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Derived representation of a digital image
A distance transform, also known as distance map or distance field, is a derived representation of a digital image. The choice of the term depends on the
Distance_transform
of transforms in mathematics. Abel transform Aboodh transform Bateman transform Fourier transform Fourier cosine transform Fourier sine transform Fractional
List_of_transforms
Mathematical transform that expresses a function of time as a function of frequency
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent
Fourier_transform
String metric for measuring edit distance
substitutions—required to transform one string into the other. Each edit has unit cost in the classical definition. The distance is named after Soviet mathematician
Levenshtein_distance
Integral transform used in various branches of mathematics
Abel transform is the integrated absorbance along a ray with closest distance y from the center of the flame, while the inverse Abel transform gives
Abel_transform
Class of algorithms used for computing distance-related functions
flooding algorithm used in the construction of Voronoi diagrams and distance transforms. The JFA was introduced by Rong Guodong at an ACM symposium in 2006
Jump_flooding_algorithm
Integral transform useful in probability theory, physics, and engineering
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable
Laplace_transform
Image comprising exactly two colors, typically black and white
binary image is the distance transform. This gives the distance of every set pixel from the nearest unset pixel. The distance transform can be efficiently
Binary_image
Plate boundary where the motion is predominantly horizontal
geological feature. Slip along transform faults does not increase the distance between the ridges it separates; the distance remains constant in earthquakes
Transform_fault
Integral transform in mathematics
In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional)
Radon_transform
Method of detecting shapes within images
The Hough transform (/hʌf/) is a feature extraction technique used in image analysis, computer vision, pattern recognition, and digital image processing
Hough_transform
In image processing, the grassfire transform is the computation of the distance from a pixel to the border of a region. It can be described as "setting
Grassfire_transform
Function in discrete mathematics
In mathematics, the discrete Fourier transform (DFT) is a discrete version of the Fourier transform that converts a finite sequence of numbers into another
Discrete_Fourier_transform
Integral transform and linear operator
In mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, u(t) of a real variable and produces
Hilbert_transform
Computer science metric of string similarity
counting the minimum number of operations required to transform one string into the other. Edit distances find applications in natural language processing
Edit_distance
Deals with digitized models or images of objects of the 2D or 3D Euclidean space
not change, or (ii) medial axis, by calculating local maxima in a distance transform of the given digitized object representation, or (B) into modified
Digital_geometry
Type of plane partition
(2006). "Jump flooding in GPU with applications to Voronoi diagram and distance transform" (PDF). In Olano, Marc; Séquin, Carlo H. (eds.). Proceedings of the
Voronoi_diagram
One-dimensional approximation to a shape
"locally maximum" in the distance transform. This is simply not the case, as even cursory comparison of a distance transform and the resulting skeleton
Topological_skeleton
Topics referred to by the same term
based on EDT (Digital) Sequential Euclidean distance transform, a distance transform using Euclidean distance, computed sequentially Single-ended double
SEDT
Number of bits that differ between two strings
number of errors that could have transformed one string into the other. In a more general context, the Hamming distance is one of several string metrics
Hamming_distance
Statistical distance measure
uncorrelated, then the Mahalanobis distance corresponds to standard Euclidean distance in the transformed space. The Mahalanobis distance is thus unitless, scale-invariant
Mahalanobis_distance
Integral transform
geometry, the Funk transform (also known as Minkowski–Funk transform, Funk–Radon transform or spherical Radon transform) is an integral transform defined by integrating
