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Tensor related to gradients
In mathematics, the structure tensor, also referred to as the second-moment matrix, is a matrix derived from the gradient of a function. It describes the
Structure_tensor
In image analysis, the generalized structure tensor (GST) is an extension of the Cartesian structure tensor to curvilinear coordinates. It is mainly used
Generalized_structure_tensor
Image edge detection algorithm
Hough transform Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection
Sobel_operator
Algebraic object with geometric applications
(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, etc.), and general relativity (stress–energy tensor, curvature tensor, etc.). In
Tensor
Topics referred to by the same term
theory General strain theory, in sociology General systems theory Generalized structure tensor Global surface temperature Glutathione S-transferase, an enzyme
GST
Piece of information about the content of an image
There are other representations of edge orientation, such as the structure tensor, which are averageable. Another example relates to motion, where in
Feature_(computer_vision)
Image edge detection algorithm
Hough transform Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection
Canny_edge_detector
Discrete differentiation operator used in image processing
Hough transform Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection
Prewitt_operator
Method of detecting shapes within images
was invented by Richard Duda and Peter Hart in 1972, who called it a "generalized Hough transform" after the related 1962 patent of Paul Hough. The transform
Hough_transform
Feature detection algorithm in computer vision
with bundle adjustment initialized from an essential matrix or trifocal tensor to build a sparse 3D model of the viewed scene and to simultaneously recover
Scale-invariant feature transform
Scale-invariant_feature_transform
Image processing method
Hough transform Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection
Edge_detection
Feature descriptor used in computer vision
C-HOG descriptor blocks against generalized Haar wavelets, PCA-SIFT descriptors, and shape context descriptors. Generalized Haar wavelets are oriented Haar
Histogram of oriented gradients
Histogram_of_oriented_gradients
Smooth manifold
complex structure. Given any linear map A on each tangent space of M; i.e., A is a tensor field of rank (1, 1), then the Nijenhuis tensor is a tensor field
Almost_complex_manifold
Particular task in computer vision
detector PCBR Lindeberg, Tony (June 2013). "Scale Selection Properties of Generalized Scale-Space Interest Point Detectors". Journal of Mathematical Imaging
Blob_detection
Analog of the continuous Laplace operator
over-sampled. Thereby, such non-linear operators e.g. Structure Tensor, and Generalized Structure Tensor which are used in pattern recognition for their total
Discrete_Laplace_operator
Type of monoidal category
collection of tensors. There are several equivalent alternative ways of defining modular tensor categories. One definition is as follows: a modular tensor category
Modular_tensor_category
Mathematical model for describing material deformation under stress
deformation tensors. In 1839, George Green introduced a deformation tensor known as the right Cauchy–Green deformation tensor or Green's deformation tensor (the
Finite_strain_theory
Property of a differential manifold that includes complex structures
generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure.
Generalized_complex_structure
Circle finding technique used in digital image processing
falsely because many quite different structures correspond to a single bucket. Too fine a grid can lead to structures not being found because votes resulting
Circle_Hough_Transform
Tensor in differential geometry
converge. Formally, it is a symmetric rank-two tensor obtained by taking a trace of the Riemann curvature tensor of a Riemannian or pseudo-Riemannian metric
Ricci_curvature
\{b-a\})\mapsto \{c-b+b-a\}} The tensor operation is a ⊗ b = a + b {\displaystyle a\otimes b=a+b} . This category structure is equivalent to one obtained
Generalized_metric_space
Object in differential geometry
differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input vectors
Torsion_tensor
Tensor index notation for tensor-based calculations
notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern
Ricci_calculus
Technique used in image processing and computer vision for edge detection
Hough transform Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection
Roberts_cross
Graphical notation for multilinear algebra calculations
essentially the composition of functions. In the language of tensor algebra, a particular tensor is associated with a particular shape with many lines projecting
Penrose_graphical_notation
in estimation of 3-D depth cues from affine distortions of local 2-D structure". Image and Vision Computing. 15 (6): 415–434. doi:10.1016/S0262-8856(97)01144-X
Hessian affine region detector
Hessian_affine_region_detector
Modification using the principle of template matching
The generalized Hough transform (GHT), introduced by Dana H. Ballard in 1981, is the modification of the Hough transform using the principle of template
Generalised_Hough_transform
Type of multi-scale signal representation
Gaussian and Laplacian image pyramids and Chapter 3 for theory about generalized binomial kernels and discrete Gaussian kernels) Lindeberg, T. and Bretzner
