children developed by a company called Embodied. Although it had limited motion, it presented itself as a lifelike avatar. It was designed to help the children learn emotional cognition, using remotely hosted large language models to direct its respons
Shearlet
In applied mathematical analysis, shearlets are a multiscale framework which allows efficient encoding of anisotropic features in multivariate problem classes. Originally, shearlets were introduced in 2006 for the analysis and sparse approximation of functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . They are a natural extension of wavelets, to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images, since wavelets, as isotropic objects, are not capable of capturing such phenomena. Shearlets are constructed by parabolic scaling, shearing, and translation applied to a few generating functions. At fine scales, they are essentially supported within skinny and directional ridges following the parabolic scaling law, which reads length² ≈ width. Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations. Although they do not constitute an orthonormal basis for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} , they still form a frame allowing stable expansions of arbitrary functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . One of the most important properties of shearlets is their ability to provide optimally sparse approximations (in the sense of optimality in ) for cartoon-like functions f {\displaystyle f} . In imaging sciences, cartoon-like functions serve as a model for anisotropic features and are compactly supported in [ 0 , 1 ] 2 {\displaystyle [0,1]^{2}} while being C 2 {\displaystyle C^{2}} apart from a closed piecewise C 2 {\displaystyle C^{2}} singularity curve with bounded curvature. The decay rate of the L 2 {\displaystyle L^{2}} -error of the N {\displaystyle N} -term shearlet approximation obtained by taking the N {\displaystyle N} largest coefficients from the shearlet expansion is in fact optimal up to a log-factor: ‖ f − f N ‖ L 2 2 ≤ C N − 2 ( log N ) 3 , N → ∞ , {\displaystyle \|f-f_{N}\|_{L^{2}}^{2}\leq CN^{-2}(\log N)^{3},\quad N\to \infty ,} where the constant C {\displaystyle C} depends only on the maximum curvature of the singularity curve and the maximum magnitudes of f {\displaystyle f} , f ′ {\displaystyle f'} and f ″ . {\displaystyle f''.} This approximation rate significantly improves the best N {\displaystyle N} -term approximation rate of wavelets providing only O ( N − 1 ) {\displaystyle O(N^{-1})} for such class of functions. Shearlets are to date the only directional representation system that provides sparse approximation of anisotropic features while providing a unified treatment of the continuum and digital realm that allows faithful implementation. Extensions of shearlet systems to L 2 ( R d ) , d ≥ 2 {\displaystyle L^{2}(\mathbb {R} ^{d}),d\geq 2} are also available. A comprehensive presentation of the theory and applications of shearlets can be found in. == Definition == === Continuous shearlet systems === The construction of continuous shearlet systems is based on parabolic scaling matrices A a = [ a 0 0 a 1 / 2 ] , a > 0 {\displaystyle A_{a}={\begin{bmatrix}a&0\\0&a^{1/2}\end{bmatrix}},\quad a>0} as a means to change the resolution, on shear matrices S s = [ 1 s 0 1 ] , s ∈ R {\displaystyle S_{s}={\begin{bmatrix}1&s\\0&1\end{bmatrix}},\quad s\in \mathbb {R} } as a means to change the orientation, and finally on translations to change the positioning. In comparison to curvelets, shearlets use shearings instead of rotations, the advantage being that the shear operator S s {\displaystyle S_{s}} leaves the integer lattice invariant in case s ∈ Z {\displaystyle s\in \mathbb {Z} } , i.e., S s Z 2 ⊆ Z 2 . {\displaystyle S_{s}\mathbb {Z} ^{2}\subseteq \mathbb {Z} ^{2}.} This indeed allows a unified treatment of the continuum and digital realm, thereby guaranteeing a faithful digital implementation. For ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} the continuous shearlet system generated by ψ {\displaystyle \psi } is then defined as SH c o n t ( ψ ) = { ψ a , s , t = a 3 / 4 ψ ( S s A a ( ⋅ − t ) ) ∣ a > 0 , s ∈ R , t ∈ R 2 } , {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )=\{\psi _{a,s,t}=a^{3/4}\psi (S_{s}A_{a}(\cdot -t))\mid a>0,s\in \mathbb {R} ,t\in \mathbb {R} ^{2}\},} and the corresponding continuous shearlet transform is given by the map f ↦ S H ψ f ( a , s , t ) = ⟨ f , ψ a , s , t ⟩ , f ∈ L 2 ( R 2 ) , ( a , s , t ) ∈ R > 0 × R × R 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(a,s,t)=\langle f,\psi _{a,s,t}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (a,s,t)\in \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} === Discrete shearlet systems === A discrete version of shearlet systems can be directly obtained from SH c o n t ( ψ ) {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )} by