Rendering equation

In computer graphics, the rendering equation is an integral equation that expresses the amount of light leaving a point on a surface as the sum of emitted light and reflected light. It was independently introduced into computer graphics by David Immel et al. and James Kajiya in 1986. The equation is important in the theory of physically based rendering, describing the relationships between the bidirectional reflectance distribution function (BRDF) and the radiometric quantities used in rendering. The rendering equation is defined at every point on every surface in the scene being rendered, including points hidden from the camera. The incoming light quantities on the right side of the equation usually come from the left (outgoing) side at other points in the scene (ray casting can be used to find these other points). The radiosity rendering method solves a discrete approximation of this system of equations. In distributed ray tracing, the integral on the right side of the equation may be evaluated using Monte Carlo integration by randomly sampling possible incoming light directions. Path tracing improves and simplifies this method. The rendering equation can be extended to handle effects such as fluorescence (in which some absorbed energy is re-emitted at different wavelengths) and can support transparent and translucent materials by using a bidirectional scattering distribution function (BSDF) in place of a BRDF. The theory of path tracing sometimes uses a path integral (integral over possible paths from a light source to a point) instead of the integral over possible incoming directions. == Equation form == The rendering equation may be written in the form L o ( x , ω o , λ , t ) = L e ( x , ω o , λ , t ) + L r ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)+L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} L r ( x , ω o , λ , t ) = ∫ Ω f r ( x , ω i , ω o , λ , t ) L i ( x , ω i , λ , t ) ( ω i ⋅ n ) d ⁡ ω i {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=\int _{\Omega }f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)(\omega _{\text{i}}\cdot \mathbf {n} )\operatorname {d} \omega _{\text{i}}} where L o ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is the total spectral radiance of wavelength λ {\displaystyle \lambda } directed outward along direction ω o {\displaystyle \omega _{\text{o}}} at time t {\displaystyle t} , from a particular position x {\displaystyle \mathbf {x} } x {\displaystyle \mathbf {x} } is the location in space ω o {\displaystyle \omega _{\text{o}}} is the direction of the outgoing light λ {\displaystyle \lambda } is a particular wavelength of light t {\displaystyle t} is time L e ( x , ω o , λ , t ) {\displaystyle L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is emitted spectral radiance L r ( x , ω o , λ , t ) {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is reflected spectral radiance ∫ Ω … d ⁡ ω i {\displaystyle \int _{\Omega }\dots \operatorname {d} \omega _{\text{i}}} is an integral over Ω {\displaystyle \Omega } Ω {\displaystyle \Omega } is the unit hemisphere centered around n {\displaystyle \mathbf {n} } containing all possible values for ω i {\displaystyle \omega _{\text{i}}} where ω i ⋅ n > 0 {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} >0} f r ( x , ω i , ω o , λ , t ) {\displaystyle f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)} is the bidirectional reflectance distribution function, the proportion of light reflected from ω i {\displaystyle \omega _{\text{i}}} to ω o {\displaystyle \omega _{\text{o}}} at position x {\displaystyle \mathbf {x} } , time t {\displaystyle t} , and at wavelength λ {\displaystyle \lambda } ω i {\displaystyle \omega _{\text{i}}} is the negative direction of the incoming light L i ( x , ω i , λ , t ) {\displaystyle L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)} is spectral radiance of wavelength λ {\displaystyle \lambda } coming inward toward x {\displaystyle \mathbf {x} } from direction ω i {\displaystyle \omega _{\text{i}}} at time t {\displaystyle t} n {\displaystyle \mathbf {n} } is the surface normal at x {\displaystyle \mathbf {x} } ω i ⋅ n {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} } is the weakening factor of outward irradiance due to incident angle, as the light flux is smeared across a surface whose area is larger than the projected area perpendicular to the ray. This is often written as cos ⁡ θ i {\displaystyle \cos \theta _{i}} . Two noteworthy features are: its linearity—it is composed only of multiplications and additions, and its spatial homogeneity—it is the same in all positions and orientations. These mean a wide range of factorings and rearrangements of the equation are possible. It is a Fredholm integral equation of the second kind, similar to those that arise in quantum field theory. Note this equation's spectral and time dependence — L o {\displaystyle L_{\text{o}}} may be sampled at or integrated over sections of the visible spectrum to obtain, for example, a trichromatic color sample. A pixel value for a single frame in an animation may be obtained by fixing t ; {\displaystyle t;} motion blur can be produced by averaging L o {\displaystyle L_{\text{o}}} over some given time interval (by integrating over the time interval and dividing by the length of the interval). Note that a solution to the rendering equation is the function L o {\displaystyle L_{\text{o}}} . The function L i {\displaystyle L_{\text{i}}} is related to L o {\displaystyle L_{\text{o}}} via a ray-tracing operation: The incoming radiance from some direction at one point is the outgoing radiance at some other point in the opposite direction. == Applications == Solving the rendering equation for any given scene is the primary challenge in realistic rendering. One approach to solving the equation is based on finite element methods, leading to the radiosity algorithm. Another approach using Monte Carlo methods has led to many different algorithms including path tracing, photon mapping, and Metropolis light transport, among others. == Limitations == Although the equation is very general, it does not capture every aspect of light reflection. Some missing aspects include the following: Transmission, which occurs when light is transmitted through the surface, such as when it hits a glass object or a water surface, Subsurface scattering, where the spatial locations for incoming and departing light are different. Surfaces rendered without accounting for subsurface scattering may appear unnaturally opaque — however, it is not necessary to account for this if transmission is included in the equation, since that will effectively include also light scattered under the surface, Polarization, where different light polarizations will sometimes have different reflection distributions, for example when light bounces at a water surface, Phosphorescence, which occurs when light or other electromagnetic radiation is absorbed at one moment and emitted at a later moment, usually with a longer wavelength (unless the absorbed electromagnetic radiation is very intense), Interference, where the wave properties of light are exhibited, Fluorescence, where the absorbed and emitted light have different wavelengths, Non-linear effects, where very intense light can increase the energy level of an electron with more energy than that of a single photon (this can occur if the electron is hit by two photons at the same time), and emission of light with higher frequency than the frequency of the light that hit the surface suddenly becomes possible, and Doppler effect, where light that bounces off an object moving at a very high speed will get its wavelength changed: if the light bounces off an object that is moving towards it, the light will be blueshifted and the photons will be packed more closely so the photon flux will be increased; if it bounces off an object moving away from it, it will be redshifted and the photon flux will be decreased. This effect becomes apparent only at speeds comparable to the speed of light, which is not the case for most rendering applications. For scenes that are either not composed of simple surfaces in a vacuum or for which the travel time for light is an important factor, researchers have generalized the rendering equation to produce a volume rendering equation suitable for volume rendering and a transient rendering equation for use with data from a time-of-flight camera.

