The Quasi-Shear rotation

International audienceRigid transformations are involved in a wide variety of image processing applications, including image registration. In this context, we recently proposed to deal with the associated optimization problem from a purely discrete point of view, using the notion of discrete rigid transformation (DRT) graph. In particular, a local search scheme within the DRT graph to compute a locally optimal solution without any numerical approximation was formerly proposed. In this article, we extend this study, with the purpose to reduce the algorithmic complexity of the proposed optimization scheme. To this end, we propose a novel algorithmic framework for just-in-time computation of sub-graphs of interest within the DRT graph. Experimental results illustrate the potential usefulness of our approach for image registration

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“…In particular, the quasi-shear rotations [7,8] were introduced to preserve bijectivity, by decomposing rotations into successive quasi-shears.…”

Section: Discrete Rotations and Discrete Rigid Transformationsmentioning

confidence: 99%

“…(7)(8), that any cell R v is directionally convex along the aaxes [16]. This implies that for any θ value where it is defined, R v is bounded by at least one upper (resp.…”

Section: Tipping Surfaces Associated To a Discrete Rigid Transformationmentioning

confidence: 99%

Efficient Neighbourhood Computing for Discrete Rigid Transformation Graph Search

Kenmochi¹,

Ngo

Talbot³

et al. 2014

Advanced Information Systems Engineering

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“…Discrete processes for the classes of rotations and affine transformations have been studied in the literature. One can cite the quasi-shear rotation [3] and quasi-affine [4] for instance. Their approach consists of decomposing transformations into three shears and then obtain the discrete transformations.…”

Section: Introductionmentioning

confidence: 99%

Combinatorial structure of rigid transformations in 2D digital images

Ngo

Kenmochi

Passat

et al. 2013

Computer Vision and Image Understanding

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International audienceRigid transformations are involved in a wide range of digital image processing applications. When applied on such discrete images, rigid transformations are however usually performed in their associated continuous space, then requiring a subsequent digitization of the result. In this article, we propose to study rigid transformations of digital images as a fully discrete process. In particular, we investigate a combinatorial structure modelling the whole space of digital rigid transformations on any subset of Z^2 of size N * N. We describe this combinatorial structure, which presents a space complexity O (N^9) and we propose an algorithm enabling to build it in linear time with respect to this space complexity. This algorithm, which handles real (i.e. non-rational) values related to the continuous transformations associated to the discrete ones, is however deﬁned in a fully discrete form, leading to exact computation

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“…It gives almost the same result as DER but an approximation of the angle. Andres described in [1], [2] some discrete rotations such as the rotation by discrete circles, the rotation by Pythagorean lines or the quasi-shear rotation. Computation executed during these rotations are exact.…”

Section: Introductionmentioning

confidence: 99%

Computing upper and lower bounds of rotation angles from digital images

Thibault

Kenmochi²,

Sugimoto

2009

Pattern Recognition

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Rotations in the discrete plane are important for many applications such as image matching or construction of mosaic images. We suppose that a digital image A is transformed to another digital image B by a rotation. In the discrete plane, there are many angles giving the rotation from A to B, which we called admissible rotation angles from A to B. For such a set of admissible rotation angles, there exist two angles that achieve the lower and the upper bounds. To find those lower and upper bounds, we use hinge angles as used in [7]. A sequence of hinge angles is a set of particular angles determined by a digital image in the sense that any angle between two consecutive hinge angles gives the identical rotation of the digital image. We propose a method for obtaining the lower and the upper bounds of admissible rotation angles using hinge angles from a given Euclidean angle or from a pair of corresponding digital images.

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The Quasi-Shear rotation

Cited by 28 publications

References 2 publications

Efficient Neighbourhood Computing for Discrete Rigid Transformation Graph Search

Efficient Neighbourhood Computing for Discrete Rigid Transformation Graph Search

Combinatorial structure of rigid transformations in 2D digital images

Computing upper and lower bounds of rotation angles from digital images

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