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With the rise of the Internet of Things, strategies for effectivelyprocessing big data are essential for discovering meaningul insights. The timeseries datasets produced by groups of interconnected devices contain valuableunderlying patterns. Recent works have extracted patterns from spatio-temporaldatasets to aid in road network generation, activity recognition, and others.The speed and accuracy of the underlying geometry reconstruction are importantin these applications. Existing methods such as kernel density estimation (KDE)have been used but are often computationally expensive. We propose modifyingedge quadtrees to utilize their effective heirarchical structure. Ourmodification estimates density using a novel trajectory count function whichprovides mathematical guarantees on the stability of the count by enforcing aninvariance to local perturbations. We evaluate our method's effectiveness atextracting the underlying geometry and representative subsample points. Forverification, we compare against a KDE variant at extracting the underlyingshape of noisy synthetic trajectories travelling alonng the shape. We comparemap extraction from GPS traces against current methods. Our methodsignificantly improves runtime while extracting the geometry better or at leastcomparably. We also compare against maxmin subsampling on an activityrecognition data set and find a significant runtime improvement with comparableperformance.

Robust Trajectory-based Density Estimation for Geometric Structure Recovery: Theory and Applications