Convolution pyramids

Zeev Farbman*, Raanan Fattal, Dani Lischinski

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations


We present a novel approach for rapid numerical approximation of convolutions with filters of large support. Our approach consists of a multiscale scheme, fashioned after the wavelet transform, which computes the approximation in linear time. Given a specific large target filter to approximate, we first use numerical optimization to design a set of small kernels, which are then used to perform the analysis and synthesis steps of our multiscale transform. Once the optimization has been done, the resulting transform can be applied to any signal in linear time. We demonstrate that our method is well suited for tasks such as gradient field integration, seamless image cloning, and scattered data interpolation, outperforming existing state-of-the-art methods.

Original languageAmerican English
Title of host publicationProceedings of the 2011 SIGGRAPH Asia Conference, SA'11
StatePublished - 2011
Event2011 SIGGRAPH Asia Conference, SA'11 - Hong Kong, China
Duration: 12 Dec 201115 Dec 2011

Publication series

NameProceedings of the 2011 SIGGRAPH Asia Conference, SA'11


Conference2011 SIGGRAPH Asia Conference, SA'11
CityHong Kong


  • Convolution
  • Green's functions
  • Poisson equation
  • Scattered data interpolation
  • Seamless cloning
  • Shepard's method


Dive into the research topics of 'Convolution pyramids'. Together they form a unique fingerprint.

Cite this