discretizing the parameter set R > 0 × R × R 2 . {\displaystyle \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} There are numerous approaches for this but the most popular one is given by { ( 2 j , k , A 2 j − 1 S k − 1 m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } ⊆ R > 0 × R × R 2 . {\displaystyle \{(2^{j},k,A_{2^{j}}^{-1}S_{k}^{-1}m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\}\subseteq \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} From this, the discrete shearlet system associated with the shearlet generator ψ {\displaystyle \psi } is defined by SH ( ψ ) = { ψ j , k , m = 2 3 j / 4 ψ ( S k A 2 j ⋅ − m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } , {\displaystyle \operatorname {SH} (\psi )=\{\psi _{j,k,m}=2^{3j/4}\psi (S_{k}A_{2^{j}}\cdot {}-m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\},} and the associated discrete shearlet transform is defined by f ↦ S H ψ f ( j , k , m ) = ⟨ f , ψ j , k , m ⟩ , f ∈ L 2 ( R 2 ) , ( j , k , m ) ∈ Z × Z × Z 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(j,k,m)=\langle f,\psi _{j,k,m}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (j,k,m)\in \mathbb {Z} \times \mathbb {Z} \times \mathbb {Z} ^{2}.} == Examples == Let ψ 1 ∈ L 2 ( R ) {\displaystyle \psi _{1}\in L^{2}(\mathbb {R} )} be a function satisfying the discrete Calderón condition, i.e., ∑ j ∈ Z | ψ ^ 1 ( 2 − j ξ ) | 2 = 1 , for a.e. ξ ∈ R , {\displaystyle \sum _{j\in \mathbb {Z} }|{\hat {\psi }}_{1}(2^{-j}\xi )|^{2}=1,{\text{for a.e. }}\xi \in \mathbb {R} ,} with ψ ^ 1 ∈ C ∞ ( R ) {\displaystyle {\hat {\psi }}_{1}\in C^{\infty }(\mathbb {R} )} and supp ψ ^ 1 ⊆ [ − 1 2 , − 1 16 ] ∪ [ 1 16 , 1 2 ] , {\displaystyle \operatorname {supp} {\hat {\psi }}_{1}\subseteq [-{\tfrac {1}{2}},-{\tfrac {1}{16}}]\cup [{\tfrac {1}{16}},{\tfrac {1}{2}}],} where ψ ^ 1 {\displaystyle {\hat {\psi }}_{1}} denotes the Fourier transform of ψ 1 . {\displaystyle \psi _{1}.} For instance, one can choose ψ 1 {\displaystyle \psi _{1}} to be a Meyer wavelet. Furthermore, let ψ 2 ∈ L 2 ( R ) {\displaystyle \psi _{2}\in L^{2}(\mathbb {R} )} be such that ψ ^ 2 ∈ C ∞ ( R ) , {\displaystyle {\hat {\psi }}_{2}\in C^{\infty }(\mathbb {R} ),} supp ψ ^ 2 ⊆ [ − 1 , 1 ] {\displaystyle \operatorname {supp} {\hat {\psi }}_{2}\subseteq [-1,1]} and ∑ k = − 1 1 | ψ ^ 2 ( ξ + k ) | 2 = 1 , for a.e. ξ ∈ [ − 1 , 1 ] . {\displaystyle \sum _{k=-1}^{1}|{\hat {\psi }}_{2}(\xi +k)|^{2}=1,{\text{for a.e. }}\xi \in \left[-1,1\right].} One typically chooses ψ ^ 2 {\displaystyle {\hat {\psi }}_{2}} to be a smooth bump function. Then ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} given by ψ ^ ( ξ ) = ψ ^ 1 ( ξ 1 ) ψ ^ 2 ( ξ 2 ξ 1 ) , ξ = ( ξ 1 , ξ 2 ) ∈ R 2 , {\displaystyle {\hat {\psi }}(\xi )={\hat {\psi }}_{1}(\xi _{1}){\hat {\psi }}_{2}\left({\tfrac {\xi _{2}}{\xi _{1}}}\right),\quad \xi =(\xi _{1},\xi _{2})\in \mathbb {R} ^{2},} is called a classical shearlet. It can be shown that the corresponding discrete shearlet system SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} constitutes a Parseval frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} consisting of bandlimited functions. Another example are compactly supported shearlet systems, where a compactly supported function ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} can be chosen so that SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} forms a frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} . In this case, all shearlet elements in SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} are compactly supported providing superior spatial localization compared to the classical shearlets, which are bandlimited. Although a compactly supported shearlet system does not generally form a Parseval frame, any function f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} can be represented by the shearlet expansion due to its frame property. == Cone-adapted shearlets == One drawback of shearlets defined as above is the directional bias of shearlet elements associated with large shearing parameters. This effect is already r
Digital image correlation and tracking
Digital image correlation and tracking is an optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements of changes in 2D images or 3D volumes. This method is often used to measure full-field displacement and strains, and it is widely applied in many areas of science and engineering. Compared to strain gauges and extensometers, digital image correlation methods provide finer details about deformation, due to the ability to provide both local and average data. == Overview == Digital image correlation (DIC) techniques have been increasing in popularity, especially in micro- and nano-scale mechanical testing applications due to their relative ease of implementation and use. Advances in computer technology and digital cameras have been the