Fig 1.
Discretization of a two-dimensional domain (left) and its quadtree representation (right).
The entire domain corresponds to the root of the tree (level 0). Each cell can then be recursively subdivided further into four children. In this example, the tree is non-graded, since the difference of level between some adjacent cells exceeds one. (Color online.)
Fig 2.
Quadtree refinement of an image.
Fig 3.
Local grid configuration near a node v0.
The schematic on the right describes a T-junction where a node is missing in the x-direction.
Fig 4.
Neighboring vertices of a node v0 in three spatial dimensions.
Fig 5.
A one-dimensional adaptive grid.
Fig 6.
Medical data processed on uniform grids (top row) and on adaptive grids (bottom row) illustrating the similarity in results.
In both cases, 268 frames with size 202 × 201 are processed. Timing is 25 minutes (1500 seconds) in the case of uniform grids and about 3.5 minutes (216 seconds) in the case of the current approach on adaptive grids.
Fig 7.
Three dimensional representation of the segmentation of Fig 6, which illustrates the changes in topology.
Fig 8.
Image sequence for a half period (T/2) for patient 12.
The top row gives the segmentation in 3D, while the remaining rows give the top, middle and bottom cross-sections of the segmentation on top of the data for t = 0, t = T/4 and t = T/2, respectively.
Fig 9.
Image sequence for a half period (T/2) for patient 13.
The top row gives the segmentation in 3D, while the remaining rows give cross-sections of the segmentation on top of the data.
Fig 10.
Image sequence for a half period (T/2) for patient 15.
The top row gives the segmentation in 3D, while the remaining rows give cross-sections of the segmentation on top of the data.
Fig 11.
Two vortex in 2D: 500 frames with size 100 × 100, performed in 637.65 seconds.