Add isotropic Gaussian kernels at own risk: more and more resilient modes in higher dimensions
Proceedings of the twenty-eighth annual symposium on Computational geometry
An output-sensitive algorithm for persistent homology
Computational Geometry: Theory and Applications
Technical Section: Topological saliency
Computers and Graphics
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Interpreting an image as a function on a compact subset of the Euclidean plane, we get its scale-space by diffusion, spreading the image over the entire plane. This generates a 1-parameter family of functions alternatively defined as convolutions with a progressively wider Gaussian kernel. We prove that the corresponding 1-parameter family of persistence diagrams have norms that go rapidly to zero as time goes to infinity. This result rationalizes experimental observations about scale-space. We hope this will lead to targeted improvements of related computer vision methods.