TY - GEN
T1 - Diffusion runs low on persistence fast
AU - Chen, Chao
AU - Edelsbrunner, Herbert
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84863031403
U2 - 10.1109/ICCV.2011.6126271
DO - 10.1109/ICCV.2011.6126271
M3 - Conference contribution
SN - 9781457711015
T3 - Proceedings of the IEEE International Conference on Computer Vision
SP - 423
EP - 430
BT - 2011 International Conference on Computer Vision, ICCV 2011
T2 - 2011 IEEE International Conference on Computer Vision, ICCV 2011
Y2 - 6 November 2011 through 13 November 2011
ER -