  Given a real inner product space V and a group G of linear isometries, max
filtering offers a rich class of G-invariant maps. In this paper, we identify
nearly sharp conditions under which these maps injectively embed the orbit
space V/G into Euclidean space, and when G is finite, we estimate the map's
distortion of the quotient metric. We also characterize when max filtering is a
positive definite kernel.
