  We develop a classification of perfectly transmitting resonances occuring in
effectively one-dimensional optical media which are decomposable into locally
reflection symmetric parts. The local symmetries of the medium are shown to
yield piecewise translation-invariant quantities, which are used to distinguish
resonances with arbitrary field profile from resonances following the medium
symmetries. Focusing on light scattering in aperiodic multilayer structures, we
demonstrate this classification for representative setups, providing insight
into the origin of perfect transmission. We further show how local symmetries
can be utilized for the design of optical devices with perfect transmission at
prescribed energies. Providing a link between resonant scattering and local
symmetries of the underlying medium, the proposed approach may contribute to
the understanding of optical response in complex systems.
