Extraction of Cardiac Motion Using Scale-Space Features Points and Gauged Reconstruction

Becciu, A.; Janssen, Bart; Assen, Hans C van; Florack, Luc; Roode, Vivian; Romeny, Bart M. Haar

doi:10.1007/978-3-642-03767-2_73

Cited by 5 publications

(7 citation statements)

References 16 publications

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“…Phantom one is a sequence consisting of 19 time-frames with size 99 × 99 pixels of purely contracting and expanding patterns ( Figure 13 column 2), whereas phantom 2 consists of 13 frames of 93 × 93 pixels in size and displays non rigid rotation (13, column 4). Equations for phantom 1 have been provided in [5], whereas detailed description of phantom 2 has been carried out in [43]. Both phantoms vanish at the boundaries.…”

Section: Methodsmentioning

confidence: 99%

“…However, in order to provide a road map to covariant derivatives of vector fields in a vector bundle we first explain the covariant derivative of a scalar function f : Ω → R with respect to an a priori gauge function h : Ω → R as introduced by T. Georgiev [17] (in an Adobe Photoshop inpainting application) and subsequently studied in [30,5]. Such a covariant derivative is given by…”

Section: Experiments On Vector Field Reconstructionmentioning

confidence: 99%

“…The regularization term includes information from a so-called gauge field and allows a better flow field reconstruction with respect to the one provided by similar techniques, which use standard derivatives [5] instead. For a different optic flow approach where pre-knowledge in the regularization term is included we refer to Nir et al [39].…”

Section: Introductionmentioning

confidence: 99%

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Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition

Becciu

Duits

Janssen

et al. 2012

Statistical Atlases and Computational Models of the Heart. Imaging and Modelling Challenges

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The investigation and quantification of cardiac movement is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider new aperture problem-free methods to track cardiac motion from 2-dimensional MR tagged images and corresponding sine-phase images. Tracking is achieved by following the movement of scale-space maxima, yielding a sparse set of linear features of the unknown optic flow vector field. Interpolation/reconstruction of the velocity field is then carried out by minimizing an energy functional which is a Sobolev-norm expressed in covariant derivatives (rather than standard derivatives). These covariant derivatives are used to express prior knowledge about the velocity field in the variational framework employed. They are defined on a fiber bundle where sections coincide with vector fields. Furthermore, the optic flow vector field is decomposed in a divergence free and a rotation free part, using our multi-scale Helmholtz decomposition algorithm that combines diffusion and Helmholtz decomposition in a single non-singular analytic kernel operator. Finally, we combine this multi-scale Helmholtz decomposition with vector field reconstruction (based on covariant derivatives) in a single algorithm and present some experiments of cardiac motion estimation. Further experiments on phantom data with ground truth show that both the inclusion of covariant derivatives and the inclusion of the multi-scale Helmholtz decomposition improves the optic flow reconstruction.

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Section: Methodsmentioning

confidence: 99%

Section: Experiments On Vector Field Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition

Becciu

Duits

Janssen

et al. 2012

Statistical Atlases and Computational Models of the Heart. Imaging and Modelling Challenges

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“…Hence,

boldV (t) = (\begin{matrix} u (t) \\ v (t) \\ w (t) \end{matrix}) = - H {(boldx (t), s, t)}^{- 1} \frac{\partial (\nabla L {(boldx (t), s, t)}^{T})}{\partial t},

where H represents the spatial Hessian matrix of image L . In the literature, similar optic flow approaches that calculate velocity estimation at feature point location using the Hessian matrix are discussed in [9, 10, 43, 45]. …”

Section: Methodsmentioning

confidence: 99%

3D Winding Number: Theory and Application to Medical Imaging

Becciu

Fuster

Pottek

et al. 2011

International Journal of Biomedical Imaging

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We develop a new formulation, mathematically elegant, to detect critical points of 3D scalar images. It is based on a topological number, which is the generalization to three dimensions of the 2D winding number. We illustrate our method by considering three different biomedical applications, namely, detection and counting of ovarian follicles and neuronal cells and estimation of cardiac motion from tagged MR images. Qualitative and quantitative evaluation emphasizes the reliability of the results.

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“…images without harmonic phase or sine phase pre-processing [52,50]. Some of the optic flow methods, such as [55,56,57], do allow direct computation on the original MRI-tagging images as well, but they are relatively expensive, complicated and technical, e.g. [20].…”

Section: Local Frequency Estimation In Cardiac Tagged Mri Imagesmentioning

confidence: 99%

Evolution equations on Gabor transforms and their applications

Duits¹,

Führ

Janssen

et al. 2013

Applied and Computational Harmonic Analysis

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We introduce a systematic approach to the design, implementation and analysis of left-invariant evolution schemes acting on Gabor transform, primarily for applications in signal and image analysis. Within this approach we relate operators on signals to operators on Gabor transforms. In order to obtain a translation and modulation invariant operator on the space of signals, the corresponding operator on the reproducing kernel space of Gabor transforms must be left invariant, i.e. it should commute with the left regular action of the reduced Heisenberg group Hr. By using the left-invariant vector fields on Hr in the generators of our evolution equations on Gabor transforms, we naturally employ the essential group structure on the domain of a Gabor transform. Here we distinguish between two tasks. Firstly, we consider non-linear adaptive left-invariant convection (reassignment) to sharpen Gabor transforms, while maintaining the original signal. Secondly, we consider signal enhancement via left-invariant diffusion on the corresponding Gabor transform. We provide numerical experiments and analytical evidence for our methods and we consider an explicit medical imaging application.

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Extraction of Cardiac Motion Using Scale-Space Features Points and Gauged Reconstruction

Cited by 5 publications

References 16 publications

Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition

Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition

3D Winding Number: Theory and Application to Medical Imaging

Evolution equations on Gabor transforms and their applications

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