The Beltrami Flow over Implicit Manifolds

Authors:
Nir Sochen;Rachid Deriche;Lucero Lopez Perez
Affiliations:
-;-;-
Venue:
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Year:
2003

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Abstract

In many medical computer vision tasks the relevant data isattached to a specific tissue such as the colon or the cortex.This situation calls for regularization techniques whichare defined over surfaces.We introduce in this paper theBeltrami flow over implicit manifolds.This new regularizationtechnique overcomes the over-smoothing of the L2flow and the staircasing effects of the L1 flow, that wererecently suggested via the harmonic map methods.The keyof our approach is first to clarify the link between the intrinsic Polyakov action and the implicit Harmonic energyfunctional and then use the geometrical understanding ofthe Beltrami Flow to generalize it to images on implicitlydefined non flat surfaces.It is shown that once again theBeltrami flow interpolates between the L2 and L1 flows onnon-flat surfaces.The implementation scheme of this flowis presented and various experimental results obtained on aset of various real images illustrate the performances of theapproach as well as the differences with the harmonic mapflows.This extension of the Beltrami flow to the case of nonflat surfaces opens new perspectives in the regularization ofnoisy data defined on manifolds.