enabling technologies for this method and while white-light optics has been the predominant approach, DIC can be and has been extended to almost any imaging technology. The concept of using cross-correlation to measure shifts in datasets has been known for a long time, and it has been applied to digital images since at least the early 1970s. The present-day applications are almost innumerable, including image analysis, image compression, velocimetry, and strain estimation. Much early work in DIC in the field of mechanics was led by researchers at the University of South Carolina in the early 1980s and has been optimized and improved in recent years. Commonly, DIC relies on finding the maximum of the correlation array between pixel intensity array subsets on two or more corresponding images, which gives the integer translational shift between them. It is also possible to estimate shifts to a finer resolution than the resolution of the original images, which is often called "sub-pixel" registration because the measured shift is smaller than an integer pixel unit. For sub-pixel interpolation of the shift, other methods do not simply maximize the correlation coefficient. An iterative approach can also be used to maximize the interpolated correlation coefficient by using non-linear optimization techniques. The non-linear optimization approach tends to be conceptually simpler and can handle large deformations more accurately, but as with most nonlinear optimization techniques, it is slower. The two-dimensional discrete cross correlation r i j {\displaystyle r_{ij}} can be defined in several ways, one possibility being: r i j = ∑ m ∑ n [ f ( m + i , n + j ) − f ¯ ] [ g ( m , n ) − g ¯ ] ∑ m ∑ n [ f ( m , n ) − f ¯ ] 2 ∑ m ∑ n [ g ( m , n ) − g ¯ ] 2 . {\displaystyle r_{ij}={\frac {\sum _{m}\sum _{n}[f(m+i,n+j)-{\bar {f}}][g(m,n)-{\bar {g}}]}{\sqrt {\sum _{m}\sum _{n}{[f(m,n)-{\bar {f}}]^{2}}\sum _{m}\sum _{n}{[g(m,n)-{\bar {g}}]^{2}}}}}.} Here f(m, n) is the pixel intensity or the gray-scale value at a point (m, n) in the original image, g(m, n) is the gray-scale value at a point (m, n) in the translated image, f ¯ {\displaystyle {\bar {f}}} and g ¯ {\displaystyle {\bar {g}}} are mean values of the intensity matrices f and g respectively. However, in practical applications, the correlation array is usually computed using Fourier-transform methods, since the fast Fourier transform is a much faster method than directly computing the correlation. F = F { f } , G = F { g } . {\displaystyle \mathbf {F} ={\mathcal {F}}\{f\},\quad \mathbf {G} ={\mathcal {F}}\{g\}.} Then taking the complex conjugate of the second result and multiplying the Fourier transforms together elementwise, we obtain the Fourier transform of the correlogram, R {\displaystyle \ R} : R = F ∘ G ∗ , {\displaystyle R=\mathbf {F} \circ \mathbf {G} ^{},} where ∘ {\displaystyle \circ } is the Hadamard product (entry-wise product). It is also fairly common to normalize the magnitudes to unity at this point, which results in a variation called phase correlation. Then the cross-correlation is obtained by applying the inverse Fourier transform: r = F − 1 { R } . {\displaystyle \ r={\mathcal {F}}^{-1}\{R\}.} At this point, the coordinates of the maximum of r i j {\displaystyle r_{ij}} give the integer shift: ( Δ x , Δ y ) = arg max ( i , j ) { r } . {\displaystyle (\Delta x,\Delta y)=\arg \max _{(i,j)}\{r\}.} == Deformation mapping == For deformation mapping, the mapping function that relates the images can be derived from comparing a set of subwindow pairs over the whole images. (Figure 1). The coordinates or grid points (xi, yj) and (xi, yj) are related by the translations that occur between the two images. If the deformation is small and perpendicular to the optical axis of the camera, then the relation between (xi, yj) and (xi, yj) can be approximated by a 2D affine transformation such as: x ∗ = x + u + ∂ u ∂ x Δ x + ∂ u ∂ y Δ y , {\displaystyle x^{}=x+u+{\frac {\partial u}{\partial x}}\Delta x+{\frac {\partial u}{\partial y}}\Delta y,} y ∗ = y + v + ∂ v ∂ x Δ x + ∂ v ∂ y Δ y . {\displaystyle y^{}=y+v+{\frac {\partial v}{\partial x}}\Delta x+{\frac {\partial v}{\partial y}}\Delta y.} Here u and v are translations of the center of the sub-image in the X and Y directions respectively. The distances from the center of the sub-image to the point (x, y) are denoted by Δ x {\displaystyle \Delta x} and Δ y {\displaystyle \Delta y} . Thus, the correlation coefficient rij is a function of displacement components (u, v) and displacement gradients ∂ u ∂ x , ∂ u ∂ y , ∂ v ∂ x , ∂ v ∂ y . {\displaystyle {\frac {\partial u}{\partial x}},{\frac {\partial u}{\partial y}},{\frac {\partial v}{\partial x}},{\frac {\partial v}{\partial y}}.