| Popis: |
During the last few years, a considerable amount of research has been conducted to study multiscale properties of images via partial differential equations. In this context, we can roughly divide the methodology into three different formulations, namely the scale space formulation, the regularization formulation, and the inverse scale space formulation. In this chapter, we propose an inverse scale space formulation for matrix valued images using the operator-algebraic approach recently introduced by Burgeth et al. in 2007 (B. Burgeth, S. Didas, L. Florack, and J. Weickert. A generic approach to diffusion filtering of matrix-fields. Computing, 81(2–3):179–197, 2007; B. Burgeth, S. Didas, L. Florack, and J. Weickert. A Generic Approach to the Filtering of Matrix Fields with Singular PDEs. In Scale Space and Variational Methods in Computer Vision. Volume 4485 of Lecture Notes in Computer Science, pages 556–567. Springer, Heidelberg, 2007). We perform numerical experiments on synthetic tensor fields and on real diffusion tensor data from DT-MRI of a human brain. |
