Eikonal-based models of random tessellations

Abstract : In this article, we propose a novel, efficient method for computing a random tessellation from its vectorial representation at each voxel of a discretized domain. This method is based upon the resolution of the Eikonal equation and has a complexity in O(N log N), N being the number of voxels used to discretize the domain. By contrast, evaluating the implicit functions of the vectorial representation at each voxel location has a complexity of O(N²) in the general case. The method also enables us to consider the generation of tessellations with rough interfaces between cells by simulating the growth of the germs on a domain where the velocity varies locally. This aspect constitutes the main contribution of the article. A final contribution is the development of an algorithm for estimating the multi-scale tortuosity of the boundaries of the tessellation cells. The algorithm computes the tortuosity of the boundary at several scales by iteratively deforming the boundary until it becomes a straight line. Using this algorithm, we demonstrate that depending on the local velocity model, it is possible to control the roughness amplitude of the cells boundaries.
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https://hal.archives-ouvertes.fr/hal-02437235
Contributor : Bruno Figliuzzi <>
Submitted on : Monday, January 13, 2020 - 4:20:25 PM
Last modification on : Sunday, January 19, 2020 - 7:51:13 PM

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Bruno Figliuzzi. Eikonal-based models of random tessellations. Image Analysis and Stereology, International Society for Stereology, 2019, 38 (1), pp.15. ⟨10.5566/ias.2061⟩. ⟨hal-02437235⟩

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