An Adaptive Level Set Method for Medical Image Segmentation

Droske, Marc; Meyer, Bernhard; Rumpf, Martin; Schaller, Carlo

doi:10.1007/3-540-45729-1_43

Cited by 67 publications

(45 citation statements)

References 10 publications

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“…To the best of our knowledge, the only published previous work that attempts to address this serious problem is a relatively small body of work based on tree structures as the underlying grid representation. For contours this typically amounts to using quadtrees [6,21,39] and more recently this idea was extended to surfaces by means of octrees [16]. Furthermore, Milne [20] and Sussman et al [29] have explored level sets in conjunction with patch based AMR.…”

Section: Previous Workmentioning

confidence: 99%

“…While tree data structures allow for multi-resolution representations, all practical tree methods appear to use uniform resolution near the interface [6,16,21,39]. This is partly due to the fact that it is hard to design reliable "refinement oracles" which can guarantee that no fine features are missed due to under-sampling as the interface propagates in time.…”

Section: Previous Workmentioning

confidence: 99%

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Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

Nielsen

Museth

2006

J Sci Comput

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Level set methods [Osher and Sethian. Fronts propagating with curvaturedependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12] have proved very successful for interface tracking in many different areas of computational science. However, current level set methods are limited by a poor balance between computational efficiency and storage requirements. Tree-based methods have relatively slow access times, whereas narrow band schemes lead to very large memory footprints for high resolution interfaces. In this paper we present a level set scheme for which both computational complexity and storage requirements scale with the size of the interface. Our novel level set data structure and algorithms are fast, cache efficient and allow for a very low memory footprint when representing high resolution level sets. We use a time-dependent and interface adapting grid dubbed the "Dynamic Tubular Grid" or DT-Grid. Additionally, it has been optimized for advanced finite difference schemes currently employed in accurate level set computations. As a key feature of the DT-Grid, the associated interface propagations are not limited to any computational box and can expand freely. We present several numerical evaluations, including a level set simulation on a grid with an effective resolution of 1024 3 .

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Section: Previous Workmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

Nielsen

Museth

2006

J Sci Comput

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“…Following this, tree based methods were introduced, allowing for adaptivity of the mesh near the interface, while not sacrificing too much complexity [34], [21], [11], [19]. The tree data structure used in these methods was well understood by the computer science community, and thus data storage and retrieval were able to be carried out in an efficient manner.…”

Section: Performing Organization Report Numbermentioning

confidence: 99%

Simplex Free Adaptive Tree Fast Sweeping and Evolution Methods for Solving Level Set Equations in Arbitrary Dimension

Cecil¹,

Osher²,

Qian³

2005

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We introduce simplex free adaptive tree numerical methods for solving static and time dependent Hamilton-Jacobi equations arising in level set problems in arbitrary dimension. The data structure upon which our method is built is a generalized n-dimensional binary tree, but it does not require the complicated splitting of cubes into simplices (aka generalized n-dimensional triangles or hypertetrahedrons) that current tree based methods require. It has enough simplicity that minor variants of standard numerical Hamiltonians developed for uniform grids can be applied, yielding consistent, monotone, convergent schemes. Combined with the fast sweeping strategy, the resulting tree based methods are highly efficient and accurate. Thus, without changing more than a few lines of code when changing dimension, we have obtained results for calculations in up to n = 7 dimensions.

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“…In medicine, imaging is used for planning surgeries, X-ray imaging for bones, Magnetic resonance imaging, endoscopies and many other useful applications [3], [4].…”

Section: Introductionmentioning

confidence: 99%