An and–or tree is a graphical representation of the reduction of problems (or goals) to conjunctions and disjunctions of subproblems (or subgoals). == Example == The and–or tree: represents the search space for solving the problem P, using the goal-reduction methods: P if Q and R P if S Q if T Q if U == Definitions == Given an initial problem P0 and set of problem solving methods of the form: P if P1 and … and Pn the associated and–or tree is a set of labelled nodes such that: The root of the tree is a node labelled by P0. For every node N labelled by a problem or sub-problem P and for every method of the form P if P1 and ... and Pn, there exists a set of children nodes N1, ..., Nn of the node N, such that each node Ni is labelled by Pi. The nodes are conjoined by an arc, to distinguish them from children of N that might be associated with other methods. A node N, labelled by a problem P, is a success node if there is a method of the form P if nothing (i.e., P is a "fact"). The node is a failure node if there is no method for solving P. If all of the children of a node N, conjoined by the same arc, are success nodes, then the node N is also a success node. Otherwise the node is a failure node. == Search strategies == An and–or tree specifies only the search space for solving a problem. Different search strategies for searching the space are possible. These include searching the tree depth-first, breadth-first, or best-first using some measure of desirability of solutions. The search strategy can be sequential, searching or generating one node at a time, or parallel, searching or generating several nodes in parallel. == Relationship with logic programming == The methods used for generating and–or trees are propositional logic programs (without variables). In the case of logic programs containing variables, the solutions of conjoint sub-problems must be compatible. Subject to this complication, sequential and parallel search strategies for and–or trees provide a computational model for executing logic programs. == Relationship with two-player games == And–or trees can also be used to represent the search spaces for two-person games. The root node of such a tree represents the problem of one of the players winning the game, starting from the initial state of the game. Given a node N, labelled by the problem P of the player winning the game from a particular state of play, there exists a single set of conjoint children nodes, corresponding to all of the opponents responding moves. For each of these children nodes, there exists a set of non-conjoint children nodes, corresponding to all of the player's defending moves. For solving game trees with proof-number search family of algorithms, game trees are to be mapped to and–or trees. MAX-nodes (i.e. maximizing player to move) are represented as OR nodes, MIN-nodes map to AND nodes. The mapping is possible, when the search is done with only a binary goal, which usually is "player to move wins the game".
Electronic sell-through
Electronic sell-through (EST) is a method of media distribution whereby consumers pay a one-time fee to download a media file for storage on a hard drive. Although EST is often described as a transaction that grants content "ownership" to the consumer, the content may become unusable after a certain period and may not be viewable using competing platforms. EST is used by a wide array of digital media products, including movies, television, music, games, and mobile applications. The term is sometimes used interchangeably with download to own (DTO). == Film and television == The film and television industry's $18.8 billion home entertainment market consists of rental and sell-through segments, the latter of which includes the electronic sell-through of digital content. In 2010, EST generated $683 million of total home entertainment revenues, putting it behind the more lucrative revenue streams of cable video-on-demand (VOD) and internet video-on-demand (iVOD), which brought in a combined $1.8 billion in the same period. In 2010, Apple's iTunes Store accounted for three quarters of the U.S. EST business. The rest of the EST market was captured by Microsoft (via its Zune Video platform), Sony, Amazon VOD (now Amazon Video), and Walmart (via its VUDU service). A number of industry trends indicate the future expansion of EST's share of digital distribution revenues. David Bishop, worldwide president of Sony Pictures Home Entertainment, describes the following outlook: "With the launch of UltraViolet (the cloud-based digital copy locker system) establishing a common digital distribution platform later this year, prices potentially coming down on digital sales, more marketing devoted to digital sellthrough, and studios adding more value to the sellthrough product by making HD available and building in smarter extra features, we see the balance tilting even more toward owning and collecting digital movies."