WiPay

WiPay is a Caribbean-based payment technology company that specializes in electronic payments for businesses. WiPay was founded in 2016 by Aldwyn Wayne Jr., a Trinidadian businessman and graduate of Georgia Tech Institute. In September 2019, WiPay partnered with MasterCard. As a result, WiPay became the only licensed Payment Facilitator (PAYFAC) on both the MasterCard and Visa networks in the region.

Evolutionary programming

Evolutionary programming is an evolutionary algorithm, where a share of new population is created by mutation of previous population without crossover. Evolutionary programming differs from evolution strategy ES( μ + λ {\displaystyle \mu +\lambda } ) in one detail. All individuals are selected for the new population, while in ES( μ + λ {\displaystyle \mu +\lambda } ), every individual has the same probability to be selected. It is one of the four major evolutionary algorithm paradigms. == History == It was first used by Lawrence J. Fogel in the US in 1960 in order to use simulated evolution as a learning process aiming to generate artificial intelligence. It was used to evolve finite-state machines as predictors.

Ordinal regression

In statistics, ordinal regression, also called ordinal classification, is a type of regression analysis used for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where only the relative ordering between different values is significant. It can be considered an intermediate problem between regression and classification. Examples of ordinal regression are ordered logit and ordered probit. Ordinal regression turns up often in the social sciences, for example in the modeling of human levels of preference (on a scale from, say, 1–5 for "very poor" through "excellent"), as well as in information retrieval. In machine learning, ordinal regression may also be called ranking learning. == Linear models for ordinal regression == Ordinal regression can be performed using a generalized linear model (GLM) that fits both a coefficient vector and a set of thresholds to a dataset. Suppose one has a set of observations, represented by length-p vectors x1 through xn, with associated responses y1 through yn, where each yi is an ordinal variable on a scale 1, ..., K. For simplicity, and without loss of generality, we assume y is a non-decreasing vector, that is, yi ≤ {\displaystyle \leq } yi+1. To this data, one fits a length-p coefficient vector w and a set of thresholds θ1, ..., θK−1 with the property that θ1 < θ2 < ... < θK−1. This set of thresholds divides the real number line into K disjoint segments, corresponding to the K response levels. The model can now be formulated as Pr ( y ≤ i ∣ x ) = σ ( θ i − w ⋅ x ) {\displaystyle \Pr(y\leq i\mid \mathbf {x} )=\sigma (\theta _{i}-\mathbf {w} \cdot \mathbf {x} )} or, the cumulative probability of the response y being at most i is given by a function σ (the inverse link function) applied to a linear function of x. Several choices exist for σ; the logistic function σ ( θ i − w ⋅ x ) = 1 1 + e − ( θ i − w ⋅ x ) {\displaystyle \sigma (\theta _{i}-\mathbf {w} \cdot \mathbf {x} )={\frac {1}{1+e^{-(\theta _{i}-\mathbf {w} \cdot \mathbf {x} )}}}} gives the ordered logit model, while using the CDF of the standard normal distribution gives the ordered probit model. A third option is to use an exponential function σ ( θ i − w ⋅ x ) = 1 − exp ⁡ ( − exp ⁡ ( θ i − w ⋅ x ) ) {\displaystyle \sigma (\theta _{i}-\mathbf {w} \cdot \mathbf {x} )=1-\exp(-\exp(\theta _{i}-\mathbf {w} \cdot \mathbf {x} ))} which gives the proportional hazards model. === Latent variable model === The probit version of the above model can be justified by assuming the existence of a real-valued latent variable (unobserved quantity) y, determined by y ∗ = w ⋅ x + ε {\displaystyle y^{}=\mathbf {w} \cdot \mathbf {x} +\varepsilon } where ε is normally distributed with zero mean and unit variance, conditioned on x. The response variable y results from an "incomplete measurement" of y, where one only determines the interval into which y falls: y = { 1 if y ∗ ≤ θ 1 , 2 if θ 1 < y ∗ ≤ θ 2 , 3 if θ 2 < y ∗ ≤ θ 3 ⋮ K if θ K − 1 < y ∗ . {\displaystyle y={\begin{cases}1&{\text{if}}~~y^{}\leq \theta _{1},\\2&{\text{if}}~~\theta _{1}

