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The two title concepts have been evolving rather rapidly, but independent of each other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image processing as it can describe a measure of similarity between images. Its minimization might, for example, suggest the best match in image alignment. On the other hand, MMOSPA estimation has been applied largely to multi-target tracking...
We consider the problem of clustering set-valued observations, i.e., each observation is a set that consists of a finite number of real vectors. For this purpose, we develop a k-means algorithm that employs the OSPA distance for measuring the distance between sets. In particular, we introduce a novel alternating optimization algorithm for the OSPA barycenter of sets with varying cardinalities that...
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