Pyramid_(image_processing)
Mathematical operation on vector spaces
two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span V ⊗ W {\displaystyle V\otimes W} in the sense
Tensor_product
Statistics models class
In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth
Generalized_additive_model
Topical guide to object recognition
detection Primal sketch Marr, Mohan and Nevatia Lowe Olivier Faugeras Generalized cylinders (Thomas Binford) Geons (Irving Biederman) Dickinson, Forsyth
Outline_of_object_recognition
Robust local feature detector
account the discrete nature of integral images and the specific filter structure. This results in filters of size 9×9, 15×15, 21×21, 27×27,.... Non-maximum
Speeded_up_robust_features
Tensor operator generalizes the notion of operators which are scalars and vectors
represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two
Tensor_operator
Operation in mathematics
In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. This example
Tensor_contraction
Approach used in computer vision systems
{\begin{bmatrix}x&y\end{bmatrix}}A{\begin{bmatrix}x\\y\end{bmatrix}},} where A is the structure tensor, A = ∑ u ∑ v w ( u , v ) [ I x ( u , v ) 2 I x ( u , v ) I y ( u ,
Corner_detection
Process in algebra
In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting
Tensor_decomposition
are known. Given at least two matching features, a multi-view affine structure from motion algorithm (see [Tomasi and Kanade 1992]) can be used to construct
3D_object_recognition
Feature detection and description computer vision algorithm
Hough transform Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection
Oriented FAST and rotated BRIEF
Oriented_FAST_and_rotated_BRIEF
the 2D discrete structure tensor matrix at each image pixel and flagging a pixel as a corner when the eigenvalues of its structure tensor are sufficiently
Chessboard_detection
Calculus of vector-valued functions
(p,q)} tensor can be formed by taking a tensor product of a ( p , 0 ) {\displaystyle (p,0)} tensor and a ( 0 , q ) {\displaystyle (0,q)} tensor, which
Vector_calculus
Differential operator in mathematics
any tensor field T {\displaystyle \mathbf {T} } ("tensor" includes scalar and vector) is defined as the divergence of the gradient of the tensor: ∇ 2
Laplace_operator
Edge detection operator
Hough transform Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection
Deriche_edge_detector
Blob detection technique
Multi-scale detection without any smoothing involved, both fine and large structure is detected. Note, however, that detection of MSERs in a scale pyramid
Maximally stable extremal regions
Maximally_stable_extremal_regions
Instantaneous rate of change of the function
quantity of a material element in a velocity field Structure tensor – Tensor related to gradients Tensor derivative (continuum mechanics) Total derivative –
Directional_derivative
Statement relating differentiable symmetries to conserved quantities
may differ from the symmetric tensor used as the source term in general relativity; see Canonical stress–energy tensor.) II. The electric charge The conservation
Noether's_theorem
Theory in physics with scalars and tensors both describing a force or interaction
In theoretical physics, a scalar–tensor theory is a field theory that includes both a scalar field and a tensor field to represent a certain interaction
Scalar–tensor_theory
Differentiable manifold with nondegenerate metric tensor
T_{p}M} . Given a metric tensor g on an n-dimensional real manifold, the quadratic form q(x) = g(x, x) associated with the metric tensor applied to each vector
Pseudo-Riemannian_manifold
mathematical structures, namely: a family of state spaces, each of which represents a physical system; a composition rule (usually corresponds to a tensor product)
Generalized probabilistic theory
Generalized_probabilistic_theory
Assignment of a tensor continuously varying across a region of space
In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space
Tensor_field
Universal construction in multilinear algebra
the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any order) with multiplication being the tensor product
Tensor_algebra
Machine learning software library
application-grade library, which became TensorFlow. In 2009, the team, led by Geoffrey Hinton, had implemented generalized backpropagation and other improvements
TensorFlow
Method of utilizing water in magnetic resonance imaging
more gradient directions, sufficient to compute the diffusion tensor. The diffusion tensor model is a rather simple model of the diffusion process, assuming
Diffusion-weighted magnetic resonance imaging
Diffusion-weighted_magnetic_resonance_imaging
Vector satisfying some of the criteria of an eigenvector
linearly independent generalized eigenvectors which form a basis for an invariant subspace of V {\displaystyle V} . Using generalized eigenvectors, a set
Generalized_eigenvector
Algorithm to detect local features in images
)\right\}\end{aligned}}} 2. the smaller eigenvalue of the structure tensor M ( p , α , τ , σ ) ⏟ structure tensor = G σ ( p ) ⏟ weighted summation ∗ ( R σ ∇ τ ∇
Scale-invariant feature operator
Scale-invariant_feature_operator
Class of mathematical software
similar to MATLAB and GNU Octave, but designed specifically for tensors. Tensor is a tensor package written for the Mathematica system. It provides many
Tensor_software
Mathematical operation on vectors in 3D space