Funk_transform
Mathematical operation
In mathematics, the Hankel transform expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind
Hankel_transform
Programming algorithm
operations. Otherwise, the distance is the minimum of the three possible ways to do the transformation: If we can transform s[1..i] to t[1..j-1] in k operations
Wagner–Fischer_algorithm
Image processing method
operation are applied to the binary image to close gaps. Then, the distance transform operation is applied to the binary image to clear the pixels far from
Edge_detection
Flip distance in triangulations
computer science, the flip distance between two triangulations of the same point set is the number of flips required to transform one triangulation into another
Flip_distance
Integral transform
represented by the matrices [abcd]=[1λz01], where z is distance, and λ is wavelength. The Laplace transform corresponds to rotation by 90° into the complex domain
Linear canonical transformation
Linear_canonical_transformation
Family of functions to transform data
In statistics, a power transform is a family of functions applied to create a monotonic transformation of data using power functions. It is a data transformation
Power_transform
Type of image
close the small gaps. To clear the blob-like shapes, it utilizes the distance transform. After all, the connected pixel groups are individual edges (or contours)
Saliency_map
Software
Ground robots and includes: standard path planning algorithms (bug, distance transform, D*, and PRM), lattice planning, kinodynamic planning (RRT), localization
Robotics_Toolbox_for_MATLAB
scan Kirkpatrick–Seidel algorithm Quickhull Euclidean distance transform: computes the distance between every point in a grid and a discrete collection
List_of_algorithms
Statistical transformation
as |ρ| is not too large and N is not too small. The behavior of this transform has been extensively studied since Fisher introduced it in 1915. Fisher
Fisher_transformation
Swedish computer programmer
McGraw-Hill. p. 145. ISBN 9780078820625. Ingemar Ragnemalm, "The Euclidean Distance Transform", Dissertation No 304, Linköping University, 1993 Home page of Ingemar
Ingemar_Ragnemalm
Branch of computer science
scan Kirkpatrick–Seidel algorithm Quickhull Euclidean distance transform: computes the distance between every point in a grid and a discrete collection
Computational_geometry
Probability theory operation
distribution, Z=exp(−X) also has a uniform distribution. Inverse transform sampling Cramér distance Dodge, Y. (2006) The Oxford Dictionary of Statistical Terms
Probability integral transform
Probability_integral_transform
Formula for the great-circle distance between two points on a sphere
considerations do not apply to transforming the latitudes - adding a constant to the latitudes may change the distance between the points. By choosing
Haversine_formula
Distance between two statistical objects
probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables
Statistical_distance
Length in solid geometry
terms of the transformed variables. Now the problem has become one of finding the nearest point on this plane to the origin, and its distance from the origin
Distance from a point to a plane
Distance_from_a_point_to_a_plane
Real function on a Euclidean space whose value depends only on distance from the origin
each point depends only on the distance between that point and the origin. The distance is usually the Euclidean distance. For example, a radial function
Radial_function
Measure of similarity
Normalized compression distance (NCD) is a way of measuring the similarity between two objects, be it two documents, two letters, two emails, two music
Normalized compression distance
Normalized_compression_distance
resulting quadrilateral. The flip distance between two triangulations is the minimum number of flips needed to transform one triangulation into another.
Rotation_distance
Motion video technology
to the average viewer at the specified viewing distance, edge effects introduced by block-based transform processing still affect the performance advantage
ZPEG
Swedish image processing researcher
Swedish computer scientist specializing in image processing, including distance transforms, topological skeletonization, and edge detection. She is a professor
Gunilla_Borgefors
focus recovery are based on depth estimation theory. The Linear canonical transform (LCT) gives a scalable kernel to fit many well-known optical effects.
