Wigner function as the expectation value of a parity operator

It is pointed out that the Wigner function $f(r, p)$ is 2/h times the expectation value of the parity operator that performs reflections about the phase-space point r, p. Thus $f(r, p)$ is proportional to the overlap of the wave function ψ with its mirror image about r, p; this is clearly a measure of how much ψ is centered about r, p, and the Wigner distribution function now appears physically more meaningful and natural than it did previously.