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Learning affine transformations
Pattern Recognition, 1999Under the assumption of weak perspective, two views of the same planar object are related through an affine transformation. In this paper, we consider the problem of training a simple neural network to learn to predict the parameters of the affine transformation.
Michael Georgiopoulos +3 more
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Affine Transformations in Bundles
Journal of Mathematical Sciences, 2020This paper is a review of results of studies of affine transformations in generalized spaces over real linear algebras over the past 15-20 years.
A. Ya. Sultanov, O. A. Monakhova
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Affine transformation in cryptography
Journal of Discrete Mathematical Sciences and Cryptography, 2008Abstract The affine transformation is the generalized shift cipher. The shift cipher is one of the important techniques in cryptography. In this paper, we show that the total number of possible affine transformations is N k ϕ(N k), that is, , for k-letter block and prime factor p of N k . It has key length two and is computationally easy.
Hari Om, Rahul Patwa
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1965
Publisher Summary The group of similarity transformations of the plane is a subgroup of a group of more general transformations that preserve collinearity and parallelism but not, in general, the lengths of segments and the sizes of angles or areas. These transformations are called affine transformations.
A.S. Parkhomenko, P.S. Modenov
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Publisher Summary The group of similarity transformations of the plane is a subgroup of a group of more general transformations that preserve collinearity and parallelism but not, in general, the lengths of segments and the sizes of angles or areas. These transformations are called affine transformations.
A.S. Parkhomenko, P.S. Modenov
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Affine Transformational Optics
Frontiers in Optics 2011/Laser Science XXVII, 2011We describe a class of devices whose refractive index distribution results from an affine transformation over piece–wise uniform space, including theoretical analysis and experimental realizations using anisotropic materials and surface nanopatterning.
Handong Sun +7 more
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Affine and Projective Transformations
2010In addition to isometries, there are two kinds of mappings that preserve lines: affine (Section 3.1) and projective (Section 3.2) transformations. Affine transformations f of \({\mathbb{R}}^{n}\) have the following property: If l is a line then f(l) is also a line, and if l ∥ k then f(l) ∥ f(k). A line in \({\mathbb{R}}^{n}\) means a set of the form {r
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2016
The name, which goes back to Mobius and Leonhard Euler, implies that, in such a transformation, infinitely distant points correspond again to infinitely distant points, so that, in a sense, the “ends” of space are preserved. In fact, the formulas show at once that x´, y´, z´ become infinite with x, y, z.
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The name, which goes back to Mobius and Leonhard Euler, implies that, in such a transformation, infinitely distant points correspond again to infinitely distant points, so that, in a sense, the “ends” of space are preserved. In fact, the formulas show at once that x´, y´, z´ become infinite with x, y, z.
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Affine Transformations in Affine Differential Geometry
Results in Mathematics, 1989openaire +2 more sources