Modes of variation

In statistics, modes of variation are a continuously indexed set of vectors or functions that are centered at a mean and are used to depict the variation in a population or sample. Typically, variation patterns in the data can be decomposed in descending order of eigenvalues with the directions represented by the corresponding eigenvectors or eigenfunctions. Modes of variation provide a visualization of this decomposition and an efficient description of variation around the mean. Both in principal component analysis (PCA) and in functional principal component analysis (FPCA), modes of variation play an important role in visualizing and describing the variation in the data contributed by each eigencomponent. In real-world applications, the eigencomponents and associated modes of variation aid to interpret complex data, especially in exploratory data analysis (EDA). == Formulation == Modes of variation are a natural extension of PCA and FPCA. === Modes of variation in PCA === If a random vector X = ( X 1 , X 2 , ⋯ , X p ) T {\displaystyle \mathbf {X} =(X_{1},X_{2},\cdots ,X_{p})^{T}} has the mean vector μ p {\displaystyle {\boldsymbol {\mu }}_{p}} , and the covariance matrix Σ p × p {\displaystyle \mathbf {\Sigma } _{p\times p}} with eigenvalues λ 1 ≥ λ 2 ≥ ⋯ ≥ λ p ≥ 0 {\displaystyle \lambda _{1}\geq \lambda _{2}\geq \cdots \geq \lambda _{p}\geq 0} and corresponding orthonormal eigenvectors e 1 , e 2 , ⋯ , e p {\displaystyle \mathbf {e} _{1},\mathbf {e} _{2},\cdots ,\mathbf {e} _{p}} , by eigendecomposition of a real symmetric matrix, the covariance matrix Σ {\displaystyle \mathbf {\Sigma } } can be decomposed as Σ = Q Λ Q T , {\displaystyle \mathbf {\Sigma } =\mathbf {Q} \mathbf {\Lambda } \mathbf {Q} ^{T},} where Q {\displaystyle \mathbf {Q} } is an orthogonal matrix whose columns are the eigenvectors of Σ {\displaystyle \mathbf {\Sigma } } , and Λ {\displaystyle \mathbf {\Lambda } } is a diagonal matrix whose entries are the eigenvalues of Σ {\displaystyle \mathbf {\Sigma } } . By the Karhunen–Loève expansion for random vectors, one can express the centered random vector in the eigenbasis X − μ = ∑ k = 1 p ξ k e k , {\displaystyle \mathbf {X} -{\boldsymbol {\mu }}=\sum _{k=1}^{p}\xi _{k}\mathbf {e} _{k},} where ξ k = e k T ( X − μ ) {\displaystyle \xi _{k}=\mathbf {e} _{k}^{T}(\mathbf {X} -{\boldsymbol {\mu }})} is the principal component associated with the k {\displaystyle k} -th eigenvector e k {\displaystyle \mathbf {e} _{k}} , with the properties E ⁡ ( ξ k ) = 0 , Var ⁡ ( ξ k ) = λ k , {\displaystyle \operatorname {E} (\xi _{k})=0,\operatorname {Var} (\xi _{k})=\lambda _{k},} and E ⁡ ( ξ k ξ l ) = 0 for l ≠ k . {\displaystyle \operatorname {E} (\xi _{k}\xi _{l})=0\ {\text{for}}\ l\neq k.