seen as the (1,2)-tensor (a mixed tensor, specifically a bilinear map) obtained from the 3-dimensional volume form, a (0,3)-tensor, by raising an index
Cross_product
Theoretical attempts to unify the forces of nature
making the metric tensor (which had previously been assumed to be symmetric and real-valued) into an asymmetric and/or complex-valued tensor, and they also
Classical unified field theories
Classical_unified_field_theories
Non-tensorial representation of the spin group
distinguished from the tensor representations given by Weyl's construction by the weights. Whereas the weights of the tensor representations are integer
Spinor
Force needed to pull a spring grows linearly with distance
is a fourth-order tensor (that is, a linear map between second-order tensors) usually called the stiffness tensor or elasticity tensor. One may also write
Hooke's_law
Array of numbers describing a metric connection
corresponding gravitational potential being the metric tensor. When the coordinate system and the metric tensor share some symmetry, many of the Γijk are zero
Christoffel_symbols
smoothing kernels in an affine group of smoothing kernels to the local image structure in neighbourhood region of a specific image point. Equivalently, affine
Affine_shape_adaptation
Theory of gravitation as curved spacetime
stress–energy tensor, which includes both energy and momentum densities as well as stress: pressure and shear. Using the equivalence principle, this tensor is readily
General_relativity
Statement about integration on manifolds
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called
Generalized_Stokes_theorem
Formulation of classical mechanics using momenta
mechanics replaces (generalized) velocities q ˙ i {\displaystyle {\dot {q}}^{i}} used in Lagrangian mechanics with (generalized) momenta. Both theories
Hamiltonian_mechanics
Ring that is also a vector space or a module
category of R-algebras. Tensor products The tensor product of two R-algebras is also an R-algebra in a natural way. See tensor product of algebras for
Associative_algebra
Model of hadrons
to all major PDF sets. Generalized parton distributions (GPDs) are a more recent approach to better understand hadron structure by representing the parton
Parton_(particle_physics)
Physical quantities taking values at each point in space and time
example of a vector field. Strain tensor, representing the deformation of matter caused by stress, is an example of a tensor field. Field theories, mathematical
Field_(physics)
Mathematical description of spacetime used in relativity
provide a basis for the cotangent space at p. The tensor product (denoted by the symbol ⊗) yields a tensor field of type (0, 2), i.e. the type that expects
Minkowski_spacetime
Non-uniformity of a diffusion process
quantitative-diffusion-tensor MRI". Journal of Magnetic Resonance, Series B, 111, 209-219. Özarslan, E. Vemuri, B.C. & Mareci, T. H. (2005). "Generalized scalar measures
Fractional_anisotropy
Broad concept generalizing scalars in mathematics and physics
quantities are a generalization of scalar quantities and can be further generalized as tensor quantities. Individual vectors may be ordered in a sequence over
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Infinite sum
University Press. ISBN 0-521-29882-2. Ryan, Raymond (2002). Introduction to tensor products of Banach spaces. London New York: Springer. ISBN 1-85233-437-1
Series_(mathematics)
Manifold upon which it is possible to perform calculus
than tensors, but his equations for electromagnetism were used as an early example of the tensor formalism; see Dimitrienko, Yuriy I. (2002), Tensor Analysis
Differentiable_manifold
Function in image processing
1-dimensional locus, or a ridge curve. Notice that the above can be modified to generalize the idea to local minima and result in what might call 1-dimensional valley
Ridge_detection
Type of derivative in mathematics
line approximation. In multivariable calculus, the same property is generalized to define the derivative of a vector-valued function or function of a
Derivative (multivariable calculus)
Derivative_(multivariable_calculus)
Type of derivative in differential geometry
differentiable manifold. Functions, tensor fields and forms can be differentiated with respect to a vector field. If T is a tensor field and X is a vector field
Lie_derivative
Method of mathematical integration
comparatively restrictive. Furthermore, the Lebesgue integral can be generalized in a straightforward way to more general spaces, measure spaces, such
Lebesgue_integral
Monster and modular connection
Ryba's conjecture should generalize to Tate cohomology of composite order elements, and the nature of any connections to generalized moonshine and other moonshine
Monstrous_moonshine
Classical field theory describing gravitation
torsion tensor T a b c = − 2 b a μ D [ b h c ] μ {\displaystyle {\mathcal {T}}^{a}{}_{bc}=-2b^{a}{}_{\mu }D_{[b}h_{c]}{}^{\mu }} curvature tensor R a b
Poincaré_gauge_theory
Generalization of vector spaces from fields to rings
smooth vector fields defined on X forms a module over C∞(X), and so do the tensor fields and the differential forms on X. More generally, the sections of
Module_(mathematics)
Application of Lagrangian mechanics to field theories
generalized for vector fields, tensor fields, and spinor fields. In physics, fermions are described by spinor fields. Bosons are described by tensor fields
