In this paper, we will give some results for developing the two-dimensional differential transform (TDDT) for double integrals. Then the TDDT method will be developed for solving a class of two-dimensional linear and nonlinear Volterra integral equations. We also give some examples to demonstrate th
Three-Dimensional linear and nonlinear transformations: An integration of light microscopical and MRI data
β Scribed by Thorsten Schormann; Karl Zilles
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 463 KB
- Volume
- 6
- Category
- Article
- ISSN
- 1065-9471
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β¦ Synopsis
The registration of image volumes derived from different imaging modalities such as MRI, PET, SPECT, and CT has been described in numerous studies in which functional and morphological data are combined on the basis of macrostructural information. However, the exact topography of architectural details is defined by microstructural information derived from histological sections. Therefore, a technique is developed for integrating micro- and macrostructural information based on 1) a three-dimensional reconstruction of the histological volume which accounts for linear and nonlinear histological deformations, and 2) a two-step procedure which transforms these volumes to a reference coordinate system. The two-step procedure uses an extended principal axes transformation (PAT) generalized to affine transformations and a fast, automated full-multigrid method (FMG) for determining high-dimensional three-dimensional nonlinear deformations in order to account for differences in the morphology of individuals. With this technique, it is possible to define upwards of 1,000 times the resolution of approximately 1 mm in MRI, making possible the identification of geometric and texture features of microscopically defined brain structures.
π SIMILAR VOLUMES
## Tari et al. [A. Tari, M.Y. Rahimi, S. Shahmorad, F. Talati, Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method, J. Comput. Appl. Math. 228 (2009) 70-76], presented some fundamental properties of TDTM for the kernel functions