A PDE Solution of Brownian Warping

TY - GEN

T1 - A PDE Solution of Brownian Warping

AU - Nielsen, Mads

AU - Johansen, Peter

N1 - Conference code: 8

PY - 2004

Y1 - 2004

N2 - A Brownian motion model in the group of diffeomorphisms has been introduced as creating a least committed prior on warps. This prior is source destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 create invertible warps. In this paper, we formulate a Partial Differential Equation for obtaining the maximum likelihood warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric.

AB - A Brownian motion model in the group of diffeomorphisms has been introduced as creating a least committed prior on warps. This prior is source destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 create invertible warps. In this paper, we formulate a Partial Differential Equation for obtaining the maximum likelihood warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric.

U2 - 10.1007/b97873

DO - 10.1007/b97873

M3 - Article in proceedings

SN - 978-3-540-21981-1

T3 - Lecture notes in computer science

SP - 180

EP - 191

BT - Computer Vision - ECCV 2004

PB - <Forlag uden navn>

T2 - European Conference on Computer Vision

Y2 - 29 November 2010

ER -