No abstract

We describe a surface compression technique to lossily compress elevation datasets. Our approach first approximates the uncompressed terrain using an over-determined system of linear equations based on the Laplacian partial differential equation. Then the approximation is refined with respect to the uncompressed terrain using an error metric. These two steps work alternately until we find an approximation that is good enough. We then further compress the result to achieve a better overall compression ratio. We present experiments and measurements using different metrics and our method gives convincing results.

We examine a smugglers and border guards scenario. We place observers on a terrain so as to optimize their visible coverage area. Then we compute a path that a smuggler would take so as to avoid detection, while also minimizing the path length. We also examine how our results are affected by using a lossy representation of the terrain instead.We propose three new application-specific error metrics for evaluating terrain compression. Our target terrain applications are the optimal placement of observers on a landscape and the navigation through the terrain by smugglers. Instead of using standard metrics such as average or maximum elevation error, we seek to optimize our compression on the specific real-world application of smugglers and border guards.

We present the GeoStar project at RPI, which researches various terrain (i.e., elevation) representations and operations thereon. This work is motivated by the large amounts of hi-res data now available. The purpose of each representation is to lossily compress terrain while maintaining important properties. Our ODETLAP representation generalizes a Laplacian partial differential equation by using two inconsistent equations for each known point in the grid, as well as one equation for each unknown point. The surface is reconstructed from a carefully-chosen small set of known points. Our second representation segments the terrain into a set of regions, each of which is simply described. Our third representation has the most long term potential: scooping, which forms the terrain by emulating surface water erosion.Siting hundreds of observers, such as border guards, so that their viewsheds jointly cover the maximum terrain is our first operation. This process allows both observer and target to be above the local terrain, and the observer to have a finite radius of interest. Planning a path so that a smuggler may get from point A to point B while maximally avoiding the border guards is our second operation. The path metric includes path length, distance traveled uphill, and amount of time visible to a guard.The quality of our representations is determined, not only by their RMS elevation error, but by how accurately they support these operations.

We present a better algorithm for path planning on complex terrain in the presence of observers and define several metrics related to path planning to evaluate the quality of various terrain compression strategies.The path-planning algorithm simulates a smugglers and border guards scenario. First, we place observers on a terrain so as to optimize their visible coverage area. Next, we compute a path that a smuggler would take to minimize detection by an observer, path length, and uphill movement. The smuggler is allowed the full range of Euclidean motion on the 2-dimensional plane, unlike alternate path planning schemes that strictly avoid obstacles. We use two runs of the A* algorithm to efficiently compute this path.We introduce new application-specific error metrics for evaluating lossy terrain compression. The target terrain applications are the optimal placement of observers on a landscape and the navigation through the terrain by smugglers. The error metrics compare the observer visibility and the cost of the optimal smuggler's route on the reconstructed terrain to the original terrain.