In the field of image processing, stairstep interpolation is a widely employed method technique for interpolating pixels after enlarging an image. The fundamental concept is to interpolate multiple times, in small increments, using any interpolation algorithm that is better than nearest-neighbor interpolation such as; bilinear interpolation, and bicubic interpolation. A common scenario is to interpolate an image by using a bicubic interpolation which increases the image size by no more than 10% (110% of the original size) at a time until the desired size is reached. Fred Miranda, a developer, popularized this method by creating and developing several Photoshop plug-ins that incorporate this technique. == Example ==
Metigo
metigo is a software application that performs image-based modelling and close range photogrammetry. It produces rectified imagery plans, true ortho-projections on planar, cylindric and conic surfaces, 3D photorealistic models, measurements from photography and mappings on a photographic base for uses in the cultural heritage sector, mainly conservation. == Products == The metigo product line currently consists of the mapping software metigo MAP, the stereo-photogrammetry modeling software metigo 3D, the free viewer metigo VIEW. These products are all standalone and are not depending on other software, such as AutoCAD. === metigo MAP === metigo MAP is mainly used to map findings and conservation measured on a uniform metric photographic base. Therefore, photos of planar surfaces can be rectified based on geometrical informations, e.g. height and width of a rectangle, or cartesian coordinates measured by total station. Beside rectified imagery several other metric mapping bases can be imported and used: true ortho-projections; scaled scans of plans and plots; CAD-files; 3D models, such as digital surface models (DSM) produced by stereo-photogrammetry, SfM or 3D scanning. metigo MAP 's strong point is that rectified imagery taken with different techniques (visual light, sided light, IR, UV, UV-fluorescence, X-ray), historic images and photos taken at various stages of the conservation process can be superimposed and evaluated mutually. The user can allocate several attributes, such as different conservation measures and damage classes, to the mapped geometries. The mappings can be analysed by geometries as well as by user-defined attributes at any stage of the project. metigo MAP targets mainly conservators in different cultural heritage fields. Using it no specialist knowledge of surveying and photogrammetric techniques are needed. === metigo 3D === metigo 3D is a stereo-photogrammetric kit that allows to calculate bundle adjustments (axios3D), create high-quality 3D point clouds using multiple stereo photo pairs combined with metric survey data, mesh these point clouds, texture the meshes with high-resolution image data to create photo-realistic models, ortho-project orientated images on digital surface models (DSM) on planes and best-fit cylinders and cones, create unwrappings and developed views of curved surfaces, analyse deformations of 3D surfaces. metigo 3D targets metric survey specialists working in the cultural heritage sector. == Supported file formats == metigo has the ability to read the following formats: images: JPEG (.jpg), Tiff (.tif), Bitmaps (.bmp), CompuServ (.gif), Encapsualated Postscript (.eps), PCX (.pcx), Photo-CD (.pcd), PICT (.pcd), PNG (.png), Targa (.tga), RAW-format of several camera brands. CAD: DBX, DXF, DWG. 3D: many ASCII-formats (.stl, .wrl, etc.) point data: format editor for ASCII files. == Supported languages == Currently, an English and German version of the software is supported. For metigo MAP beside these a French and Polish GUI is offered for sale. == Applications == The main applications of metigo are: conservation in the cultural heritage context, e.g. stone conservation paintings tapestry etc. architecture, archaeology, many other are possible, e.g. forensics. == History == The first public release of metigo was in 2000.
Legendre moment
In mathematics, Legendre moments are a type of image moment and are achieved by using the Legendre polynomial. Legendre moments are used in areas of image processing including: pattern and object recognition, image indexing, line fitting, feature extraction, edge detection, and texture analysis. Legendre moments have been studied as a means to reduce image moment calculation complexity by limiting the amount of information redundancy through approximation. == Legendre moments == Source: With order of m + n, and object intensity function f(x,y): L m n = ( 2 m + 1 ) ( 2 n + 1 ) 4 ∫ − 1 1 ∫ − 1 1 P m ( x ) P n ( y ) f ( x , y ) d x d y {\displaystyle L_{mn}={\frac {(2m+1)(2n+1)}{4}}\int \limits _{-1}^{1}\int \limits _{-1}^{1}P_{m}(x)P_{n}(y)f(x,y)\,dx\,dy} where m,n = 1, 2, 3, ...∞ with the nth-order Legendre polynomials being: P n ( x ) = ∑ k = 0 n a k , n x k = ( − 1 ) n 2 n n ! ( d d x ) [ ( 1 − x 2 ) n ] {\displaystyle P_{n}(x)=\sum _{k=0}^{n}a_{k,n}x^{k}={\frac {(-1)^{n}}{2^{n}n!}}\left({\frac {d}{dx}}\right)[(1-x^{2})^{n}]} which can also be written: P n ( x ) = ∑ k = 0 D ( n ) ( − 1 ) k ( 2 n − 2 k ) ! 2 n k ! ( n − k ) ! ( n − 2 k ) ! x n − 2 k = ( 2 n ) ! 2 n ( n ! ) 2 x n − ( 2 n − 2 ) ! 2 n 1 ! ( n − 1 ) ! ( n − 2 ) ! x n − 2 + ⋯ {\displaystyle {\begin{aligned}P_{n}(x)&=\sum _{k=0}^{D(n)}(-1)^{k}{\frac {(2n-2k)!}{2^{n}k!(n-k)!(n-2k)!}}x^{n-2k}\\[5pt]&={\frac {(2n)!}{2^{n}(n!)^{2}}}x^{n}-{\frac {(2n-2)!}{2^{n}1!(n-1)!(n-2)!}}x^{n-2}+\cdots \end{aligned}}} where D(n) = floor(n/2). The set of Legendre polynomials {Pn(x)} form an orthogonal set on the interval [−1,1]: ∫ − 1 1 P n ( x ) P m ( x ) d x = 2 2 n + 1 δ n m {\displaystyle \int _{-1}^{1}P_{n}(x)P_{m}(x)\,dx={\frac {2}{2n+1}}\delta _{nm}} A recurrence relation can be used to compute the Legendre polynomial: ( n + 1 ) P n + 1 ( x ) − ( 2 n + 1 ) x P n ( x ) + n P n − 1 ( x ) = 0 {\displaystyle (n+1)P_{n+1}(x)-(2n+1)xP_{n}(x)+nP_{n-1}(x)=0} f(x,y) can be written as an infinite series expansion in terms of Legendre polynomials [−1 ≤ x,y ≤ 1.]: f ( x , y ) = ∑ m = 0 ∞ ∑ n = 0 ∞ λ m n P m ( x ) P n ( y ) {\displaystyle f(x,y)=\sum _{m=0}^{\infty }\sum _{n=0}^{\infty }\lambda _{mn}P_{m}(x)P_{n}(y)}
Corpus of Linguistic Acceptability
Corpus of Linguistic Acceptability (CoLA) is a dataset the primary purpose of which is to serve as a benchmark for evaluating the ability of artificial neural networks, including large language models, to judge the grammatical correctness of sentences. It consists of 10,657 English sentences from published linguistics literature that were manually labeled either as grammatical or ungrammatical. == Public version == The publicly available version of CoLA contains 9,594 sentences that belong to training and development sets. It excludes 1,063 sentences reserved for a held-out test set.
