Optical Flow

Becker, Florian; Petra, Stefania; Schnörr, Christoph

doi:10.1007/978-1-4939-0790-8_38

Cited by 13 publications

(25 citation statements)

References 131 publications

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“…Since φ(t, · ) is given by ν ∈ L 2 ([0, 1], V ) through (10), it should be possible to express the time derivative of the right-hand-side of (28) entirely in terms of f and ν. Furthermore,…”

Section: Group Actionsmentioning

confidence: 99%

“…This allows one to formulate the following variational approach to the spatiotemporal image reconstruction problem: In the above, I ∈ X is the starting image. The curve of diffeomorphism t → φ ν 0,t is generated by the velocity field ν as a solution to (10), W : G V × X → X is given by the group action, and L : X → R is the spatiotemporal analogue of (23), i.e., L(f ) := µR(f ) + D T (f ), g t for f ∈ X.…”

Section: 2mentioning

confidence: 99%

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Indirect Image Registration with Large Diffeomorphic Deformations

Chen

Öktem

2018

SIAM J. Imaging Sci.

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The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends so zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data.

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Section: Group Actionsmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Indirect Image Registration with Large Diffeomorphic Deformations

Chen

Öktem

2018

SIAM J. Imaging Sci.

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“…The lower semi-continuity of the regularizer and the data term is shown similar as in Theorem 3.3. Consequently, ϕ is a minimizer of our functional (11).…”

Section: Higher Regularity Of ϕmentioning

confidence: 99%

“…Again, the second regularizer in (11) ensures that R(∇ϕ) is well-defined for a.e. x ∈ Ω as soon as the energy is finite.…”

Section: Higher Regularity Of ϕmentioning

confidence: 99%

“…Variational optical flow methods for estimating the displacement between image frames go back to Horn and Schunck [41]. Meanwhile, there exists a vast number of refinements and extensions of their approach and we refer to [11] for a comprehensive overview. In particular, optical flow models with priors containing higher order derivatives of the displacement field were successfully used, e.g., in [40,55,66,73,74].…”

Section: Introductionmentioning

confidence: 99%

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An Image Registration Model in Electron Backscatter Diffraction

Gräf¹,

Neumayer²,

Hielscher³

et al. 2021

Preprint

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Recently, variational methods were successfully applied for computing the optical flow in gray and RGB-valued image sequences. A crucial assumption in these models is that pixel-values do not change under transformations. Nowadays, modern image acquisition techniques such as electron backscatter tomography (EBSD), which is used in material sciences, can capture images with values in nonlinear spaces. Here, the image values belong to the quotient space SO(3)/S of the special orthogonal group modulo the discrete symmetry group of the crystal. For such data, the assumption that pixel-values remain unchanged under transformations appears to be no longer valid. Hence, we propose a variational model for determining the optical flow in SO(3)/Svalued image sequences, taking the dependence of pixel-values on the transformation into account. More precisely, the data is transformed according to the rotation part in the polar decomposition of the Jacobian of the transformation. To model non-smooth transformations without obtaining so-called staircasing effects, we propose to use a total generalized variation like prior. Then, we prove existence of a minimizer for our model and explain how it can be discretized and minimized by a primal-dual algorithm. Numerical examples illustrate the performance of our method.

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