  With the aim of understanding the effect of the environment on the star
formation history and morphological transformation of galaxies, we present a
detailed analysis of the colour, morphology and internal structure of cluster
and field galaxies at $0.4 \le z \le 0.8$. We use {\em HST} data for over 500
galaxies from the ESO Distant Cluster Survey (EDisCS) to quantify how the
galaxies' light distribution deviate from symmetric smooth profiles. We
visually inspect the galaxies' images to identify the likely causes for such
deviations. We find that the residual flux fraction ($RFF$), which measures the
fractional contribution to the galaxy light of the residuals left after
subtracting a symmetric and smooth model, is very sensitive to the degree of
structural disturbance but not the causes of such disturbance. On the other
hand, the asymmetry of these residuals ($A_{\rm res}$) is more sensitive to the
causes of the disturbance, with merging galaxies having the highest values of
$A_{\rm res}$. Using these quantitative parameters we find that, at a fixed
morphology, cluster and field galaxies show statistically similar degrees of
disturbance. However, there is a higher fraction of symmetric and passive
spirals in the cluster than in the field. These galaxies have smoother light
distributions than their star-forming counterparts. We also find that while
almost all field and cluster S0s appear undisturbed, there is a relatively
small population of star-forming S0s in clusters but not in the field. These
findings are consistent with relatively gentle environmental processes acting
on galaxies infalling onto clusters.
