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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
Algebraic object with geometric applications
(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, etc.), and general relativity (stress–energy tensor, curvature tensor, etc.). In
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
Computer vision algorithm
y\end{pmatrix}}M{\begin{pmatrix}\Delta x\\\Delta y\end{pmatrix}},} where M is the structure tensor, M = ∑ ( x , y ) ∈ W [ I x 2 I x I y I x I y I y 2 ] = [ ∑ ( x , y
Harris_corner_detector
Tensor that describes the 4D geometry of spacetime
manifold M {\displaystyle M} and the metric tensor is given as a covariant, second-degree, symmetric tensor on M {\displaystyle M} , conventionally denoted
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
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
Structure defining distance on a manifold
metric field on M consists of a metric tensor at each point p of M that varies smoothly with p. A metric tensor g is positive-definite if g ( v , v ) >
Metric_tensor
Concept in machine learning
learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data
Tensor_(machine_learning)
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
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
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
Image edge detection algorithm
Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection Affine shape
Sobel_operator
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
Image edge detection algorithm
Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection Affine shape
Canny_edge_detector
Method of detecting shapes within images
Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection Affine shape
Hough_transform
Image processing method
Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection Affine shape
Edge_detection
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
Mathematical wave functions
Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems and fluids. Tensor networks
Tensor_network
Type of multi-scale signal representation
Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection Affine shape
Pyramid_(image_processing)
Signal processing technique
}\otimes \nabla I_{\sigma })} refers to the tensor product obtained by using this gradient. The structure tensor obtained is convolved with a Gaussian kernel
Compressed_sensing
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
Muscle of the thigh
The tensor fasciae latae (or tensor fasciæ latæ or, formerly, tensor vaginae femoris) is a muscle of the thigh. Together with the gluteus maximus, it acts
Tensor_fasciae_latae_muscle
Measure of the curvature of a pseudo-Riemannian manifold
Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic. The Weyl tensor differs from the Riemann
Weyl_tensor
Concept in mathematics
In mathematics, the tensor bundle of a manifold is the direct sum of all tensor products of the tangent bundle and the cotangent bundle of that manifold
Tensor_bundle
Feature descriptor used in computer vision
resulting gradient field HOG (GF-HOG) descriptor captured local spatial structure in sketches or image edge maps. This enabled the descriptor to be used
Histogram of oriented gradients
Histogram_of_oriented_gradients
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
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
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
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
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
Tensor operator generalizes the notion of operators which are scalars and vectors
graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which
Tensor_operator
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)
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
Operation that pairs a left and a right R-module into an abelian group
universal property of the tensor product of vector spaces extends to more general situations in abstract algebra. The tensor product of an algebra and
Tensor_product_of_modules
Particular task in computer vision
is strongly dependent on the relationship between the size of the blob structures in the image domain and the size of the Gaussian kernel used for pre-smoothing
Blob_detection
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
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
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
Field-equations in general relativity
Einstein in 1915 in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum
Einstein_field_equations
Physical quantity that expresses internal forces in a continuous material
the first and second Piola–Kirchhoff stress tensors, the Biot stress tensor, and the Kirchhoff stress tensor. Bending Compressive strength Critical plane
Stress_(mechanics)
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
in 1959, and the lamp was commercialized in 1960 by the Tensor Corporation. The first Tensor lamp consisted of a 12-volt automobile light bulb and a reflector
Tensor_lamp
Machine learning software library
May 2019, Google announced TensorFlow Graphics for deep learning in computer graphics. In May 2016, Google announced its Tensor processing unit (TPU), an
TensorFlow
Muscle of the middle ear
