What are the Even and Odd Components of a 2D Signal A signal $x$ can be decomposed into 
its even, $x_e$, and odd, $x_o$, parts.
By,

$$
x_e(t) = \frac{1}{2} [x(t) + x(-t)]
$$

$$
x_o(t) = \frac{1}{2} [x(t) - x(-t)]
$$

What would be the equivalent for a multidimensional signal, such as a image signal?
The even part of a 2D image $x[n,m]$ is defined as:

$$x_e[n,m] = \frac{x[n,m] + x[-n,-m] }{2} $$

and the odd part is
$$x_o[n,m] = \frac{x[n,m] - x[-n,-m] }{2} $$.