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 point of view on the object in question: whether the initial image is transformed into another representation, or it is simply endowed with an additional map or field. Distance fields can also be signed, in the case where it is important to distinguish whether the point is inside or outside of the shape. The map labels each pixel of the image with the distance to the nearest obstacle pixel. A most common type of obstacle pixel is a boundary pixel in a binary image. See the image for an example of a Chebyshev distance transform on a binary image. Usually the transform/map is qualified with the chosen metric. For example, one may speak of Manhattan distance transform, if the underlying metric is Manhattan distance. Common metrics are: * Euclidean distance * Taxicab geometry, also known as City block distance or Manhattan distance. * Chebyshev distance There are several algorithms to compute the distance transform for these different distance metrics, however the computation of the exact Euclidean distance transform (EEDT) needs special treatment if it is computed on the image grid. Applications are digital image processing (e.g., blurring effects, skeletonizing), motion planning in robotics, medicalimage analysis for prenatal genetic testing, and even pathfinding.Uniformly-sampled signed distance fields have been used for GPU-accelerated font smoothing, for example by Valve researchers. Signed distance fields can also be used for (3D) solid modelling. Rendering on typical GPU hardware requires conversion to polygon meshes, e.g. by the marching cubes algorithm. (Wikipedia).
How far is it from everywhere to somewhere?
Computing the Euclidean Distance Transform on a regular grid. A fundamental operation in image processing, used as part of separating objects, finding best matches, finding sizes of objects, and so on. The algorithm presented here is described in: J. Wang and Ying Tan, Efficient Euclide
From playlist Summer of Math Exposition Youtube Videos
k-NN 4: which distance function?
[http://bit.ly/k-NN] The nearest-neighbour algorithm is sensitive to the choice of distance function. Euclidean distance (L2) is a common choice, but it may lead to sub-optimal performance. We discuss Minkowski (p-norm) distance functions, which generalise the Euclidean distance, and can a
From playlist Nearest Neighbour Methods
Determine the distance between two points using distance formula ex 1, A(3, 2) and B(6, 3)
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Example: Determine the Distance Between Two Points
This video shows an example of determining the length of a segment on the coordinate plane by using the distance formula. Complete Video List: http://www.mathispower4u.yolasite.com or http://www.mathispower4u.wordpress.com
From playlist Using the Distance Formula / Midpoint Formula
Determine the distance between two points on a coordinate axis
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Find the distance between the two coordinate points ex 1
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Find the distance between two coordinate points ex1
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Find the distance between two coordinate points ex 2
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Learn to use the distance formula to find the distance between two points
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
Lecture 15 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood introduces a new application of the Fourier Transforms that includes deltas, properties of deltas, and physical interpretation of deltas. The F
From playlist Lecture Collection | The Fourier Transforms and Its Applications
Vanessa Robins (9/8/22): The Extended Persistent Homology Transform for Manifolds with Boundary
The Persistent Homology Transform (PHT) is a topological transform introduced by Turner, Mukherjee and Boyer in 2014. Its input is a shape embedded in Euclidean space; then to each unit vector the transform assigns the persistence module of the height function over that shape with respect
From playlist AATRN 2022
Elchanan Solomon (7/20/20): Intrinsic Topological Transforms via the Distance Kernel Embedding
Title: Intrinsic Topological Transforms via the Distance Kernel Embedding Abstract: Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measurements. The first two topo
From playlist ATMCS/AATRN 2020
Symmetries, Duality, and the Unity of Physics (Lecture – 01) by Nathan Seiberg
DATE: 08 January 2018, 16:00 to 17:30 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Lecture 1: 8 January 2018, 16:00 to 17:30 Title: Symmetries, Duality, and the Unity of Physics Abstract: Global symmetries and gauge symmetries have played a crucial role in physics. The idea of duality d
From playlist Infosys-ICTS Chandrasekhar Lectures
What is the best way to design a voting system? Governments and other institutions have been experimenting for decades with all sorts of different systems, "ranked choice" being a trendy system recently. In the 1950's, mathematician and economist Kenneth Arrow laid out a very mild set of c
From playlist Summer of Math Exposition Youtube Videos
Geometry of Growth and Form: Commentary on D'Arcy Thompson | John Milnor
John Milnor, Co-Director of the Institute for Mathematical Sciences at Stony Brook University http://www.math.sunysb.edu/~jack September 24, 2010 In this lecture, John Milnor, Co-Director of the Institute for Mathematical Sciences at Stony Brook University and a former member of the Facul
From playlist Mathematics
Lecture 5 | Quantum Entanglements, Part 3 (Stanford)
Lecture 5 of Leonard Susskind's course concentrating on Quantum Entanglements (Part 3, Spring 2007). Recorded May 7, 2007 at Stanford University. This Stanford Continuing Studies course is the third of a three-quarter sequence of classes exploring the "quantum entanglements" in modern t
From playlist Lecture Collection | Quantum Entanglements: Part 3 (Spring 2007)
Lens 1F System - Lens Fourirer Transforms
https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. In this video
From playlist Fourier Optics
Lecture 5 | Introduction to Robotics
Lecture by Professor Oussama Khatib for Introduction to Robotics (CS223A) in the Stanford Computer Science Department. Professor Khatib shows a short video on the Brachiation Robot, then goes into a lecture on Frame Attachment. CS223A is an introduction to robotics which covers topics s
From playlist Lecture Collection | Introduction to Robotics
Determine the distance of two points on a number line
👉 Learn how to find the distance between two points. The distance between two points is the length of the line joining the two points in the coordinate plane. To find the distance between two points in the coordinate plane, we make use of the formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2). 👏
From playlist Find the Distance of the Line Segment
For the latest information, please visit: http://www.wolfram.com Speaker: Adam Strzebonski Mathematica 10 introduces systemwide support for computation with mesh-based, discretized, and exact symbolically specified geometric regions. This talk focuses on symbolically specified regions, d
From playlist Wolfram Technology Conference 2014