Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Extreme Elevation on a 2-Manifold
Discrete & Computational Geometry
On the Local Behavior of Spaces of Natural Images
International Journal of Computer Vision
Zigzag persistent homology and real-valued functions
Proceedings of the twenty-fifth annual symposium on Computational geometry
Foundations of Computational Mathematics
Computing Robustness and Persistence for Images
IEEE Transactions on Visualization and Computer Graphics
Alexander duality for functions: the persistent behavior of land and water and shore
Proceedings of the twenty-eighth annual symposium on Computational geometry
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The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. Our account of the subject is expository, devoid of proofs, and written for non-experts in algebraic topology.