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Title: Elastic analysis of irregularly and sparsely sampled curves Authors:  Lisa Steyer - Humboldt University of Berlin (Germany) [presenting]
Almond Stoecker - Humboldt University of Berlin (Germany)
Sonja Greven - Humboldt University of Berlin (Germany)
Abstract: Even though functional shape data is assumed to consist of continuous curves (up to invariances), these curves are usually not observed in practice. In real applications, the outline of an object, for example a bone, is often observed only at a small number of discrete points, which even might not correspond for different curves. To approximate the elastic distance between irregularly and sparsely sampled curves, we interpret them as polygons, hence treat them as piece-wise linear. We can show that the warping problem simplifies in this case where at least one of the curves is piece-wise linear, and use this to improve computations. We use this approximation to provide distance-based methods for observed curves modulo warping and to compute smooth means for samples of curves.