Geometry in computer vision

Semi-global matching

Semi-global matching (SGM) is a computer vision algorithm for the estimation of a dense disparity map from a rectified stereo image pair, introduced in 2005 by Heiko Hirschmüller while working at the German Aerospace Center. Given its predictable run time, its favourable trade-off between quality of the results and computing time, and its suitability for fast parallel implementation in ASIC or FPGA, it has encountered wide adoption in real-time stereo vision applications such as robotics and advanced driver assistance systems. (Wikipedia).

Semi-global matching
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Bipartite perfect matching is in quasi-NC - Fenner

Computer Science/Discrete Mathematics Seminar I Topic: Bipartite perfect matching is in quasi-NC Speaker: Stephen Fenner Date:Monday, February 8 We show that the bipartite perfect matching problem is in quasi 𝖭𝖢2quasi-NC2. That is, it has uniform circuits of quasi-polynomial size and O(

From playlist Mathematics

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Parallels and the double triangle | Universal Hyperbolic Geometry 18 | NJ Wildberger

We discuss Euclid's parallel postulate and the confusion it led to in the history of hyperbolic geometry. In Universal Hyperbolic Geometry we define the parallel to a line through a point, NOT the notion of parallel lines. This leads us to the useful construction of the double triangle of

From playlist Universal Hyperbolic Geometry

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Identifying congruent parts between two polygons

👉 Learn how to solve with similar polygons. Two polygons are said to be similar if the corresponding angles are congruent (equal). When two polygons are similar the corresponding sides are proportional. Knowledge of the length of the sides or the proportion of the side lengths of one of th

From playlist Congruent Polygons

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How to use proportions for an isosceles triangle

👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side

From playlist Similar Triangles

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Pattern Matching - Being Flexible

As your patterns become more complex you'll need to build patterns that can match expressions with different but similar forms. Activity Link: https://teacher.desmos.com/activitybuilder/custom/60626999811e664d596ece18

From playlist Pattern Matching with Computation Layer

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Fractional Perfect Matchings in Hypergraphs - Andrzej Rucinski

Andrzej Rucinski Adam Mickiewicz University in Polznan, Poland; Emory University November 15, 2010 A perfect matching in a k-uniform hypergraph H = (V, E) on n vertices is a set of n/k disjoint edges of H, while a fractional perfect matching in H is a function w : E → [0, 1] such that for

From playlist Mathematics

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Alberto Del Pia: Proximity in concave integer quadratic programming

A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of n∆ on the proximity of optimal solutions of an Integer Linear Programming problem and its standard linear relaxation. In this bound, n is the number of variables and ∆ denotes the maximum of the absolute va

From playlist Workshop: Tropical geometry and the geometry of linear programming

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Rank optimality for the Burer-Monteiro factorization - Waldspurger - Workshop 3 - CEB T1 2019

Irène Waldspurger (CNRS and Paris-Dauphine) / 03.04.2019 Rank optimality for the Burer-Monteiro factorization In the last decades, semidefinite programs have emerged as a a powerful way to solve difficult combinatorial optimization problems in polynomial time. Unfortunately, they are di

From playlist 2019 - T1 - The Mathematics of Imaging

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Irène Waldspurger: Rank optimality for the Burer-Monteiro factorization

The Burer-Monteiro factorization is a classical heuristic used to speed up the solving of large scale semidefinite programs when the solution is expected to be low rank: One writes the solution as the product of thinner matrices, and optimizes over the (low-dimensional) factors instead of

From playlist Control Theory and Optimization

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What are supplementary angles

👉 Learn how to define angle relationships. Knowledge of the relationships between angles can help in determining the value of a given angle. The various angle relationships include: vertical angles, adjacent angles, complementary angles, supplementary angles, linear pairs, etc. Vertical a

From playlist Angle Relationships

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Irène Waldspurger: "Rank optimality of the Burer-Monteiro factorization"

High Dimensional Hamilton-Jacobi PDEs 2020 Workshop II: PDE and Inverse Problem Methods in Machine Learning "Rank optimality of the Burer-Monteiro factorization" Irène Waldspurger - Université Paris Dauphine Abstract: The Burer-Monteiro factorization is a classical heuristic used to spee

From playlist High Dimensional Hamilton-Jacobi PDEs 2020

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Can p-adic integrals be computed? - Thomas Hales

Automorphic Forms Thomas Hales April 6, 2001 Concepts, Techniques, Applications and Influence April 4, 2001 - April 7, 2001 Support for this conference was provided by the National Science Foundation Conference Page: https://www.math.ias.edu/conf-automorphicforms Conference Agena: ht

From playlist Mathematics

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Endoscopy theory for symplectic and orthogonal similitude groups - Bin Xu

Bin Xu Member, School of Mathematics January 29, 2015 The endoscopy theory provides a large class of examples of Langlands functoriality, and it also plays an important role in the classification of automorphic forms. The central part of this theory are some conjectural identities of Hari

From playlist Mathematics

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Approximating Max Cut with Subexponential Linear Programs - Tselil Schramm

Computer Science/Discrete Mathematics Seminar I Topic: Approximating Max Cut with Subexponential Linear Programs Speaker: Tselil Schramm Affiliation: Stanford University Date: March 29, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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Tudor Dimofte - 3d SUSY Gauge Theory and Quantum Groups at Roots of Unity

Topological twists of 3d N=4 gauge theories naturally give rise to non-semisimple 3d TQFT's. In mathematics, prototypical examples of the latter were constructed in the 90's (by Lyubashenko and others) from representation categories of small quantum groups at roots of unity; they were rece

From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory

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Local-Global principles for tori over arithmetic surfaces - Hartmann - Workshop 1 - CEB T2 2019

Julia Hartmann (University of Pennsylvania) / 22.05.2019 Local-Global principles for tori over arithmetic surfaces Given a field F and a collection of overfields Fi (i ∈ I), we say that the local global principle holds for an F-variety Z if the existence of a rational point over each Fi

From playlist 2019 - T2 - Reinventing rational points

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KÄHLER--RICCI FLOW (new results) -- GANG TIAN

Lecture given by Professor Gang Tian (Princeton University, Beijing University, Massachusetts Institute of Technology) on "New Results on Kähler--Ricci flow". This was recorded at the Banff International Research Station, the conference being Geometric Flows: Recent Developments and Applic

From playlist Research Lectures

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Some recent results and open problems on random matrices - Van Vu

Van Vu Yale April 3, 2014 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Introduction to Similarity

This video introduces similarity and explains how to determine if two figures are similar or not. http://mathispower4u.com

From playlist Number Sense - Decimals, Percents, and Ratios

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Structure from motion | Computer stereo vision | High-pass filter | Image rectification | Hamming distance | Dynamic programming | Computational complexity | Mutual information | Viterbi algorithm | Graph cut optimization | Algorithm | Mathematical morphology