What does the visual representation of matched filtering of images look like?
There's really nothing special about image processing here: the matched filter is still the hermetian, spatially-inverse filter (=convolution kernel) to the original filter (=convolution kernel).
Since images tend to be real-valued, most convolutional kernels are, too. In which case you just flip the kernel along both axes and are done.
If the original kernel is symmetrical along both axes, it's its own matched filter.
The explanations used for the one-dimensional matched filter are the same as for the 2D case:
Cauchy-Schwarz inequality says that, for any given filter energy, a filter that fulfills the above criteria leads to the highest SNR in the additive uncorrelated noise case.