Combining Different Types of Scale Space Interest Points Using Canonical Sets

Kanters, Frans; Denton, Trip; Shokoufandeh, Ali; Florack, Luc; Romeny, Bart ter Haar

doi:10.1007/978-3-540-72823-8_32

“…The minimizer of g → (g, g) k,λ coincides with orthogonal projection of the input image on the span of the corresponding Riesz-representatives {κ i } N i=1 . Visually most appealing results are obtained for 1 < k < 1.5, λ ≈ 10 for bounded domain Sobolev norms, [32,31], while including other features [41,47] such as the top-points of the Laplacian [36,31]. Using covariant derivatives further improves the result in our faster coarse to fine iterative scheme, cf.…”

Section: Input: Tagged Mr Imagesmentioning

confidence: 90%

A variational approach to cardiac motion estimation based on covariant derivatives and multi-scale Helmholtz decomposition

Duits

¹

,

Janssen

²

,

Becciu

³

et al. 2012

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The investigation and quantification of cardiac motion is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider a new method to track cardiac motion from magnetic resonance (MR) tagged images. Tracking is achieved by following the spatial maxima in scale-space of the MR images over time. Reconstruction of the velocity field is then carried out by minimizing an energy functional which is a Sobolev norm expressed in covariant derivatives. These covariant derivatives are used to express prior knowledge about the velocity field in the variational framework employed. Furthermore, we propose a multi-scale Helmholtz decomposition algorithm that combines diffusion and Helmholtz decomposition in one nonsingular analytic kernel operator in order to decompose the optic flow vector field in a divergence-free and a rotation-free part. Finally, we combine both the multi-scale Helmholtz decomposition and our vector field reconstruction (based on covariant derivatives) in a single algorithm and show the practical benefit of this approach by an experiment on real cardiac images.

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“…The minimizer of g → (g, g) k,λ coincides with orthogonal projection of the input image on the span of the corresponding Riesz representatives {κ i } N i=1 . Visually most appealing results are obtained for 1 < k < 1.5, λ ≈ 10 for bounded domain Sobolev norms,[32,31], while including other features[41,47] such as the top-points of the Laplacian[36,31]. Using covariant derivatives further improves the result in our faster coarse to fine iterative scheme; cf [33,31]…”

mentioning

confidence: 92%

Untitled

2013

Quart. Appl. Math.

0

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The investigation and quantification of cardiac motion is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider a new method to track cardiac motion from magnetic resonance (MR) tagged images. Tracking is achieved by following the spatial maxima in scale-space of the MR images over time. Reconstruction of the velocity field is then carried out by minimizing an energy functional which is a Sobolev norm expressed in covariant derivatives. These covariant derivatives are used to express prior knowledge about the velocity field in the variational framework employed. Furthermore, we propose a multi-scale Helmholtz decomposition algorithm that combines diffusion and Helmholtz decomposition in one nonsingular analytic kernel operator in order to decompose the optic flow vector field in a divergence-free and a rotation-free part. Finally, we combine both the multi-scale Helmholtz decomposition and our vector field reconstruction (based on covariant derivatives) in a single

show abstract