  The Crab Pulsar is the prime example of an emitter of giant pulses. These
short, very bright pulses are thought to originate near the light cylinder, at
$\sim\!1600{\rm\;km}$ from the pulsar. The pulsar's location inside the Crab
Nebula offers an unusual opportunity to resolve the emission regions, using the
nebula, which scatters radio waves, as a lens. We attempt to do this using a
sample of 61998 giant pulses found in coherently combined European VLBI network
observations at $18{\rm\;cm}$. These were taken at times of relatively strong
scattering and hence good effective resolution, and from correlations between
pulse spectra, we show that the giant pulse emission regions are indeed
resolved. We infer apparent diameters of $\sim\!2000$ and $\sim\!2400{\rm\;km}$
for the main and interpulse components, respectively, and show that with these
sizes the correlation amplitudes and decorrelation timescales and bandwidths
can be understood quantitatively, both in our observations and in previous
ones. Using pulse-spectra statistics and correlations between polarizations, we
also show that the nebula resolves the nanoshots that comprise individual giant
pulses. The implied diameters of $\sim\!1100{\rm\;km}$ far exceed light
travel-time estimates, suggesting the emitting plasma is moving
relativistically, with $\gamma\simeq10^{4}$, as inferred previously from
drifting bands during the scattering tail of a giant pulse. If so, the emission
happens over a region extended along the line of sight by
$\sim\!10^{7}{\rm\;km}$. We conclude that relativistic motion likely is
important for producing giant pulses, and may be similarly for other sources of
short, bright radio emission, such as fast radio bursts.
