1. Parallel ODETLAP for Terrain Compression and Reconstruction
Jared Stookey, Zhongyi Xie, W. Randolph Franklin,
Marcus A. Andrade, Barbara Cutler, Daniel Tracy
Rensselaer Polytechnic Institute, Troy, NY
Abstract:
We introduce a parallel approximation of an Over-determined Laplacian Partial Differential Equation solver (ODETLAP) applied to the compression and restoration of terrain data used for Geographical Information Systems (GIS). With previous
methods, the time to execute ODETLAP does not scale well with the size of the input elevation map, resulting in running times that are prohibitively long for large data sets. Our algorithm divides the data set into patches, runs ODETLAP on each patch, and then merges the patches together.
ODETLAP:
Two sets of equations make the system over-determined: Laplacian Equation: every non-border point is the average of its neighbors:
4zij = zi-1,j+ zi+1,j + zi,j-1 + zi,j+1
New equation: Some points are already known:
zij = hij
Use a smoothness parameter R to interpolate the two, R reflect the relative importance of accuracy vs. smoothness.
Adds capabilities to the classical system
Local maxima inference
Inconsistent data conflation
Result:
1. Speedup by cutting into smaller pieces
2. Speedup from parallelism
3. Accuracy loss due to merging patches
The terrain is divided into overlapping patches. ODETLAP is solved separately on each patches, which will be merged into a whole patch using bilinear interpolation at the end
4. Detailed view of a challenging 100*100 patch
Merging Patches: We experimented with naively merging, simple overlapping merging and bilinear interpolation