} DIC has proven to be very effective at mapping deformation in macroscopic mechanical testing, where the application of specular markers (e.g. paint, toner powder) or surface finishes from machining and polishing provide the needed contrast to correlate images well. However, these methods for applying surface contrast do not extend to the application of free-standing thin films for several reasons. First, vapor deposition at normal temperatures on semiconductor grade substrates results in mirror-finish quality films with RMS roughnesses that are typically on the order of several nanometers. No subsequent polishing or finishing steps are required, and unless electron imaging techniques are employed that can resolve microstructural features, the films do not possess enough useful surface contrast to adequately correlate images. Typically this challenge can be circumvented by applying paint that results in a random speckle pattern on the surface, although the large and turbulent forces resulting from either spraying or applying paint to the surface of a free-standing thin film are too high and would break the specimens. In addition, the sizes of individual paint particles are on the order of μms, while the film thickness is only several hundred nanometers, which would be analogous to supporting a large boulder on a thin sheet of paper. == Digital volume correlation == Digital Volume Correlation (DVC, and sometimes called Volumetric-DIC) extends the 2D-DIC algorithms into three dimensions to calculate the full-field 3D deformation from a pair of 3D images. This technique is distinct from 3D-DIC, which only calculates the 3D deformation of an exterior surface using conventional optical images. The DVC algorithm is able to track full-field displacement information in the form of voxels instead of pixels. The theory is similar to above except that another dimension is added: the z-dimension. The displacement is calculated from the correlation of 3D subsets of the reference and deformed volumetric images, which is analogous to the correlation of 2D subsets described above. DVC can be performed using volumetric image datasets. These images can be obtained using confocal microscopy, X-ray computed tomography, Magnetic Resonance Imaging or other techniques. Similar to the other DIC techniques, the images must exhibit a distinct, high-contrast 3D "speckle pattern" to ensure accurate displacement measurement. DVC was first developed in 1999 to study the deformation of trabecular bone using X-ray computed tomography images. Since then, applications of DVC have grown to include granular materials, metals, foams, composites and biological materials. To date it has been used with images acquired by MRI imaging, Computer Tomography (CT), micro-CT, confocal microscopy, and lightsheet microscopy. DVC is currently considered to be ideal in the research world for 3D quantification of local displacements, strains, and stress in biological specimens. It is preferred because of the non-invasiveness of the method over traditional experimental methods. Two of the key challenges are improving the speed and reliability of the DVC measurement. The 3D imaging techniques produce noisier images than conventional 2D optical images, which reduces the quality of the displacement measurement. Computational speed is restricted by the file sizes of 3D images, which are significantly larger than 2D images. For example, an
VGACAD
VGACAD was the parent of a suite of shareware graphic utilities made for the MS-DOS operating system used in the IBM PC and clones. It was popular for editing and capturing images using BSAVE (graphics image format) and provided an early graphic editing suite compatible with multiple graphic cards and resolutions, used on the IBM PC. == Usage == Written by Lawrence Gozum in 1987, it was the genesis of multiple versions and improvements over 10 years. Ran with his brother, Marvin initially helped with design ideas, strategic focus, technical support calls, and managing the early shareware business. The growth of the VGACAD suite grew quickly to preoccupy most of their time. Lawrence then focused more of his efforts on software and formed Applied Insights, to manage VGACAD and its offspring, VidFun, and Ai Picture Explorer. At its peak, its users ranged from individuals, Federal government offices, museums and major newspapers. == Features == VGACAD was a misnomer, and meant VGA-Computer Assisted Drawing, rather than computer-aided design, as CAD is commonly referred to today. Its longevity was due to its color accuracy, speed, small size, and that its suite of small utilities often worked stand-alone. One called VGACAP, for 'capture', dumped video memory into a file that could later be converted to popular graphic image formats, later made commonplace when Microsoft Windows programmed the print screen key to dump graphics into the clipboard. However, VGACAP ran insulated apart from early versions of Windows, and thus could capture screens were applications prohibited such function.