Tensorial manifest invariant index notation is the most common notation
used to express invariants.
is the result of applying filter
to an image, hence
is a second order tensor. A polynomial invariant of the L terms can be
constructed by expanding the Manifest Invariant notation using Einstein
summation [
7
]. For example the second order invariant
expands as follows in two dimensions:
As well as the L tensors,
represents a constant tensor known as Epsilon or the Levi-Civita tensor.
In D dimensions Epsilon has D indices and is defined as follows:
Kevin Walker