Affine Transformation from Fundamental Matrix and Two Directions

2020 ◽  
Author(s):  
Nghia Minh ◽  
Levente Hajder
Keyword(s):  
Fundamental Matrix ◽  
Affine Transformation

The Standard Metric

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Affine Transformation ◽  
Convex Sets ◽  
Finite Dimension ◽  
Affine Subspace ◽  
Affine Transformations ◽  
Real Vector ◽  
Euclidean Metric ◽  
Affine Hyperplane ◽  
Tits Building ◽  
Convex Closure

This chapter presents some results about groups generated by reflections and the standard metric on a Bruhat-Tits building. It begins with definitions relating to an affine subspace, an affine hyperplane, an affine span, an affine map, and an affine transformation. It then considers a notation stating that the convex closure of a subset a of X is the intersection of all convex sets containing a and another notation that denotes by AGL(X) the group of all affine transformations of X and by Trans(X) the set of all translations of X. It also describes Euclidean spaces and assumes that the real vector space X is of finite dimension n and that d is a Euclidean metric on X. Finally, it discusses Euclidean representations and the standard metric.

A quasi-affine transformation artificial bee colony algorithm for global optimization

2021 ◽  
pp. 1-18
Author(s):  
Baohua Zhao ◽  
Tien-Wen Sung ◽  
Xin Zhang
Keyword(s):  
Affine Transformation ◽  
Artificial Bee Colony ◽  
Triangular Matrix ◽  
Convergence Speed ◽  
Test Set ◽  
Abc Algorithm ◽  
Bee Colony ◽  
Search Mechanism ◽  
Multiple Dimensions ◽  
Collaborative Search

The artificial bee colony (ABC) algorithm is one of the classical bioinspired swarm-based intelligence algorithms that has strong search ability, because of its special search mechanism, but its development ability is slightly insufficient and its convergence speed is slow. In view of its weak development ability and slow convergence speed, this paper proposes the QABC algorithm in which a new search equation is based on the idea of quasi-affine transformation, which greatly improves the cooperative ability between particles and enhances its exploitability. During the process of location updating, the convergence speed is accelerated by updating multiple dimensions instead of one dimension. Finally, in the overall search framework, a collaborative search matrix is introduced to update the position of particles. The collaborative search matrix is transformed from the lower triangular matrix, which not only ensures the randomness of the search, but also ensures its balance and integrity. To evaluate the performance of the QABC algorithm, CEC2013 test set and CEC2014 test set are used in the experiment. After comparing with the conventional ABC algorithm and some famous ABC variants, QABC algorithm is proved to be superior in efficiency, development ability, and robustness.

scholarly journals Affine transformation of virtual 3D object using 2D localization of fingertips

2020 ◽  
Vol 2 (6) ◽  
pp. 534-555
Author(s):  
Mohammad Mahmudul Alam ◽  
S.M. Mahbubur Rahman
Keyword(s):  
Affine Transformation ◽  
3D Object

scholarly journals Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

2021 ◽  
Author(s):  
Mareike Dressler ◽  
Adam Kurpisz ◽  
Timo de Wolff
Keyword(s):  
Computer Science ◽  
Affine Transformation ◽  
Optimization Problems ◽  
Polynomial Optimization ◽  
Theoretical Computer Science ◽  
Sums Of Squares ◽  
Theoretical Computer ◽  
Complexity Bounds ◽  
Polynomial Optimization Problems ◽  
Transformation Of Variables

AbstractVarious key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most $$n+d$$ n + d . Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most $$n^{O(d)}$$ n O ( d ) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

Fundamental matrix of planar catadioptric stereo systems

2010 ◽  
Vol 4 (2) ◽  
pp. 85 ◽  
Author(s):  
H.-H.P. Wu ◽  
S.-H. Chang
Keyword(s):  
Fundamental Matrix

The Structure of the Fundamental Matrix of a System of Coupled-Mode Equations

1978 ◽  
Vol 22 (2) ◽  
pp. 311-325
Author(s):  
S. V. Reznichenko
Keyword(s):  
Fundamental Matrix ◽  
Coupled Mode

Affine transformation in random iterated function systems

2001 ◽  
Vol 22 (7) ◽  
pp. 820-826 ◽  
Author(s):  
Xiong Yong ◽  
Shi Ding-hua
Keyword(s):  
Affine Transformation ◽  
Iterated Function Systems ◽  
Iterated Function

Breast image registration by using non-linear local affine transformation

2013 ◽  
Author(s):  
Feiyu Chen ◽  
Peng Zheng ◽  
Penglong Xu ◽  
Andrew D. A. Maidment ◽  
Predrag R. Bakic ◽  
...  
Keyword(s):  
Image Registration ◽  
Affine Transformation ◽  
Breast Image ◽  
Non Linear

Stream cipher based on pseudorandom number generation using optical affine transformation

2000 ◽  
Author(s):  
Toru Sasaki ◽  
Hiroyuki Togo ◽  
Jun Tanida ◽  
Yoshiki Ichioka
Keyword(s):  
Affine Transformation ◽  
Stream Cipher ◽  
Pseudorandom Number ◽  
Number Generation ◽  
Pseudorandom Number Generation
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