Research
A computational method using multiresolution for volumetric data integration
1 Department of Mathematics, Bilecik Seyh Edebali University, Bilecik, 11210, Turkey
2 Department of Mathematics, Yildiz Technical University, Istanbul, 34220, Turkey
3 Department of Mathematical Engineering, Yildiz Technical University, Istanbul, 34220, Turkey
4 School of Electrical Eng. and Computer Science, Ohio University, Athens, OH, 45701-2979, USA
Boundary Value Problems 2012, 2012:115 doi:10.1186/1687-2770-2012-115
Published: 17 October 2012Abstract
In this paper, we present a new method for integration of 3-D medical data by utilizing
the advantages of 3-D multiresolution analysis and techniques of variational calculus.
We first express the data integration problem as a variational optimal control problem
where we express the displacement field in terms of wavelet expansions and, secondly,
we write the components of the displacement field in terms of wavelet coefficients.
We solve this optimization problem with a blockwise descent algorithm. We demonstrate
the registration of 3-D brain MR images in the size of 
as an application of the present method. Experimental results indicate that the method
can integrate 3-D MR images better than only variational or only wavelet-based methods.
MSC: 68U10, 65D18, 65J05, 97N40.
