Co-dimension 2 Geodesic Active Contours for MRA Segmentation

Lorigo, Liana M.; Faugeras, Olivier; Grimson, W. Eric L.; Keriven, Renaud; Kikinis, Ron; Westin, Carl‐Fredrik

doi:10.1007/3-540-48714-x_10

Cited by 100 publications

(60 citation statements)

References 13 publications

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“…For instance, Whitaker [23] proposes a nonlinear reweighting scheme that favors the smaller curvature and preserves cylindrical structures. Lorigo et al [24] propose a smoothing by the minimum curvature.…”

Section: Related Workmentioning

confidence: 99%

Higher-order nonlinear priors for surface reconstruction

Taşdizen

Whitaker

2004

IEEE Trans. Pattern Anal. Machine Intell.

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Abstract-For surface reconstruction problems with noisy and incomplete range data, a Bayesian estimation approach can improve the overall quality of the surfaces. The Bayesian approach to surface estimation relies on a likelihood term, which ties the surface estimate to the input data, and the prior, which ensures surface smoothness or continuity. This paper introduces a new high-order, nonlinear prior for surface reconstruction. The proposed prior can smooth complex, noisy surfaces, while preserving sharp, geometric features, and it is a natural generalization of edge-preserving methods in image processing, such as anisotropic diffusion. An exact solution would require solving a fourth-order partial differential equation (PDE), which can be difficult with conventional numerical techniques. Our approach is to solve a cascade system of two second-order PDEs, which resembles the original fourth-order system. This strategy is based on the observation that the generalization of image processing to surfaces entails filtering the surface normals. We solve one PDE for processing the normals and one for refitting the surface to the normals. Furthermore, we implement the associated surface deformations using level sets. Hence, the algorithm can accommodate very complex shapes with arbitrary and changing topologies. This paper gives the mathematical formulation and describes the numerical algorithms. We also show results using range and medical data.

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Section: Related Workmentioning

confidence: 99%

Higher-order nonlinear priors for surface reconstruction

Taşdizen

Whitaker

2004

IEEE Trans. Pattern Anal. Machine Intell.

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“…Comparison is based on the orientation discrepancy (function δ in Equation 7) between the estimated and the truth flow iso-surface normals 4 . In OT, a 5 × 5 × 5 filter window with relative bandwidth B equals 2 and center frequency ρ equals π 2 √ 2 has been used; a 3 × 3 Gaussian kernel with σ = 1 has been employed for tensor averaging (for further details, see Chapter 6 in [22]).…”

Section: Validation Of Local Orientation Estimationmentioning

confidence: 99%

“…For instance, authors in [2], [3] demonstrated that the expectation maximization (EM) algorithm and a maximum likelihood (ML) estimate can be used to segment vascular structures automatically with a proper statistical mixture model. The use of gradient information to drive evolving contours with the level set method and topologically adaptable surfaces to segment vasculature in the angiograms has been proposed in [4], [5], [6], [7]. Region-growing approaches to segmenting the angiograms with initial segmentations have been illustrated in [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Local Orientation Smoothness Prior for Vascular Segmentation of Angiography

Wong

Chung

2004

Lecture Notes in Computer Science

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Abstract. We present a new generic method for vascular segmentation of angiography. Angiography is used for the medical diagnosis of arterial diseases. To facilitate an effective and efficient review of the vascular information in the angiograms, segmentation is a first stage for other post-processing routines. The method we propose uses a novel a priori -local orientation smoothness prior -to enforce an adaptive regularization constraint for the vascular segmentation within the Bayes' framework. It aspires to segment a variety of angiographies and is aimed at improving the quality of segmentation in low blood flow regions. Our algorithm is tested on numerical phantoms and clinical datasets. The experimental results show that our method produces better segmentations than the maximum likelihood estimation and the estimation with a multi-level logistic Markov random field model. Furthermore, the novel algorithm produces aneurysm segmentations comparable to the manual segmentations obtained from an experienced consultant radiologist.

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“…To smooth the tracts while segmenting them we regularize the flow by adding a curvature dependent speed. Lorigo et al introduced the use of a curvature definition from codimension 2 flows on surfaces with a thin, tubular structure [21]. Instead of using either mean curvature or gaussian curvature, which will normally destroy the tubular structure, they use the smaller principal curvature which is a combination of both curvatures.…”

Section: Regularizationmentioning

confidence: 99%

White Matter Mapping in DT-MRI Using Geometric Flows

Jonasson

Hagmann

Bresson

et al. 2003

Computer Aided Systems Theory - EUROCAST 2003

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Abstract. We present a 3D geometric flow designed to evolve in Diffusion Tensor Magnetic Resonance Images(DT-MRI) along fiber tracts by measuring the diffusive similarity between voxels. Therefore we define a front propagation speed that is proportional to the similarity between the tensors lying on the surface and its neighbor in the propagation direction. The method is based on the assumption that successive voxels in a tract have similar diffusion properties. The front propagation is implemented using level set methods by Osher and Sethian [1] to simplify the handling of topology changes and provides an elegant tool for smoothing the segmented tracts. While many methods demand a regularized tensor field, our geometrical flow performs a regularization as it evolves along the fibers. This is done by a curvature dependent smoothing term adapted for thin tubular structures. The purpose of our approach is to get a quantitative measure of the diffusion in segmented fiber tracts. This kind of information can also be used for white matter registration and for surgical planning.

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Co-dimension 2 Geodesic Active Contours for MRA Segmentation

Cited by 100 publications

References 13 publications

Higher-order nonlinear priors for surface reconstruction

Higher-order nonlinear priors for surface reconstruction

Local Orientation Smoothness Prior for Vascular Segmentation of Angiography

White Matter Mapping in DT-MRI Using Geometric Flows

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