List of computer graphics journals
List of computer graphics journals includes notable peer-reviewed scientific and academic journals that focus on computer graphics, visualization, and related areas such as rendering, animation, image processing, and geometric modeling. == Journals == ACM Transactions on Graphics Computers & Graphics IEEE Computer Graphics and Applications IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems Graphical Models Journal of Computer Graphics Techniques Presence: Teleoperators and Virtual Environments Virtual Reality Simulation & Gaming
Shape analysis (digital geometry)
This article describes shape analysis to analyze and process geometric shapes. == Description == Shape analysis is the (mostly) automatic analysis of geometric shapes, for example using a computer to detect similarly shaped objects in a database or parts that fit together. For a computer to automatically analyze and process geometric shapes, the objects have to be represented in a digital form. Most commonly a boundary representation is used to describe the object with its boundary (usually the outer shell, see also 3D model). However, other volume based representations (e.g. constructive solid geometry) or point based representations (point clouds) can be used to represent shape. Once the objects are given, either by modeling (computer-aided design), by scanning (3D scanner) or by extracting shape from 2D or 3D images, they have to be simplified before a comparison can be achieved. The simplified representation is often called a shape descriptor (or fingerprint, signature). These simplified representations try to carry most of the important information, while being easier to handle, to store and to compare than the shapes directly. A complete shape descriptor is a representation that can be used to completely reconstruct the original object (for example the medial axis transform). == Application fields == Shape analysis is used in many application fields: archeology for example, to find similar objects or missing parts architecture for example, to identify objects that spatially fit into a specific space medical imaging to understand shape changes related to illness or aid surgical planning virtual environments or on the 3D model market to identify objects for copyright purposes security applications such as face recognition entertainment industry (movies, games) to construct and process geometric models or animations computer-aided design and computer-aided manufacturing to process and to compare designs of mechanical parts or design objects. == Shape descriptors == Shape descriptors can be classified by their invariance with respect to the transformations allowed in the associated shape definition. Many descriptors are invariant with respect to congruency, meaning that congruent shapes (shapes that could be translated, rotated and mirrored) will have the same descriptor (for example moment or spherical harmonic based descriptors or Procrustes analysis operating on point clouds). Another class of shape descriptors (called intrinsic shape descriptors) is invariant with respect to isometry. These descriptors do not change with different isometric embeddings of the shape. Their advantage is that they can be applied nicely to deformable objects (e.g. a person in different body postures) as these deformations do not involve much stretching but are in fact near-isometric. Such descriptors are commonly based on geodesic distances measures along the surface of an object or on other isometry invariant characteristics such as the Laplace–Beltrami spectrum (see also spectral shape analysis). There are other shape descriptors, such as graph-based descriptors like the medial axis or the Reeb graph that capture geometric and/or topological information and simplify the shape representation but can not be as easily compared as descriptors that represent shape as a vector of numbers. From this discussion it becomes clear, that different shape descriptors target different aspects of shape and can be used for a specific application. Therefore, depending on the application, it is necessary to analyze how well a descriptor captures the features of interest.