Focus recovery based on the linear canonical transform
Focus_recovery_based_on_the_linear_canonical_transform
Geometric transformation that preserves lines but not angles nor the origin
transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation is an automorphism
Affine_transformation
On distance sets of high-dimensional sets
(1987), "Spherical averages of Fourier transforms of measures with finite energy; dimension of intersections and distance sets", Mathematika, 34 (2): 207–228
Falconer's_conjecture
Information distance is the distance between two finite objects (represented as computer files) expressed as the number of bits in the shortest program
Information_distance
Measure of similarity between two graphs
Exact algorithms for computing the graph edit distance between a pair of graphs typically transform the problem into one of finding the minimum cost
Graph_edit_distance
Concept in physics
Action at a distance is the concept in physics that an object's motion can be affected by another object without the two being in physical contact; that
Action_at_a_distance
Development in distance education that began in the mid-1980s
courses. As theories of distance education evolve, digital technologies to support learning and pedagogy continue to transform as well. The first correspondence
Online learning in higher education
Online_learning_in_higher_education
Measure of linear correlation
location and scale in the two variables. That is, we may transform X to a + bX and transform Y to c + dY, where a, b, c, and d are constants with b, d
Pearson correlation coefficient
Pearson_correlation_coefficient
Mathematical transformation
In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface
Legendre_transformation
methods such as Fourier transform and DCT, the spectral distance is the measure to compare the transformed signals. LSD incorporates the logarithmic characteristics
Log-spectral_distance
Study of health and disease within a population
the forward-looking ability of modern risk management approaches that transform health risk factors, incidence, prevalence and mortality statistics (derived
Epidemiology
The Mojette transform is an application of discrete geometry. More specifically, it is a discrete and exact version of the Radon transform, thus a projection
Mojette_transform
Simple potential between quarks
potential consists of two parts. The first one, −43αsr dominate at short distances, typically for r<0.1 fm. It arises from the one-gluon exchange between
Cornell_potential
Function for integral Fourier-like transform
wavelet transform (SWT) Fractional Fourier transform (FRFT) Fractional wavelet transform (FRWT) There are a number of generalized transforms of which
Wavelet
Phase stretch transform (PST) is a computational approach to signal and image processing. One of its utilities is for feature detection and classification
Phase_stretch_transform
Example of census transform The census transform (CT) is an image operator that associates to each pixel of a grayscale image a binary string, encoding
Census_transform
Method of data analysis
analysis, visualization and data preprocessing. The data are linearly transformed onto a new coordinate system such that the directions (principal components)
Principal_component_analysis
interface – Direct manipulation interface – Disk storage – Distance transform – Distance map – Distance field – Docblock – DVD – DVI (TeX) – Dvorak keyboard
Index_of_computing_articles
Indian inventor and engineer (1893–1974)
innovator, inventor, industrialist, and educator. He redesigned and transformed imported technologies into practical and affordable innovations for India
G._D._Naidu
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
Curve for which the time to roll to the end is equal for all starting points
known, we can compute its Laplace transform, calculate the Laplace transform of dℓ/dy and then take the inverse transform (or try to) to find dℓ/dy. For
Tautochrone_curve
Near-field diffraction
where a is the characteristic size (e.g. radius) of the aperture, L is the distance of a screen (where the diffraction pattern is observed) from the aperture
Fresnel_diffraction
Feature detection algorithm in computer vision
The scale-invariant feature transform (SIFT) is a computer vision algorithm to detect, describe, and match local features in images, invented by David
Scale-invariant feature transform
Scale-invariant_feature_transform
Square matrix containing the distances between elements in a set
science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements
Distance_matrix
Style of human–computer interaction
Interfaces For The Visually Impaired Using Force Feedback Devices And Distance Transforms, Information Technology and Disabilities Journal, Vol. X, No. 2,
WIMP_(computing)
Mathematical function
Patterns Using Distance-Based Pattern Modeling, Mathematical Geosciences, 42: 487–517 Haberman, Richard (2013). "10.3.3 Inverse Fourier transform of a Gaussian"
Gaussian_function
Mathematical explanation of far field diffraction
distance r' from the origin is given by A(ρ′)=exp(−[ρ′σ]2) giving U(ρ,z)=2π∫0∞exp(−[ρ′σ]2)J0(2πρ′ρλz)ρ′dρ′ The Fourier–Bessel or Hankel transform is
Fraunhofer diffraction equation
Fraunhofer_diffraction_equation
Prolonged gaze or fixed look
such as staring into space, staring into the distance, staring at nothing, and staring into the middle distance describe looking outward wherein the apparent
Staring
Star at the centre of the Solar System
at a distance of 24,000 to 28,000 light-years. Its mean distance from Earth is about 1.496×108 kilometres or about 8 light-minutes. The distance between
Sun
Unit of information
