  We apply a new approach to quantifying galaxy morphology and identifying
galaxy mergers to the rest-frame far-ultraviolet images of 82 z ~ 4 Lyman break
galaxies (LBGs) and 55 1.2 < z < 1.8 emission-line galaxies in the GOODS and
Ultra Deep Fields. We compare the distributions of the Gini coefficient (G),
second-order moment of the brightest 20% of galaxy light (M20), and
concentration (C) for high-redshift and low-redshift galaxies with average
signal to noise per pixel > 2.5 and Petrosian radii > 0.3 arcsec. Ten of the 82
LBGs have M20 >= -1.1 and possess bright double or multiple nuclei, implying a
major-merger fraction of star-forming galaxies ~ 10-25% at M_{FUV} < -20,
depending on our incompleteness corrections. Galaxies with bulge-like
morphologies (G >= 0.55, M20 < -1.6) make up ~ 30% of the z ~ 4 LBG sample,
while the remaining ~ 50% have G and M20 values higher than expected for smooth
bulges and disks and may be star-forming disks, minor-mergers or post-mergers.
The star-forming z ~ 1.5 galaxy sample has a morphological distribution which
is similar to the UDF z ~ 4 LBGs, with an identical fraction of major-merger
candidates but fewer spheroids. The observed morphological distributions are
roughly consistent with current hierarchical model predictions for the
major-merger rates and minor-merger induced starbursts at z ~ 1.5 and ~4. We
also examine the rest-frame FUV-NUV and FUV-B colors as a function of
morphology and find no strong correlations at either epoch.
