  Advances in vectorial polarisation-resolved imaging are bringing new
capabilities to applications ranging from fundamental physics through to
clinical diagnosis. Imaging polarimetry requires determination of the Mueller
matrix (MM) at every point, providing a complete description of an object's
vectorial properties. Despite forming a comprehensive representation, the MM
does not usually provide easily-interpretable information about the object's
internal structure. Certain simpler vectorial metrics are derived from subsets
of the MM elements. These metrics permit extraction of signatures that provide
direct indicators of hidden optical properties of complex systems, while
featuring an intriguing asymmetry about what information can or cannot be
inferred via these metrics. We harness such characteristics to reveal the
spin-Hall effect of light, infer microscopic structure within laser-written
photonic waveguides, and conduct rapid pathological diagnosis through analysis
of healthy and cancerous tissue. This provides new insight for the broader
usage of such asymmetric inferred vectorial information.