Lagrangian_(field_theory)
invariant saliency detector it also has the drawback of favoring isotropic structure, since the discriminative measure W D {\displaystyle W_{D}} is measured
Kadir–Brady_saliency_detector
Theorem in mathematics
is a local diffeomorphism. The inverse function theorem can also be generalized to differentiable maps between Banach spaces X and Y. Let U be an open
Inverse_function_theorem
Fundamental construction of differential calculus
has near a point. The Lie derivative is the rate of change of a vector or tensor field along the flow of another vector field. On vector fields, it is an
Generalizations of the derivative
Generalizations_of_the_derivative
manifold Tensor analysis Tangent vector Tangent space Tangent bundle Cotangent space Cotangent bundle Tensor Tensor bundle Vector field Tensor field Differential
List of differential geometry topics
List_of_differential_geometry_topics
Algebraic structure used in topology
this gives the notion of a generalized homology theory or a generalized cohomology theory, defined below. There are generalized cohomology theories such
Cohomology
Operation in algebra and mathematics
space V {\displaystyle V} to its tensor algebra T ( V ) {\displaystyle T(V)} , and which maps linear maps to their tensor product. We then have a natural
Monad_(category_theory)
Operator generalizing the Laplacian in differential geometry
Hessian tensor. Because the covariant derivative extends canonically to arbitrary tensors, the Laplace–Beltrami operator defined on a tensor T by Δ T
Laplace–Beltrami_operator
Generalization of the product rule in calculus
{2}{k}}f^{(2-k)}(x)g^{(k)}(x)}=f''(x)g(x)+2f'(x)g'(x)+f(x)g''(x).} The formula can be generalized to the product of m differentiable functions f1,...,fm. ( f 1 f 2 ⋯ f
General_Leibniz_rule
Operation in mathematical calculus
infinitesimally thin vertical slabs. In the early 20th century, Henri Lebesgue generalized Riemann's formulation by introducing what is now referred to as the Lebesgue
Integral
Algebra based on a vector space with a quadratic form
algebra generated by V may be written as the tensor algebra ⨁n≥0 V ⊗ ⋯ ⊗ V, that is, the direct sum of the tensor product of n copies of V over all n. Therefore
Clifford_algebra
Branch of mathematics
where N J {\displaystyle N_{J}} is a tensor of type (2, 1) related to J {\displaystyle J} , called the Nijenhuis tensor (or sometimes the torsion). An almost
Differential_geometry
References Tensor algebra, Tensor analysis, Tensor calculus, Tensor theory the study and use of tensors, which are generalizations of vectors. A tensor algebra
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Quantum field theory enjoying conformal symmetry
involve several independent tensor structures, the structure constants and conformal blocks depend on these tensor structures, and the primary field O p
Conformal_field_theory
Relationship between derivatives and integrals
by James Gregory (1638–1675). Isaac Barrow (1630–1677) proved a more generalized version of the theorem, while his student Isaac Newton (1642–1727) completed
Fundamental theorem of calculus
Fundamental_theorem_of_calculus
Physical quantity that is a vector
quantities are a generalization of scalar quantities and can be further generalized as tensor quantities. Individual vectors may be ordered in a sequence over
Vector_quantity
Algebra associated to any vector space
algebra) inherits a bialgebra structure, and, indeed, a Hopf algebra structure, from the tensor algebra. See the article on tensor algebras for a detailed treatment
Exterior_algebra
Supergeometric generalization of a manifold
smooth supermanifold is a locally ringed space whose structure sheaf is locally isomorphic to the tensor product of the ring of ordinary smooth functions
Supermanifold
typically be classified into two categories: intensity-based detectors and structure-based detectors. Intensity-based detectors depend on analyzing local differential
Principal curvature-based region detector
Principal_curvature-based_region_detector
Tensor in general relativity
In mathematics, a Killing tensor or Killing tensor field is a generalization of a Killing vector, for symmetric tensor fields instead of just vector fields
Killing_tensor
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
inertia tensor of a body calculated at its center of mass, and R {\displaystyle \mathbf {R} } be the displacement vector of the body. The inertia tensor of
Moment_of_inertia
GENERALIZED STRUCTURE-TENSOR
GENERALIZED STRUCTURE-TENSOR
Girl/Female
Hindu, Indian, Telugu
The Structure of God
Girl/Female
Indian
Shape, Structure
Boy/Male
Afghan, Arabic, Gujarati, Indian, Muslim
Solid Structure; Lifetime
Girl/Female
Indian
Structure
Boy/Male
Muslim
Solid structure
Girl/Female
Tamil
Shape, Structure
Boy/Male
Indian
Good Structure
Girl/Female
Indian
Shape, Structure
Girl/Female
Tamil
Shape, Structure
Surname or Lastname
English
English : status name from Middle English squyer ‘esquire’, ‘a man belonging to the feudal rank immediately below that of knight’ (from Old French esquier ‘shield bearer’). At first it denoted a young man of good birth attendant on a knight, or by extension any attendant or servant, but by the 14th century the meaning had been generalized, and referred to social status rather than age. By the 17th century, the term denoted any member of the landed gentry, but this is unlikely to have influenced the development of the surname.