Signal transfer function
The signal transfer function (SiTF) is a measure of the signal output versus the signal input of a system such as an infrared system or sensor. There are many general applications of the SiTF. Specifically, in the field of image analysis, it gives a measure of the noise of an imaging system, and thus yields one assessment of its performance. == SiTF evaluation == In evaluating the SiTF curve, the signal input and signal output are measured differentially; meaning, the differential of the input signal and differential of the output signal are calculated and plotted against each other. An operator, using computer software, defines an arbitrary area, with a given set of data points, within the signal and background regions of the output image of the infrared sensor, i.e. of the unit under test (UUT), (see "Half Moon" image below). The average signal and background are calculated by averaging the data of each arbitrarily defined region. A second order polynomial curve is fitted to the data of each line. Then, the polynomial is subtracted from the average signal and background data to yield the new signal and background. The difference of the new signal and background data is taken to yield the net signal. Finally, the net signal is plotted versus the signal input. The signal input of the UUT is within its own spectral response. (e.g. color-correlated temperature, pixel intensity, etc.). The slope of the linear portion of this curve is then found using the method of least squares. == SiTF curve == The net signal is calculated from the average signal and background, as in signal to noise ratio (imaging)#Calculations. The SiTF curve is then given by the signal output data, (net signal data), plotted against the signal input data (see graph of SiTF to the right). All the data points in the linear region of the SiTF curve can be used in the method of least squares to find a linear approximation. Given n {\displaystyle n\,} data points ( x i , y i ) {\displaystyle (x_{i}\,,y_{i}\,)} a best fit line parameterized as y = m x + b {\displaystyle y=mx+b\,} is given by: m = ∑ x i y i n − ∑ x i n ∑ y i n ∑ x i 2 n − ( ∑ x i n ) 2 b = ∑ y i n − m ∑ x i n {\displaystyle m={\frac {{\frac {\sum x_{i}y_{i}}{n}}-{\frac {\sum x_{i}}{n}}{\frac {\sum y_{i}}{n}}}{{\frac {\sum x_{i}^{2}}{n}}-({\frac {\sum x_{i}}{n}})^{2}}}\qquad \qquad b={\frac {\sum y_{i}}{n}}-m{\frac {\sum x_{i}}{n}}}
Learnable function class
In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.
Artbreeder
Artbreeder, formerly known as Ganbreeder, is a collaborative, machine learning-based art website. Using the models StyleGAN and BigGAN, the website allows users to generate and modify images of faces, landscapes, and paintings, among other categories. == Overview == On Artbreeder, users mainly interact through the remixing - referred to as 'breeding' - of other users' images found in the publicly accessible database of images. The creation of new variations can be done by tweaking sliders on an image's page, known as "genes", which in the "Portraits" model can range from color balance to gender, facial hair, and glasses. Additionally, any image can be "crossbred" with other publicly viewable images from the database, using a slider to control how much of each image should influence the resulting "child". The site also allows for uploading new images, which the model will attempt to convert into the latent space of the network. == Notable usages == The similarly AI-driven text adventure game AI Dungeon uses Artbreeder to generate profile pictures for its users, and The Static Age's Andrew Paley has used Artbreeder to create the visuals for his music videos. Artbreeder has been used to create portraits of characters from popular novels such as Harry Potter and Twilight. They have also been used to add realistic features to ancient portraits. Artbreeder was used to create characters in the sequel to Ben Drowned with the titular villain, an AI-construct itself, created entirely using the website. == Changes to Artbreeder == ArtBreeder underwent an overhaul, introducing several features to enhance the user experience. Among these updates is the integration SD-XL, developed by stability.ai. Additionally, ArtBreeder also added a functionality known as ControlNet, which enables users to create images based on specific poses. With ControlNet, users can incorporate various poses into their AI Artworks. More features that were introduced into Artbreeder, are Pattern, which creates AI Pattern Images, Outpainting or Uncropping was also an added feature to Artbreeder, that allows the user to expand the image beyond the normal dimensions of the image. == Reception == The artwork generated by users of the website has been described as "beautiful" and "surreal," drawing comparisons to "weird, incomprehensible dreams" that "somehow touch the deep, unconscious parts of [the] mind". However, the generated faces were noted as "creepy and 'off'", and still nowhere near the quality attained by actual digital artists. Additionally, the site faced criticism for perceived confusing aspects of the AI's behavior. Jonathan Bartlett of Mind Matters News noted that "As is always the case with AI, sometimes the [gene] knobs don't work as expected and sometimes the results are... strange," while conceding that Artbreeder was still "probably the start of a new future of made-to-order stock images." Writers from Hyperallergic also took issue with perceived racial biases in the Portraits model, citing a comment from a user who faced difficulty from the neural network while attempting to darken the skin of a portrait to match a source image.