Slope preserving lossy terrain compression

Abstract

Accurate terrain representation with appropriate preservation of important terrain characteristics, especially slope steepness, is becoming more crucial and fundamental as the geographical models are becoming more complex. Based on our earlier success with Overdetermined Laplacian Partial Differential Equations (ODETLAP), which allows for compact yet accurate compression of the Digital Elevation Model (DEM), we propose a new terrain compression technique that focuses on improving slope accuracy in compression of high resolution terrain data. With high slope accuracy and a high compression ratio, this technique will help geographical applications that require a high precision in slope yet also have strict constraints on data size. Our proposed technique has the following contribution: we modify the ODETLAP system by adding slope equations for some key points picked automatically so that we can compress the elevation without explicitly storing slope values. By adding these slope equations, we can perturb the elevation in such a way that when slope is computed from the reconstructed surface, they are accurate. Note we are not storing the slope explicitly, instead we only store the elevation difference at a few locations. Since the ultimate goal is to have a compact terrain representation, encoding is also an integral part of this research. We have used Run Length Encoding (RLE) and linear prediction in the past, which gave us substantial file size reduction. In addition to that, we also propose a Minimum Spanning Tree based encoding scheme that takes advantage of the spatial correlation between selected points. On a typical test, our technique is able to achieve a 1:10 compression at the cost of 4.23 degree of RMS slope error and 3.30 meters of RMS elevation error.

Chest X-Ray Image Annotation based on Spatial Relationship Feature Extraction

“…An incline slope occurs when the degree of slope is smaller than the right angle (90 0 ), while a decline slope occurs when the degree of slope is bigger than the right angle. Slope values are calculated using two methods namely trigonometry and geometry [40].…”