@article{Figliuzzi_2019, title={EIKONAL-BASED MODELS OF RANDOM TESSELLATIONS}, volume={38}, url={https://www.ias-iss.org/ojs/IAS/article/view/2061}, DOI={10.5566/ias.2061}, abstractNote={<p>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.</p>}, number={1}, journal={Image Analysis and Stereology}, author={Figliuzzi, Bruno}, year={2019}, month={Apr.}, pages={15–23} }