Topological Map: An Efficient Tool to Compute Incrementally Topological Features on 3D Images

Abstract : In this paper, we show how to use the three dimensional topological map in order to compute efficiently topological features on objects contained in a 3D image. These features are useful for example in image processing to control operations or in computer vision to characterize objects. Topological map is a combinatorial model which represents both topological and geometrical information of a three dimensional labeled image. This model can be computed incrementally by using only two basic operations: the removal and the fictive edge shifting. In this work, we show that Euler characteristic can be computed incrementally during the topological map construction. This involves an efficient algorithm and open interesting perspectives for other features.
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11th International Workshop on Combinatorial Image Analysis (IWCIA 2006), Jun 2006, Berlin, Germany. Springer, Lecture Notes in Computer Science, 4040, pp.1-15, 2006, Combinatorial Image Analysis 11th International Workshop, IWCIA 2006, Berlin, Germany, June 19-21, 2006. Proceedings. 〈https://link.springer.com/chapter/10.1007/11774938_1〉. 〈10.1007/11774938_1〉
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Guillaume Damiand, Samuel Peltier, Laurent Fuchs, Pascal Lienhardt. Topological Map: An Efficient Tool to Compute Incrementally Topological Features on 3D Images. 11th International Workshop on Combinatorial Image Analysis (IWCIA 2006), Jun 2006, Berlin, Germany. Springer, Lecture Notes in Computer Science, 4040, pp.1-15, 2006, Combinatorial Image Analysis 11th International Workshop, IWCIA 2006, Berlin, Germany, June 19-21, 2006. Proceedings. 〈https://link.springer.com/chapter/10.1007/11774938_1〉. 〈10.1007/11774938_1〉. 〈hal-00366101〉

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