Task: Summarization
Input (English): We introduce an analytic distance function for moderately sized point sets of known cardinality that is shown to have very desirable properties, both as a loss function as well as a regularizer for machine learning applications. We compare our novel construction to other point set distance functions and show proof of concept experiments for training neural networks end-to-end on point set prediction tasks such as object detection.
Output (English): Proposes a new loss for points registration (aligning two point sets) with preferable permutation invariant property.