Labelled opening and top-hat
We indicate by A(?,?) the set of points for which the angular values a(x) are in the sector [?, ?+?] A(?, ?) = { x : x ? E, a(x) ? [?, ? +?] }
Let {gl, l > 0} be an opening of size l.
The opening gl[A(?, ?)] behaves like an opening on a binary set.
In order to isotropise it, we take the union of the transformations gl [A(?, ?)] with 0 ? a ? 2p: g(l, w) = ?{gl [A(?, ?)], 0 ? a ?2p}
The top-hat residue is g(l, w) [inverse]