Boy/Male
Indian
Solid structure
Surname or Lastname
English
English : occupational name for a wattler, Middle English watelere, i.e. someone who made the panels of interwoven twigs that were used to fill the spaces between the structural timbers of a timber frame building. See also Dauber.
Girl/Female
Indian, Kashmiri
Body Structure
GENERALIZED STRUCTURE-TENSOR
GENERALIZED STRUCTURE-TENSOR
Girl/Female
Indian, Sanskrit, Telugu
Beneficial; Suitable; Friendly
Girl/Female
Indian
Praise, Lauding
Surname or Lastname
English
English : regional name for someone from the French province of Artois, from Anglo-Norman French Arteis (from Latin Atrebates, the name of the local Gaulish tribe).French : from Old French artis ‘woodworm’, Old Occitan arta ‘moth’, possibly applied as a nickname for someone suffering from a wasting disease, perhaps leprosy.
Girl/Female
Australian, Finnish
Guest; Stranger
Girl/Female
Tamil
Prinaka | பà¯à®°à®¿à®¨à®¾à®•à®¾
Girl who brings heaven to earth
Surname or Lastname
English (Kent)
English (Kent) : habitational name, probably from a lost place, Holmherst in Smarden, Kent; Holnest in Dorset is another possibility. Both are named from Old English holegn ‘holly’ + Old English hyrst ‘wooded hill’.English (Kent) : reduced form of Holderness.
Boy/Male
Tamil
Lakshmana | லகà¯à®·à¯à®®à®£à®¾
Reviver of lakshmanas life
Boy/Male
Hindu
The first drop of nature water, The Moon, White
Boy/Male
Hindu, Indian
Place of Lord Shiva
Biblical
the new city
GENERALIZED STRUCTURE-TENSOR
GENERALIZED STRUCTURE-TENSOR
GENERALIZED STRUCTURE-TENSOR
GENERALIZED STRUCTURE-TENSOR
GENERALIZED STRUCTURE-TENSOR
v. t.
To apply to other genera or classes; to use with a more extensive application; to extend so as to include all special cases; to make universal in application, as a formula or rule.
n.
A generalized concept of magnitude.
a.
Comprising structural characters which are separated in more specialized forms; synthetic; as, a generalized type.
n.
Manner of organization; the arrangement of the different tissues or parts of animal and vegetable organisms; as, organic structure, or the structure of animals and plants; cellular structure.
v. i.
To form into a genus; to view objects in their relations to a genus or class; to take general or comprehensive views.
v. t.
To derive or deduce (a general conception, or a general principle) from particulars.
n.
That which is built; a building; esp., a building of some size or magnificence; an edifice.
n.
Manner of building; form; make; construction.
imp. & p. p.
of Generalize
v. t.
To bring under a genus or under genera; to view in relation to a genus or to genera.
a.
Of or pertaining to organit structure; as, a structural element or cell; the structural peculiarities of an animal or a plant.
n.
Arrangement of parts, of organs, or of constituent particles, in a substance or body; as, the structure of a rock or a mineral; the structure of a sentence.
n.
The act of building; the practice of erecting buildings; construction.
a.
Having a definite organic structure; showing differentiation of parts.
p. pr. & vb. n.
of Generalize
v. t.
To make universal; to generalize.
n.
A localized morbid contraction of any passage of the body. Cf. Organic stricture, and Spasmodic stricture, under Organic, and Spasmodic.
a.
Of or pertaining to structure; affecting structure; as, a structural error.
n.
One who takes general or comprehensive views.
a.
Affected with a stricture; as, a strictured duct.