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- research-articleJuly 2014
A Certified Reduction Strategy for Homological Image Processing
ACM Transactions on Computational Logic (TOCL), Volume 15, Issue 3Article No.: 23, Pages 1–23https://doi.org/10.1145/2630789The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this article, we describe a certified reduction strategy to deal with digital images, but one preserving their ...
- research-articleNovember 2013
Computing persistent homology within Coq/SSReflect
ACM Transactions on Computational Logic (TOCL), Volume 14, Issue 4Article No.: 26, Pages 1–16https://doi.org/10.1145/2528929Persistent homology is one of the most active branches of computational algebraic topology with applications in several contexts such as optical character recognition or analysis of point cloud data. In this article, we report on the formal development ...
- ArticleMay 2012
Triangle mesh compression and homological spanning forests
CTIC'12: Proceedings of the 4th international conference on Computational Topology in Image ContextPages 108–116https://doi.org/10.1007/978-3-642-30238-1_12Triangle three-dimensional meshes have been widely used to represent 3D objects in several applications. These meshes are usually surfaces that require a huge amount of resources when they are stored, processed or transmitted. Therefore, many algorithms ...
- ArticleNovember 2002
A Computational Algebraic Topology Model for the Deformation of Curves
A new method for the deformation of curves is presented. It is based upon a decomposition of the linear elasticity problem into basic physical laws. Unlike other methods which solve the partial differential equation arising from the physical laws by ...