TY - JOUR
T1 - Fast inversion of matrices arising in image processing
AU - Fischer, Bernd
AU - Modersitzki, Jan
PY - 1999/1/1
Y1 - 1999/1/1
N2 - In recent years, new nonlinear partial differential equation (PDE) based approaches have become popular for solving image processing problems. Although the outcome of these methods is often very promising, their actual realization is in general computationally intensive. Therefore, accurate and efficient schemes are needed. The aim of this paper is twofold. First, we will show that the three dimensional alignment problem of a histological data set of the human brain may be phrased in terms of a nonlinear PDE. Second, we will devise a fast direct solution technique for the associated structured large systems of linear equations. In addition, the potential of the derived method is demonstrated on real-life data.
AB - In recent years, new nonlinear partial differential equation (PDE) based approaches have become popular for solving image processing problems. Although the outcome of these methods is often very promising, their actual realization is in general computationally intensive. Therefore, accurate and efficient schemes are needed. The aim of this paper is twofold. First, we will show that the three dimensional alignment problem of a histological data set of the human brain may be phrased in terms of a nonlinear PDE. Second, we will devise a fast direct solution technique for the associated structured large systems of linear equations. In addition, the potential of the derived method is demonstrated on real-life data.
UR - http://www.scopus.com/inward/record.url?scp=0033454590&partnerID=8YFLogxK
U2 - 10.1023/A:1019194421221
DO - 10.1023/A:1019194421221
M3 - Journal articles
AN - SCOPUS:0033454590
SN - 1017-1398
VL - 22
SP - 1
EP - 11
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 1
ER -