The Elevation Pyramid

The elevation pyramid, a pyramid-based representation for storing gridded elevation data, is described. Associated with the root of the pyramid is the corresponding grid's minimum elevation and range. The elevation value for a specified grid pixel is calculated by transversing a path from the pyramid root to the corresponding leaf node. As the transversal proceeds, the minimum and range values are refined by interpreting the codes stored at each node along the path. At the leaf level, the final minimum value equals the associated elevation value. We present results from experiments using 2,3 and 4 bit code words. For the two bit code, since the total number of nodes in the pyramid is 4/3 the number of pixels required for the bottom level of the pyramid, the amortized storage cost is less than 3 bits per pixel, regardless of vertical resolution. This corresponds to a 5:1 compression rate for a 16 bit gridded elevation data. The elevation pyramid is most appropriate for efficient secondary storage archival, such as on a CD-ROM. It allows efficient retrieval of complete elevation data from any sub-region, at multiple scales, within the entire elevation database. This is a lossless encoding when the difference between sibling pixels is not "too great." Rapid changes in elevation between adjacent pixels will be smoothed. Most data sets contain relatively few pixels that cannot be encoded by the techniques studied. Such pixels can be efficiently stored in an auxiliary table if perfec reconstruction is required. "Elevation" pyramids can be used to store any 2D surface or 3D density data.