they represent data. An analog computer represents a datum as a voltage, distance, position, or other physical quantity. A digital computer represents a
Data
Equation in statistical mechanics
colloidal particles. The pair correlation function is related via Fourier transform to the static structure factor, which can be determined experimentally
Ornstein–Zernike_equation
Global system of connected computer networks
television, paper mail, newspapers, and print publishing, have been transformed by the internet, giving rise to new media such as email, online music
Internet
American computer scientist
Felzenszwalb, Pedro F.; Huttenlocher, Daniel P. (September 2012). "Distance Transforms of Sampled Functions". Theory of Computing. 8 (19): 415–428. doi:10
Pedro_Felipe_Felzenszwalb
length f will produce the exact Fourier transform at a distance f behind the lens of an object placed f distance in front of the lens. So that complex amplitudes
Optical_correlator
Metric that measures the distance between two strings of text
deletions needed in order to transform one input string into another. Simplistic string metrics such as Levenshtein distance have expanded to include phonetic
String_metric
Classification algorithm
transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set
Whitening_transformation
Distance function defined between probability distributions
In mathematics, the Wasserstein distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given
Wasserstein_metric
Tensor that rotates the reference frame to simplify analysis
reference frame to eliminate the effect of time-varying inductances and transforms the system into a linear time-invariant system. The Park transformation
Direct-quadrature-zero transformation
Direct-quadrature-zero_transformation
Movement of Earth's lithosphere
determines the type of plate boundary (or fault): convergent, divergent, or transform. The relative movement of the plates typically ranges from zero to 10
Plate_tectonics
layer equations to the plane boundary layer equations. The transformation transforms the equations of axisymmetric boundary layer with external velocity U
Mangler_Transformation
Fundamental theorem in probability theory and statistics
statement can be made about Fourier transforms, since the characteristic function is essentially a Fourier transform. Let Sn be the sum of n random variables
Central_limit_theorem
Parts of a whole which carry only relative information
regression. The alr transform is not an isometry, meaning that distances on transformed values will not be equivalent to distances on the original compositions
Compositional_data
Ways in which length, distance or range can be measured
Length measurement, distance measurement, or range measurement (ranging) all refer to the many ways in which length, distance, or range can be measured
Length_measurement
beamformer. Steered-response power with phase transform (SRP-PHAT) is a variant using a "phase transform" to make it more robust in adverse acoustic environments
Steered-response_power
Measure of similarity and diversity between sets
Jaccard distance is commonly used to calculate an n × n matrix for clustering and multidimensional scaling of n sample sets. These distance measures
Jaccard_index
Measure of variation in statistics
mean and identity covariance. This is called the Mahalanobis whitening transform. The mean and the standard deviation of a set of data are descriptive
Standard_deviation
Concept in inversive geometry
inversive distance remains unchanged if the circles are inverted, or transformed by a Möbius transformation. One pair of circles can be transformed to another
Inversive_distance
2024 Chinese drama film
her daughter, Chen Lu. She has always tried to make up for her emotional distance from Chen Lu by taking care of Chunhe. As Chunhe works to fulfill his grandmother's
Big_World_(film)
Probabilistic problem-solving algorithm
phenomenon in question. Pseudo-random number sampling algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed
Monte_Carlo_method
Relation between sides of a right triangle
coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared distance between two points equals the sum of squares
Pythagorean_theorem
Result used in the theory of propagation of waves
the two-dimensional Fourier transform with cylindrical symmetry, i.e., the Hankel transform. It is found by transforming the spherical wave along the
Sommerfeld_identity
Reducing photographic perspective distortion
vertical distance), constructed perspective considers only the horizontal distance and considers the top and bottom to be the same distance away; make
Perspective_control
In a Fourier transformation (FT), the Fourier transformed function f̂(s) is obtained from f(t) by: f̂(s)=∫−∞∞f(t)e−istdt where i is defined as i2=−1.
Indirect Fourier transformation
Indirect_Fourier_transformation
Mathematical space with a notion of distance
together with a notion of distance between its points. The distance is measured by a function called a metric or distance function. Metric spaces are
Metric_space
Local pressure deviation caused by a sound wave
Z(s)=p̂(s)Q̂(s), where p̂(s) is the Laplace transform of sound pressure,[citation needed] Q̂(s) is the Laplace transform of sound volume flow rate. Specific acoustic
Sound_pressure
American political activist (1993–2025)
Kirk, titled Stop, in the Name of God: Why Honoring the Sabbath Will Transform Your Life, was released by Winning Team Publishing on December 9, 2025
Charlie_Kirk
Family of linear transformations
is referred to as raising an index. To transform a covariant vector Aμ, first raise its index, then transform it according to the same rule as for contravariant
Lorentz_transformation
travel, tourism, insurance
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