  The problem of isometry for threshold-based sampling such as
integrate-and-fire (IF) or send-on-delta (SOD) is addressed. While for uniform
sampling the Parseval theorem provides isometry and makes the Euclidean metric
canonical, there is no analogy for threshold-based sampling. The relaxation of
the isometric postulate to quasi-isometry, however, allows the discovery of the
underlying metric structure of threshold-based sampling. This paper
characterizes this metric structure making Hermann Weyl's discrepancy measure
canonical for threshold-based sampling.
