Author:
Bordenave Charles,Gousseau Yann,Roueff François
Abstract
In this article, we study a particular example of general random tessellation, the dead leaves model. This model, first studied by the mathematical morphology school, is defined as a sequential superimposition of random closed sets, and provides the natural tool to study the occlusion phenomenon, an essential ingredient in the formation of visual images. We generalize certain results of G. Matheron and, in particular, compute the probability of n compact sets being included in visible parts. This result characterizes the distribution of the boundary of the dead leaves tessellation.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference27 articles.
1. [10] Gousseau Y. (2002). Texture synthesis through level sets. In Texture 2002 (Proc. 2nd Internat. Workshop Texture Anal. Synthesis, Copenhagen, 2002), 5pp. Available at http://www.cee.hw.ac.uk/∼texture2002/index.html#ab044.
2. [6] Cowan R. and Tsang A. K. L. (1995). Random mosaics with cells of general topology. Res. Rep. 89, University of Hong Kong.
3. Perfect simulation in stochastic geometry
Cited by
39 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Fully synthetic training for image restoration tasks;Computer Vision and Image Understanding;2023-08
2. Granulometric Analysis of Maltodextrin Particles Observed by Scanning Electron Microscopy;2023 IEEE 13th International Conference on Pattern Recognition Systems (ICPRS);2023-07-04
3. Multifractal analysis of sums of random pulses;Mathematical Proceedings of the Cambridge Philosophical Society;2023-06-22
4. Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees;Random Structures & Algorithms;2023-03-15
5. Random sequential covering;Journal of Statistical Mechanics: Theory and Experiment;2023-03-01