stapedius. The tensor tympani is supplied by the tensor tympani nerve, a branch of the mandibular branch of the trigeminal nerve. As the tensor tympani is
Tensor_tympani_muscle
Tensor used in continuum mechanics
The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed
Viscous_stress_tensor
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
Ring produced from two fields
In mathematics, the tensor product of two fields is their tensor product as algebras over a common subfield. If no subfield is explicitly specified, the
Tensor_product_of_fields
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
Second-order tensor
In Riemannian geometry the Schouten tensor is a second-order tensor introduced by Jan Arnoldus Schouten defined for n ≥ 3 by: P = 1 n − 2 ( R i c − R
Schouten_tensor
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 structure in atomic physics
3-dimensional rank-2 tensor, the quadrupole moment has 32 = 9 components. From the definition of the components it is clear that the quadrupole tensor is a symmetric
Hyperfine_structure
various mathematical structures and techniques are utilized. The main tools used in this geometrical theory of gravitation are tensor fields defined on a
Mathematics of general relativity
Mathematics_of_general_relativity
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
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
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
Image noise reducing technique
is a function of image position and assumes a matrix (or tensor) value (see structure tensor). Although the resulting family of images can be described
Anisotropic_diffusion
additional structures on the modular tensor category. On the level of skeletonization, a unitary modular tensor category has the same structure as a modular
Unitary modular tensor category
Unitary_modular_tensor_category
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
Computer vision technique for optical flow estimation
{\displaystyle n} . The matrix A T A {\displaystyle A^{T}A} is often called the structure tensor of the image at the point p {\displaystyle p} . The plain least squares
Lucas–Kanade_method
Concept in mathematics
In mathematics, the tensor-hom adjunction is the statement that the tensor product − ⊗ X {\displaystyle -\otimes X} and hom-functor Hom ( X , − ) {\displaystyle
Tensor–hom_adjunction
Tensor product of algebras over a field; itself another algebra
In mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra. This gives the tensor product of algebras. When the
Tensor_product_of_algebras
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
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
Topics referred to by the same term
General strain theory, in sociology General systems theory Generalized structure tensor Global surface temperature Glutathione S-transferase, an enzyme family
GST
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
Thigh muscle
lateralis. The term tensor vastus intermedius was given by Grob et al. in 2016, although the structure had been reported previously. The tensor vastus intermedius
Tensor vastus intermedius muscle
Tensor_vastus_intermedius_muscle
Topical guide to object recognition
010. Jung, Ho Gi; Kim, Dong Suk; Yoon, Pal Joo; Kim, Jaihie (2006). "Structure Analysis Based Parking Slot Marking Recognition for Semi-automatic Parking
Outline_of_object_recognition
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
Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection Affine shape
GLOH
Object in differential geometry
The contorsion tensor (or contortion tensor) in differential geometry is the difference between a connection with and without torsion in it. It commonly
Contorsion_tensor
Equation that describes density changes of a material that is diffusing in a medium
obtains the random walk. The product rule is used to rewrite the anisotropic tensor diffusion equation, in standard discretization schemes, because direct discretization
Diffusion_equation
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
Tensor product space endowed with a special inner product
analysis, the tensor product of Hilbert spaces is a way to extend the tensor product construction so that the result of taking a tensor product of two
Tensor product of Hilbert spaces
Tensor_product_of_Hilbert_spaces
Gradient whose components are spatial derivatives
rate Grade (slope) Image gradient Time derivative Material derivative Structure tensor Surface gradient Kreyszig, E. (1999). Advanced Engineering Mathematics
Spatial_gradient
Branch of mathematics
various areas, including: Classical treatment of tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket notation Multilinear subspace learning
Multilinear_algebra
Muscle of the soft palate
The tensor veli palatini muscle (tensor palati or tensor muscle of the velum palatinum) is a thin, triangular muscle of the head that tenses the soft palate
Tensor_veli_palatini_muscle
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
Operation in graph theory
nowadays more commonly refers to the tensor product. The cross symbol shows visually the two edges resulting from the tensor product of two edges. This product
Tensor_product_of_graphs
Modification using the principle of template matching
this approach unfeasible for most cases. If the shape S has a composite structure consisting of subparts S1, S2, .. SN and the reference points for the
