A Singular Value Decomposition based Maximal Poisson-disk Sampling for adaptive Digital Elevation Model simplification

The proposed method is to do simplification for Digital Elevation Model (DEM), which uses a few of original nodes representing the terrain surface while maintaining the accuracy. The original DEM nodes are sampled using the Maximal Poisson-disk Sampling (MPS), in which, the disk’s size of each sample is computed on basis of the Singular Value Decomposition (SVD). MPS can generate the hyper-uniformly distributed samples and was taken to do DEM adaptive sampling by being combined with the geodesic metric. However, the geodesic distance computation is complex and the requirement for memory is high. As such, this paper proposes an extension of the classic MPS based method for selecting quasi-randomly distributed points from DEM nodes based on the distribution of eigenvalues, accounting for surface heterogeneity. To achieve this objective, uniform MPS is conducted to sample the DEM nodes by setting the related disk radius to be inversely proportional to the local terrain complexity, which is defined as an index expressing the local terrain variation. Then, the geodesic metric related parameters are implicitly contained in the defined index. As a result, more samples are concentrated in the rugged regions, and vice versa. The proposed method shows better perfermance, at least the results are comparable with the geodesic distance based Poisson disk sampling method. Meanwhile, it greatly accelerates the sampling process and reduces the memory cost.