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C. Chen, H. Edelsbrunner:
"Diffusion runs low on persistence fast";
Vortrag: 13th IEEE International Conference on Computer Vision, Barcelona, Spanien; 06.11.2011 - 13.11.2011; in: "13th IEEE International Conference on Computer Vision", (2011), S. 1 - 8.

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 deï¬ ned
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 inï¬ nity. This result rationalizes experimental
observations about scale-space. We hope this will lead to
targeted improvements of related computer vision methods.