Context : Luminous Compact Galaxies ( LCGs ) ( M _ { B } \leq - 20 , R _ { 1 / 2 } \leq 4.5 kpc and EW _ { 0 } ( OII ) \geq 15Å ) constitute one of the most rapidly evolving galaxy populations over the last \sim 8 Gyr history of the universe . Due to their inherently compact sizes , any detailed quantitative analysis of their morphologies has proved to be difficult in the past . Hence , the morphologies and thereby the local counterparts of these enigmatic sources have been hotly debated . Aims : Our aim is to use the high angular resolution , deep , multiband HST/ACS imaging data , from the HST/ACS GOODS survey , to study the quantitative morphology of a complete sample of LCGs in the redshift range 0.5 \leq z \leq 1.2 . Methods : We have derived structural parameters for a representative sample of 39 LCGs selected from the GOODS-S HST/ACS field , using full 2-dimensional surface brightness profile fitting of the galaxy images in each of the four filters available . B _ { 435 W } - z _ { 850 LP } color maps are constructed for the sample to aid in the morphological classification . We then use the rest frame B band bulge flux fraction ( B/T ) to determine the morphological class of galaxies which are well fit by a bulge+disk two dimensional structure . Mergers were essentially identified visually by the presence of multiple maxima of comparable intensity in the rest frame B band images , aided by the color maps to distinguish them from HII regions . We also make use of the Spitzer 24 \mu m source catalog of sources in the CDFS to derive the dust enshrouded star formation rates ( SFR ) for some of the sample LCGs Results : We derive the following morphological mix for our sample of intermediate redshift LCGs : Mergers : \sim 36 % , Disk dominated : \sim 22 % , S0 : \sim 20 % , Early types : \sim 7 % , Irr/tadpole : \sim 15 % . We establish that our sample LCGs are intermediate mass objects with stellar mass ranging from 9.44 \leq Log _ { 10 } ( M / M _ { \odot } ) \leq 10.96 , with a median mass of Log _ { 10 } ( M / M _ { \odot } ) = 10.32 . We also derive SFR values ranging from a few to \sim 65 M _ { \odot } /year as expected for this class of objects . We find that LCGs account for \sim 26 % of the M _ { B } \leq - 20 galaxy population in the redshift range 0.5 \leq z \leq 1.2 . We estimate a factor \sim 11 fall in the comoving number density of blue LCGs from redshifts 0.5 \leq z \leq 1.2 to the current epoch , even though this number is subject to large uncertainities given the small sample size at zero redshift available from the literature . Conclusions : The strong redshift evolution exhibited by LCGs , and the fact that a significant fraction of LCGs are in merging systems , seem to indicate that LCGs might be an important phase in the hierarchical evolution of galaxies . We envisage that some of the LCGs that are classified as merging systems , might go on to rebuild their disks and evolve into disk galaxies in the local universe .