Diffusion Runs Low on Persistence Fast

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.

• Type: Journal
• Year: 2011
• Where: ICCV
• Authors: Chao Chen, Herbert Edelsbrunner
• Keywords: Compact Subset, Computer Vision, Computer Vision Methods, Gaussian Kernel, ICCV 2011