} Then the k {\displaystyle k} -th mode of variation of X {\displaystyle \mathbf {X} } is the set of vectors, indexed by α {\displaystyle \alpha } , m k , α = μ ± α λ k e k , α ∈ [ − A , A ] , {\displaystyle \mathbf {m} _{k,\alpha }={\boldsymbol {\mu }}\pm \alpha {\sqrt {\lambda _{k}}}\mathbf {e} _{k},\alpha \in [-A,A],} where A {\displaystyle A} is typically selected as 2 or 3 {\displaystyle 2\ {\text{or}}\ 3} . === Modes of variation in FPCA === For a square-integrable random function X ( t ) , t ∈ T ⊂ R p {\displaystyle X(t),t\in {\mathcal {T}}\subset R^{p}} , where typically p = 1 {\displaystyle p=1} and T {\displaystyle {\mathcal {T}}} is an interval, denote the mean function by μ ( t ) = E ⁡ ( X ( t ) ) {\displaystyle \mu (t)=\operatorname {E} (X(t))} , and the covariance function by G ( s , t ) = Cov ⁡ ( X ( s ) , X ( t ) ) = ∑ k = 1 ∞ λ k φ k ( s ) φ k ( t ) , {\displaystyle G(s,t)=\operatorname {Cov} (X(s),X(t))=\sum _{k=1}^{\infty }\lambda _{k}\varphi _{k}(s)\varphi _{k}(t),} where λ 1 ≥ λ 2 ≥ ⋯ ≥ 0 {\displaystyle \lambda _{1}\geq \lambda _{2}\geq \cdots \geq 0} are the eigenvalues and { φ 1 , φ 2 , ⋯ } {\displaystyle \{\varphi _{1},\varphi _{2},\cdots \}} are the orthonormal eigenfunctions of the linear Hilbert–Schmidt operator G : L 2 ( T ) → L 2 ( T ) , G ( f ) = ∫ T G ( s , t ) f ( s ) d s . {\displaystyle G:L^{2}({\mathcal {T}})\rightarrow L^{2}({\mathcal {T}}),\,G(f)=\int _{\mathcal {T}}G(s,t)f(s)ds.} By the Karhunen–Loève theorem, one can express the centered function in the eigenbasis, X ( t ) − μ ( t ) = ∑ k = 1 ∞ ξ k φ k ( t ) , {\displaystyle X(t)-\mu (t)=\sum _{k=1}^{\infty }\xi _{k}\varphi _{k}(t),} where ξ k = ∫ T ( X ( t ) − μ ( t ) ) φ k ( t ) d t {\displaystyle \xi _{k}=\int _{\mathcal {T}}(X(t)-\mu (t))\varphi _{k}(t)dt} is the k {\displaystyle k} -th principal component with the properties E ⁡ ( ξ k ) = 0 , Var ⁡ ( ξ k ) = λ k , {\displaystyle \operatorname {E} (\xi _{k})=0,\operatorname {Var} (\xi _{k})=\lambda _{k},} and E ⁡ ( ξ k ξ l ) = 0 for l ≠ k . {\displaystyle \operatorname {E} (\xi _{k}\xi _{l})=0{\text{ for }}l\neq k.} Then the k {\displaystyle k} -th mode of variation of X ( t ) {\displaystyle X(t)} is the set of functions, indexed by α {\displaystyle \alpha } , m k , α ( t ) = μ ( t ) ± α λ k φ k ( t ) , t ∈ T , α ∈ [ − A , A ] {\displaystyle m_{k,\alpha }(t)=\mu (t)\pm \alpha {\sqrt {\lambda _{k}}}\varphi _{k}(t),\ t\in {\mathcal {T}},\ \alpha \in [-A,A]} that are viewed simultaneously over the range of α {\displaystyle \alpha } , usually for A = 2 or 3 {\displaystyle A=2\ {\text{or}}\ 3} . == Estimation == The formulation above is derived from properties of the population. Estimation is needed in real-world applications. The key idea is to estimate mean and covariance. === Modes of variation in PCA === Suppose the data x 1 , x 2 , ⋯ , x n {\displaystyle \mathbf {x} _{1},\mathbf {x} _{2},\cdots ,\mathbf {x} _{n}} represent n {\displaystyle n} independent drawings from some p {\displaystyle p} -dimensional population X {\displaystyle \mathbf {X} } with mean vector μ {\displaystyle {\boldsymbol {\mu }}} and covariance matrix Σ {\displaystyle \mathbf {\Sigma } } . These data yield the sample mean vector x ¯ {\displaystyle {\overline {\mathbf {x} }}} , and