Generalised_Hough_transform
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
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
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 constructing an image from multiple viewpoints
In computer vision, the trifocal tensor (also tritensor) is a 3×3×3 array of numbers (i.e., a tensor) that incorporates all projective geometric relationships
Trifocal_tensor
Algorithm for reducing the dimension of tensors
algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such a
Tensor_sketch
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)
Expression of time reference in grammar
In grammar, tense is a category that expresses time reference. Tenses are usually manifested by the use of specific forms of verbs, particularly in their
Grammatical_tense
Hough transform Generalized Hough transform Structure tensor Structure tensor Generalized structure tensor Affine invariant feature detection Affine shape
Robinson_compass_mask
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
Term in differential geometry
curvature tensor, i.e. R ( X , Y ) = Ω ( X , Y ) , {\displaystyle \,R(X,Y)=\Omega (X,Y),} using the standard notation for the Riemannian curvature tensor. If
Curvature_form
Mathematical model for describing material deformation under stress
tensors used in finite strain theory, e.g. the Lagrangian finite strain tensor E {\displaystyle \mathbf {E} } , and the Eulerian finite strain tensor
Infinitesimal_strain_theory
Physical property that measures stiffness of material
materials. These constants form the elements of the stiffness matrix in tensor notation, which relates stress to strain through linear equations in anisotropic
Elastic_modulus
Sub-branch of Optical Physics
the relative permittivity tensor or dielectric tensor. Consequently, the refractive index of the medium must also be a tensor. Consider a light wave propagating
Crystal_optics
Tense used in the Latin language
The main Latin tenses can be divided into two groups: the present system (also known as infectum tenses), consisting of the present, future, and imperfect;
Latin_tenses
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
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
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
Branch of mathematics
Representation theory – Branch of mathematics that studies abstract algebraic structures Tensor – Algebraic object with geometric applications When understood in
Algebra
mathematics and physics, a recurrent tensor, with respect to a connection ∇ {\displaystyle \nabla } on a manifold M, is a tensor T for which there is a one-form
Recurrent_tensor
Associative algebra together with a Lie bracket that satisfies Leibniz's law
the tensor algebra of the underlying vector space of the Lie algebra. The tensor algebra is simply the disjoint union (direct sum ⊕) of all tensor products
Poisson_algebra
Second-rank tensor in quantum chromodynamics
In theoretical particle physics, the gluon field strength tensor is a second-order tensor field characterizing the gluon interaction between quarks. The
Gluon_field_strength_tensor
STRUCTURE TENSOR
STRUCTURE TENSOR
Boy/Male
Indian
Solid structure
Girl/Female
Indian
Shape, Structure
Girl/Female
Hindu, Indian, Telugu
The Structure of God
Girl/Female
Indian
Shape, 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
Boy/Male
Afghan, Arabic, Gujarati, Indian, Muslim
Solid Structure; Lifetime
Boy/Male
Muslim
Solid structure
Girl/Female
Indian
Structure
Girl/Female
Tamil
Shape, Structure
Girl/Female
Tamil
Shape, Structure
Boy/Male
Indian
Good Structure
STRUCTURE TENSOR
STRUCTURE TENSOR
Girl/Female
Arabic
Queen of Arab
Girl/Female
Indian, Marathi
Close to Heart
Boy/Male
Hindu
Cloud, God
Boy/Male
Anglo Saxon
Name of a king.
Girl/Female
English
A well-established compound of Jo-.
Girl/Female
Tamil
Lady
Boy/Male
Indian
Adorable; New Part
Surname or Lastname
Greek and Turkish
Greek and Turkish : nickname for a rich man, from Turkish gani ‘rich’, of Arabic origin.English : unexplained.
Biblical
basis; foundation; the Lord
Boy/Male
Hindu
Lord Shiva, The cosmic serpent Shesh
STRUCTURE TENSOR
STRUCTURE TENSOR
STRUCTURE TENSOR
STRUCTURE TENSOR
STRUCTURE TENSOR
a.
Of or pertaining to structure; affecting structure; as, a structural error.
n.
A stria.
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.
n.
Union of parts; structure.
n.
Strictness.
a.
Affected with a stricture; as, a strictured duct.
a.
Having a definite organic structure; showing differentiation of parts.
n.
A touch of adverse criticism; censure.
a.
Of or pertaining to organit structure; as, a structural element or cell; the structural peculiarities of an animal or a plant.
n.
The act of building; the practice of erecting buildings; construction.
n.
Composition, or structure.
n.
That which is built; a building; esp., a building of some size or magnificence; an edifice.
n.
Framework; structure; edifice; building.
a.
Of lofty structure; tall.
n.
Manner of building; form; make; construction.
a.
Resembling shale in structure.
n.
A stroke; a glance; a touch.
n.
A localized morbid contraction of any passage of the body. Cf. Organic stricture, and Spasmodic stricture, under Organic, and Spasmodic.
n.
Organic structure; organization.
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.