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57 relations: Affine transformation, Bayes' theorem, Calculus of variations, Computer vision, Corner detection, CT scan, Diagonal matrix, Doubly stochastic matrix, Element (mathematics), Entropy (information theory), Euclidean distance, Expectation–maximization algorithm, Feature extraction, Gaussian function, Gradient descent, Graph matching, Identity matrix, Image registration, Independent and identically distributed random variables, Iterative closest point, Kernel (statistics), Kernel density estimation, Least squares, Levenberg–Marquardt algorithm, Lookup table, Loss function, M-estimator, Magnetic resonance imaging, Mixture model, Nearest neighbor search, Newton's method, Normal distribution, Normal mode, Optical character recognition, Pattern recognition, Point cloud, Point Cloud Library, Pose (computer vision), Positive-definite kernel, Posterior probability, Probability density function, Pseudocode, Rangefinder, Rigid transformation, Rotation, Scaling (geometry), Shear mapping, Simulated annealing, Singular-value decomposition, Slack variable, ..., Softmax function, Thin plate spline, Time complexity, Trace (linear algebra), Transformation (function), Translation (geometry), 3D scanner. Expand index (7 more) »
Affine transformation
In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.
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Bayes' theorem
In probability theory and statistics, Bayes’ theorem (alternatively Bayes’ law or Bayes' rule, also written as Bayes’s theorem) describes the probability of an event, based on prior knowledge of conditions that might be related to the event.
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Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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Computer vision
Computer vision is a field that deals with how computers can be made for gaining high-level understanding from digital images or videos.
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Corner detection
Corner detection is an approach used within computer vision systems to extract certain kinds of features and infer the contents of an image.
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CT scan
A CT scan, also known as computed tomography scan, makes use of computer-processed combinations of many X-ray measurements taken from different angles to produce cross-sectional (tomographic) images (virtual "slices") of specific areas of a scanned object, allowing the user to see inside the object without cutting.
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Diagonal matrix
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.
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Doubly stochastic matrix
In mathematics, especially in probability and combinatorics, a doubly stochastic matrix (also called bistochastic), is a square matrix A.
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Element (mathematics)
In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
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Entropy (information theory)
Information entropy is the average rate at which information is produced by a stochastic source of data.
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Euclidean distance
In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.
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Expectation–maximization algorithm
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables.
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Feature extraction
In machine learning, pattern recognition and in image processing, feature extraction starts from an initial set of measured data and builds derived values (features) intended to be informative and non-redundant, facilitating the subsequent learning and generalization steps, and in some cases leading to better human interpretations.
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Gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the form: for arbitrary real constants, and.
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Gradient descent
Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function.
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Graph matching
Graph matching is the problem of finding a similarity between graphs.
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Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
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Image registration
Image registration is the process of transforming different sets of data into one coordinate system.
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Independent and identically distributed random variables
In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent.
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Iterative closest point
Iterative closest point (ICP) is an algorithm employed to minimize the difference between two clouds of points.
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Kernel (statistics)
The term kernel is a term in statistical analysis used to refer to a window function.
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Kernel density estimation
In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable.
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Least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
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Levenberg–Marquardt algorithm
In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems.
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Lookup table
In computer science, a lookup table is an array that replaces runtime computation with a simpler array indexing operation.
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Loss function
In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.
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M-estimator
In statistics, M-estimators are a broad class of estimators, which are obtained as the minima of sums of functions of the data.
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Magnetic resonance imaging
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body in both health and disease.
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Mixture model
In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs.
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Nearest neighbor search
Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point.
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Newton's method
In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
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Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
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Normal mode
A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation.
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Optical character recognition
Optical character recognition (also optical character reader, OCR) is the mechanical or electronic conversion of images of typed, handwritten or printed text into machine-encoded text, whether from a scanned document, a photo of a document, a scene-photo (for example the text on signs and billboards in a landscape photo) or from subtitle text superimposed on an image (for example from a television broadcast).
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Pattern recognition
Pattern recognition is a branch of machine learning that focuses on the recognition of patterns and regularities in data, although it is in some cases considered to be nearly synonymous with machine learning.
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Point cloud
A point cloud is a set of data points in space.
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Point Cloud Library
The Point Cloud Library (PCL) is an open-source library of algorithms for point cloud processing tasks and 3D geometry processing, such as occur in three-dimensional computer vision.
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Pose (computer vision)
In computer vision and robotics, a typical task is to identify specific objects in an image and to determine each object's position and orientation relative to some coordinate system.
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Positive-definite kernel
In operator theory, a branch of mathematics, a positive definite kernel is a generalization of a positive definite function or a positive-definite matrix.
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Posterior probability
In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence or background is taken into account.
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Probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
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Pseudocode
Pseudocode is an informal high-level description of the operating principle of a computer program or other algorithm.
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Rangefinder
A rangefinder is a device that measures distance from the observer to a target, in a process called ranging.
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Rigid transformation
In mathematics, a rigid transformation or Euclidean isometry of a Euclidean space preserves distances between every pair of points.
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Rotation
A rotation is a circular movement of an object around a center (or point) of rotation.
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Scaling (geometry)
In Euclidean geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions.
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Shear mapping
In plane geometry, a shear mapping is a linear map that displaces each point in fixed direction, by an amount proportional to its signed distance from a line that is parallel to that direction.
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Simulated annealing
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function.
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Singular-value decomposition
In linear algebra, the singular-value decomposition (SVD) is a factorization of a real or complex matrix.
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Slack variable
In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it into an equality.
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Softmax function
In mathematics, the softmax function, or normalized exponential function, is a generalization of the logistic function that "squashes" a -dimensional vector \mathbf of arbitrary real values to a -dimensional vector \sigma(\mathbf) of real values, where each entry is in the range (0, 1, and all the entries add up to 1. The function is given by In probability theory, the output of the softmax function can be used to represent a categorical distribution – that is, a probability distribution over different possible outcomes. In fact, it is the gradient-log-normalizer of the categorical probability distribution. The softmax function is also the gradient of the LogSumExp function. The softmax function is used in various multiclass classification methods, such as multinomial logistic regression (also known as softmax regression), multiclass linear discriminant analysis, naive Bayes classifiers, and artificial neural networks. Specifically, in multinomial logistic regression and linear discriminant analysis, the input to the function is the result of distinct linear functions, and the predicted probability for the 'th class given a sample vector and a weighting vector is: This can be seen as the composition of linear functions \mathbf \mapsto \mathbf^\mathsf\mathbf_1, \ldots, \mathbf \mapsto \mathbf^\mathsf\mathbf_K and the softmax function (where \mathbf^\mathsf\mathbf denotes the inner product of \mathbf and \mathbf). The operation is equivalent to applying a linear operator defined by \mathbf to vectors \mathbf, thus transforming the original, probably highly-dimensional, input to vectors in a -dimensional space \mathbb^K.
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Thin plate spline
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Trace (linear algebra)
In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.
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Transformation (function)
In mathematics, particularly in semigroup theory, a transformation is a function f that maps a set X to itself, i.e..
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Translation (geometry)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.
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3D scanner
A 3D scanner is a device that analyses a real-world object or environment to collect data on its shape and possibly its appearance (e.g. colour).
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References
[1] https://en.wikipedia.org/wiki/Point_set_registration