the sample covariance matrix S {\displaystyle \mathbf {S} } with eigenvalue-eigenvector pairs ( λ ^ 1 , e ^ 1 ) , ( λ ^ 2 , e ^ 2 ) , ⋯ , ( λ ^ p , e ^ p ) {\displaystyle ({\hat {\lambda }}_{1},{\hat {\mathbf {e} }}_{1}),({\hat {\lambda }}_{2},{\hat {\mathbf {e} }}_{2}),\cdots ,({\hat {\lambda }}_{p},{\hat {\mathbf {e} }}_{p})} . Then the k {\displaystyle k} -th mode of variation of X {\displaystyle \mathbf {X} } can be estimated by m ^ k , α = x ¯ ± α λ ^ k e ^ k , α ∈ [ − A , A ] . {\displaystyle {\hat {\mathbf {m} }}_{k,\alpha }={\overline {\mathbf {x} }}\pm \alpha {\sqrt {{\hat {\lambda }}_{k}}}{\hat {\mathbf {e} }}_{k},\alpha \in [-A,A].} === Modes of variation in FPCA === Consider n {\displaystyle n} realizations X 1 ( t ) , X 2 ( t ) , ⋯ , X n ( t ) {\displaystyle X_{1}(t),X_{2}(t),\cdots ,X_{n}(t)} of a square-integrable random function X ( t ) , t ∈ T {\displaystyle X(t),t\in {\mathcal {T}}} with the mean function μ ( t ) = E ⁡ ( X ( t ) ) {\displaystyle \mu (t)=\operatorname {E} (X(t))} and the covariance function G ( s , t ) = Cov ⁡ ( X ( s ) , X ( t ) ) {\displaystyle G(s,t)=\operatorname {Cov} (X(s),X(t))} . Functional principal component analysis provides methods for the estimation of μ ( t ) {\displaystyle \mu (t)} and G ( s , t ) {\displaystyle G(s,t)} in detail, often involving point wise estimate and interpolation. Substituting estimates for the unknown quantities, the k {\displaystyle k} -th mode of variation of X ( t ) {\displaystyle X(t)} can be estimated by m ^ k , α ( t ) = μ ^ ( t ) ± α λ ^ k φ ^ k ( t ) , t ∈ T , α ∈ [ − A , A ] . {\displaystyle {\hat {m}}_{k,\alpha }(t)={\hat {\mu }}(t)\pm \alpha {\sqrt {{\hat {\lambda }}_{k}}}{\hat {\varphi }}_{k}(t),t\in {\mathcal {T}},\alpha \in [-A,A].} == Applications == Modes of variation are useful to visualize and describe the variation patterns in the data sorted by the eigenvalues. In real-world applications, modes of variation associated with eigencomponents allow to interpret complex data, such as the evolution of function traits and other infinite-dimensional data. To illustrate how modes of variation work in practice, two examples are shown in the graphs to the right, which display the first two modes of variation. The solid curve represents the sample mean function. The dashed, dot-dashed, and dotted curves correspond to modes of variation with α = ± 1 , ± 2 , {\displaystyle \alpha =\pm 1,\pm 2,} and ± 3 {\displaystyle \pm 3} , respectively. The first graph displays the first two modes of variation of female mortality data from 41 countries in 2003. The object of interest is log hazard function between ages 0 and 100 years. The first mode of variation suggests that the variation of female mortality is smaller for ages around 0 or 100, and larger for ages around 25. An appropriate and intuitive interpretation is that mortality around 25 is driven by accidental death, while around 0 or 100, mortality is related to congenital disease or natural death. Compared to female mortality

