Proximal groups: Extension of topological groups. Application in the concise representation of Hilbert envelopes on oscillatory motion waveforms

In this paper, we introduce proximal groups that are a generalization of topological groups. A straight-forward application of proximal groups is given in the concise representation of collections of overlapping Hilbert envelope lobes attached to the peak points on oscillatory motion waveforms that occur in sequences of video frames that track object movements.