Bigram
A bigram or digram is a sequence of two adjacent elements from a string of tokens, which are typically letters, syllables, or words. A bigram is an n-gram for n=2. The frequency distribution of every bigram in a string is commonly used for simple statistical analysis of text in many applications, including in computational linguistics, cryptography, and speech recognition. Gappy bigrams or skipping bigrams are word pairs which allow gaps (perhaps avoiding connecting words, or allowing some simulation of dependencies, as in a dependency grammar). == Applications == Bigrams, along with other n-grams, are used in most successful language models for speech recognition. Bigram frequency attacks can be used in cryptography to solve cryptograms. See frequency analysis. Bigram frequency is one approach to statistical language identification. Some activities in logology or recreational linguistics involve bigrams. These include attempts to find English words beginning with every possible bigram, or words containing a string of repeated bigrams, such as logogogue. == Bigram frequency in the English language == The frequency of the most common letter bigrams in a large English corpus is: th 3.56% of 1.17% io 0.83% he 3.07% ed 1.17% le 0.83% in 2.43% is 1.13% ve 0.83% er 2.05% it 1.12% co 0.79% an 1.99% al 1.09% me 0.79% re 1.85% ar 1.07% de 0.76% on 1.76% st 1.05% hi 0.76% at 1.49% to 1.05% ri 0.73% en 1.45% nt 1.04% ro 0.73% nd 1.35% ng 0.95% ic 0.70% ti 1.34% se 0.93% ne 0.69% es 1.34% ha 0.93% ea 0.69% or 1.28% as 0.87% ra 0.69% te 1.20% ou 0.87% ce 0.65%
Three-factor learning
In neuroscience and machine learning, three-factor learning is the combination of Hebbian plasticity with a third modulatory factor to stabilise and enhance synaptic learning. This third factor can represent various signals such as reward, punishment, error, surprise, or novelty, often implemented through neuromodulators. == Description == Three-factor learning introduces the concept of eligibility traces, which flag synapses for potential modification pending the arrival of the third factor, and helps temporal credit assignement by bridging the gap between rapid neuronal firing and slower behavioral timescales, from which learning can be done. Biological basis for Three-factor learning rules have been supported by experimental evidence. This approach addresses the instability of classical Hebbian learning by minimizing autocorrelation and maximizing cross-correlation between inputs.
Stereo cameras
The stereo cameras approach is a method of distilling a noisy video signal into a coherent data set that a computer can begin to process into actionable symbolic objects, or abstractions. Stereo cameras is one of many approaches used in the broader fields of computer vision and machine vision. == Calculation == In this approach, two cameras with a known physical relationship (i.e. a common field of view the cameras can see, and how far apart their focal points sit in physical space) are correlated via software. By finding mappings of common pixel values, and calculating how far apart these common areas reside in pixel space, a rough depth map can be created. This is very similar to how the human brain uses stereoscopic information from the eyes to gain depth cue information, i.e. how far apart any given object in the scene is from the viewer. The camera attributes must be known, focal length and distance apart etc., and a calibration done. Once this is completed, the systems can be used to sense the distances of objects by triangulation. Finding the same singular physical point in the two left and right images is known as the correspondence problem. Correctly locating the point gives the computer the capability to calculate the distance that the robot or camera is from the object. On the BH2 Lunar Rover the cameras use five steps: a bayer array filter, photometric consistency dense matching algorithm, a Laplace of Gaussian (LoG) edge detection algorithm, a stereo matching algorithm and finally uniqueness constraint. == Uses == This type of stereoscopic image processing technique is used in applications such as 3D reconstruction, robotic control and sensing, crowd dynamics monitoring and off-planet terrestrial rovers; for example, in mobile robot navigation, tracking, gesture recognition, targeting, 3D surface visualization, immersive and interactive gaming. Although the Xbox Kinect sensor is also able to create a depth map of an image, it uses an infrared camera for this purpose, and does not use the dual-camera technique. Other approaches to stereoscopic sensing include time of flight sensors and ultrasound.