Hierarchical Blocksize Experiments

in Chapter 3

These experiments decompose the five test DEMs using variable block size based on the quality of the compressed block. If error in the compressed block is over a certain user-specified RMSE, the block is recursively subdivided until all blocks are under the specified error.

All of the following "map tables" show the difference between the original DEM and a set of degraded DEMs created using different maximum block RMSE tolerances and quality levels. The left hand map table decomposes the each block into four sub-blocks, while the right hand map table decomposes each block into nine overlapping sub-blocks. In each table,  rows represent quantization levels. Row one is q-level 1, row two is q-level 2, row three is q-level 4, row four is q-level 8, and row five is q-level 16. The color scale for images in each table is the following:
 
 

Cactus, CA (100 x 100)

Blocking artifacts are apparent in both images for the low RMSE/high q-levels. Using overlapping blocks removes some but not all of this error.
 

Krypton, Kentucky

Blk RMSE 3

Blk RMSE 6

Blk RMSE 9

Blk RMSE 3

Blk RMSE 6

Blk RMSE 9

Error is much higher overall than for Cactus. Blocking errors are more apparent in a few of the non-overlapping blocks, but in general this is not a major component of error. Error magnitude is greater for RMSE 9, q-level 2 than it is for higher q-level settings. There is very little difference between RMSE settings at high q-levels. This is because error at those settings persists even at small block sizes.

The very low error patch in the upper left corner of most images is a relatively flat valley. This is captured well, even at high q-levels.

Looney, Virginia

Blk RMSE 2

Blk RMSE 4

Blk RMSE 8

Blk RMSE 2

Blk RMSE 4

Blk RMSE 8

The overlapping method reduces blocking artifacts for low q-value settings on Looney, and little error remains for DEMs employing smaller block size / lower q-value settings. At high blocksize / quality settings artifacts take on a characteristic "ripple" look; compare with Saline, for example. Blocking artifacts are very noticeable in the high q-level, lower RMSE maps.

McHenry's Peak, Colorado

Blk RMSE 2

Blk RMSE 4

Blk RMSE 8

Blk RMSE 2

Blk RMSE 4

Blk RMSE 8

Compare the error maps with low RMSE / high q-value setting to those for the uniform block case with blocksize 4. There is little or no difference, because the almost all blocks have been subdivided to the minimum size.
 

Saline, Michigan

Blk RMSE 2

Blk RMSE 4

Blk RMSE 8

Blk RMSE 2

Blk RMSE 4

Blk RMSE 8

Blocking artifacts are present especially for the non-overlapping block table. Error takes on the characteristic "ripple look" in the lower right-hand portion of the tables. This effect is mitigated for intermediate levels by the variable block sizes.