Approximate isocontours and spatial summaries for sensor networks

13 years 10 months ago

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We consider the problem of approximating a family of isocontours in a sensor ﬁeld with a topologically-equivalent family of simple polygons. Our algorithm is simple and distributed, it gracefully adapts to any user-speciﬁed representation size k, and it delivers a worst-case guarantee for the quality of approximation. In particular, we prove that the topology-respecting Hausdorﬀ error in our k-vertex approximation is within a small constant factor of the optimal error possible with Θ(k/ log m) vertices, where m is the number of contours. Evaluation of the algorithm on real data suggests that the size increase factor in practice is a constant near 2.6, and shows no error increase. Our simulation results using a variety of synthetic and real data show that the algorithm smoothly handles complex isocontours, even for representation sizes as small as 32 or 48. Because isocontours are widely used to represent and communicate bi-variate signals, our technique is broadly applicable to...

Sorabh Gandhi, John Hershberger, Subhash Suri

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