Visual Turing Test

The Visual Turing Test is “an operator-assisted device that produces a stochastic sequence of binary questions from a given test image”. The query engine produces a sequence of questions that have unpredictable answers given the history of questions. The test is only about vision and does not require any natural language processing. The job of the human operator is to provide the correct answer to the question or reject it as ambiguous. The query generator produces questions such that they follow a “natural story line”, similar to what humans do when they look at a picture. == History == Research in computer vision dates back to the 1960s when Seymour Papert first attempted to solve the problem. This unsuccessful attempt was referred to as the Summer Vision Project. The reason why it was not successful was because computer vision is more complicated than what people think. The complexity is in alignment with the human visual system. Roughly 50% of the human brain is devoted in processing vision, which indicates that it is a difficult problem. Later there were attempts to solve the problems with models inspired by the human brain. Perceptrons by Frank Rosenblatt, which is a form of the neural networks, was one of the first such approaches. These simple neural networks could not live up to their expectations and had certain limitations due to which they were not considered in future research. Later with the availability of the hardware and some processing power the research shifted to image processing which involves pixel-level operations, like finding edges, de-noising images or applying filters to name a few. There was some great progress in this field but the problem of vision which was to make the machines understand the images was still not being addressed. During this time the neural networks also resurfaced as it was shown that the limitations of the perceptrons can be overcome by Multi-layer perceptrons. Also in the early 1990s convolutional neural networks were born which showed great results on digit recognition but did not scale up well on harder problems. The late 1990s and early 2000s saw the birth of modern computer vision. One of the reasons this happened was due to the availability of key, feature extraction and representation algorithms. Features along with the already present machine learning algorithms were used to detect, localise and segment objects in Images. While all these advancements were being made, the community felt the need to have standardised datasets and evaluation metrics so the performances can be compared. This led to the emergence of challenges like the Pascal VOC challenge and the ImageNet challenge. The availability of standard evaluation metrics and the open challenges gave directions to the research. Better algorithms were introduced for specific tasks like object detection and classification. Visual Turing Test aims to give a new direction to the computer vision research which would lead to the introduction of systems that will be one step closer to understanding images the way humans do. == Current evaluation practices == A large number of datasets have been annotated and generalised to benchmark performances of difference classes of algorithms to assess different vision tasks (e.g., object detection/recognition) on some image domain (e.g., scene images). One of the most famous datasets in computer vision is ImageNet which is used to assess the problem of object level Image classification. ImageNet is one of the largest annotated datasets available and has over one million images. The other important vision task is object detection and localisation which refers to detecting the object instance in the image and providing the bounding box coordinates around the object instance or segmenting the object. The most popular dataset for this task is the Pascal dataset. Similarly there are other datasets for specific tasks like the H3D dataset for human pose detection, Core dataset to evaluate the quality of detected object attributes such as colour, orientation, and activity. Having these standard datasets has helped the vision community to come up with well performing algorithms for all these tasks. The next logical step is to create a larger task encompassing of these smaller subtasks. Having such a task would lead to building systems that would understand images, as understanding images would inherently involve detecting objects, localising them and segmenting them. == Details == The Visual Turing Test (VTT) unlike the Turing test has a query engine system which interrogates a computer vision system in the presence of a human co-ordinator. It is a system that generates a random sequence of binary questions specific to the test image, such that the answer to any question k is unpredictable given the true answers to the previous k − 1 questions (also known as history of questions). The test happens in the presence of a human operator who serves two main purposes: removing the ambiguous questions and providing the correct answers to the unambiguous questions. Given an Image infinite possible binary questions can be asked and a lot of them are bound to be ambiguous. These questions if generated by the query engine are removed by the human moderator and instead the query engine generates another question such that the answer to it is unpredictable given the history of the questions. The aim of the Visual Turing Test is to evaluate the Image understanding of a computer system, and an important part of image understanding is the story line of the image. When humans look at an image, they do not think that there is a car at ‘x’ pixels from the left and ‘y’ pixels from the top, but instead they look at it as a story, for e.g. they might think that there is a car parked on the road, a person is exiting the car and heading towards a building. The most important elements of the story line are the objects and so to extract any story line from an image the first and the most important task is to instantiate the objects in it, and that is what the query engine does. === Query engine === The query engine is the core of the Visual Turing Test and it comprises two main parts : Vocabulary and Questions ==== Vocabulary ==== Vocabulary is a set of words that represent the elements of the images. This vocabulary when used with appropriate grammar leads to a set of questions. The grammar is defined in the next section in a way that it leads to a space of binary questions. The vocabulary V {\displaystyle {\mathcal {V}}} consist of three components: Types of Objects T {\displaystyle {\mathcal {T}}} Type-dependent attributes of objects A ( t ) {\displaystyle {\mathcal {A}}(t)} Type-dependent relationships between two objects R ( t , t ′ ) {\displaystyle {\mathcal {R}}(t,t')} For Images of urban street scenes the types of objects include people, vehicle and buildings. Attributes refer to the properties of these objects, for e.g. female, child, wearing a hat or carrying something, for people and moving, parked, stopped, one tire visible or two tires visible for vehicles. Relationships between each pair of object classes can be either “ordered” or “unordered”. The unordered relationships may include talking, walking together and the ordered relationships include taller, closer to the camera, occluding, being occluded etc. Additionally all of this vocabulary is used in context of rectangular image regions w \in W which allow for the localisation of objects in the image. An extremely large number of such regions are possible and this complicates the problem, so for this test, regions at specific scales are only used which include 1/16 the size of image, 1/4 the size of image, 1/2 the size of image or larger. ==== Questions ==== The question space is composed of four types of questions: Existence questions: The aim of the existence questions is to find new objects in the image that have not been uniquely identified previously. They are of the form : Qexist = 'Is there an instance of an object of type t with attributes A partially visible in region w that was not previously instantiated?' Uniqueness questions: A uniqueness question tries to uniquely identify an object to instantiate it. Quniq = 'Is there a unique instance of an object of type t with attributes A partially visible in region w that was not previously instantiated?' The uniqueness questions along with the existence questions form the instantiation questions. As mentioned earlier instantiating objects leads to other interesting questions and eventually a story line. Uniqueness questions follow the existence questions and a positive answer to it leads to instantiation of an object. Attribute questions: An attribute question tries to find more about the object once it has been instantiated. Such questions can query about a single attribute, conjunction of two attributes or disjunction of two attributes. Qatt(ot) = {'Does object ot have attribute a?' , 'Does object

