A system for the generation of curves on 3D brain images

Bartesaghi, Alberto; Sapiro, Guillermo

doi:10.1002/hbm.1037

Cited by 49 publications

(40 citation statements)

References 47 publications

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“…Both curvature [31], [32], [35] and depth features [37], [38] were used in previous works on sulci detection. In this work, we use the mean curvature as the feature function f because it is easy to compute and very effective in summarizing the geometric characteristics of the cortical surface.…”

Section: Graph-cut Segmentationmentioning

confidence: 99%

Hamilton–Jacobi Skeleton on Cortical Surfaces

Shi

Thompson

Dinov

et al. 2008

IEEE Trans. Med. Imaging

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In this paper, we propose a new method to construct graphical representations of cortical folding patterns by computing skeletons on triangulated cortical surfaces. In our approach, a cortical surface is first partitioned into sulcal and gyral regions via the solution of a variational problem using graph cuts, which can guarantee global optimality. After that, we extend the method of Hamilton-Jacobi skeleton [1] to subsets of triangulated surfaces, together with a geometrically intuitive pruning process that can trade off between skeleton complexity and the completeness of representing folding patterns. Compared with previous work that uses skeletons of 3D volumes to represent sulcal patterns, the skeletons on cortical surfaces can be easily decomposed into branches and provide a simpler way to construct graphical representations of cortical morphometry. In our experiments, we demonstrate our method on two different cortical surface models, its ability of capturing major sulcal patterns and its application to compute skeletons of gyral regions.

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Section: Graph-cut Segmentationmentioning

confidence: 99%

Hamilton–Jacobi Skeleton on Cortical Surfaces

Shi

Thompson

Dinov

et al. 2008

IEEE Trans. Med. Imaging

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“…In particular, curves representing anatomical features can be used to match brain surfaces [1,2,3]. The curves of sulcal fundi can be viewed as crestlines [5], sulcal roots [4], or as weighted geodesic curves [3,6], where the weight is usually computed from the local properties (e.g., mean curvature) of the surface [3,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…The resulting curve is restricted to travel along the edges of the surface, therefore depends on the parameterization of the surface and suffers from metric distortion. More recently, an algorithm based on the FMM has been reported to extract curves of sulcal fundi [3,6]. In the algorithm, the weight is set to be a function of local "valley-ness".…”

Section: Introductionmentioning

confidence: 99%

Using the Fast Marching Method to Extract Curves with Given Global Properties

Tao

Davatzikos

Prince

2005

Lecture Notes in Computer Science

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Abstract. Curves are often used as anatomical features to match surfaces that represent biological objects, such as the human brain. Automated and semi-automated methods for extracting these curves usually rely on local properties of the surfaces such as the mean surface curvature without considering the global appearance of the curves themselves. These methods may require additional human intervention, and sometimes produce erroneous results. In this paper, we present an algorithm that is based on the fast marching method (FMM) to extract weighted geodesic curves. Instead of directly using the local image properties as a weight function, we use the surface properties, together with the global properties of the curves, to compute a weight function. This weight function is then used by the FMM to extract curves between given points. The general framework can be used to extract curves with different global properties. The resulting curves are guaranteed to be weighted geodesic curves without cusps usually introduced by intermediate points through which the curves are forced to pass. We show some results on both a simulated image and a highly convoluted human brain cortical surface.

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“…As a result, several algorithms for computing approximate shortest paths have been proposed [6], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. These methods are appropriate for applications such as interactive visualization and texture mapping, where extremely rapid solutions are desired and some loss of accuracy can be tolerated.…”

Section: Introductionmentioning

confidence: 99%

Exact Geodesics and Shortest Paths on Polyhedral Surfaces

Balasubramanian

Polimeni

Schwartz

2009

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-We present two algorithms for computing distances along convex and non-convex polyhedral surfaces. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimal-geodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.Index Terms-Differential geometry, flat maps, triangular meshes, surface-based analysis, computational geometry.

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A system for the generation of curves on 3D brain images

Cited by 49 publications

References 47 publications

Hamilton–Jacobi Skeleton on Cortical Surfaces

Hamilton–Jacobi Skeleton on Cortical Surfaces

Using the Fast Marching Method to Extract Curves with Given Global Properties

Exact Geodesics and Shortest Paths on Polyhedral Surfaces

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