Synaptic transistor

A synaptic transistor is an electrical device that can learn in ways similar to a neural synapse. It optimizes its own properties for the functions it has carried out in the past. The device mimics the behavior of the property of neurons called spike-timing-dependent plasticity, or STDP. == Structure == Its structure is similar to that of a field effect transistor, where an ionic liquid takes the place of the gate insulating layer between the gate electrode and the conducting channel. That channel is composed of samarium nickelate (SmNiO3, or SNO) rather than the field effect transistor's doped silicon. == Function == A synaptic transistor has a traditional immediate response whose amount of current that passes between the source and drain contacts varies with voltage applied to the gate electrode. It also produces a much slower learned response such that the conductivity of the SNO layer varies in response to the transistor's STDP history, essentially by shuttling oxygen ions between the SNO and the ionic liquid. The analog of strengthening a synapse is to increase the SNO's conductivity, which essentially increases gain. Similarly, weakening a synapse is analogous to decreasing the SNO's conductivity, lowering the gain. The input and output of the synaptic transistor are continuous analog values, rather than digital on-off signals. While the physical structure of the device has the potential to learn from history, it contains no way to bias the transistor to control the memory effect. An external supervisory circuit converts the time delay between input and output into a voltage applied to the ionic liquid that either drives ions into the SNO or removes them. A network of such devices can learn particular responses to "sensory inputs", with those responses being learned through experience rather than explicitly programmed.