There is a scientific journal article having a line:
"In order to study the star formation scenario in the radial direction of the LMC...."
What is meant by 'radial direction' of a galaxy ?
'Radial direction' typically means from the center, moving outwards. Typically, these kinds of studies will break a galaxy up into several annuli, or rings, and examine the star formation activity within each ring. (Imagine drawing a series of concentric circles, each one a little bigger than the last.) Then, if the star formation rate or star formation history changes as a function of radius, those changes can be more easily quantified.
It is often difficult to do this well because galaxies are not perfectly symmetric. The LMC, for instance, is a dwarf irregular galaxy, meaning its structure is not nearly as orderly as some other galaxies (e.g. The Milky Way, which is a spiral). The LMC does contain more stars near its center, and it even has a bar, but it is difficult to discern much more structure than that. To define the center of such a galaxy, the total light profile is measured and the centroid calculated.
Since we are rarely fortunate enough to be looking at another galaxy perfectly face-on, we also have to consider the effects of inclination on our observations. (If you were to hold up a plate and angle it a little bit, it would begin to look like an oval, but that doesn't mean it isn't still actually round.) If they have taken inclination into account, they should reference the "deprojected radius." That means that they know that the inclination to our line of sight makes some parts of the galaxy look closer to the center than they actually are, and they corrected for that effect.
In spherical coordinates (galaxy viewed as a ball) it would mean any vector going through the center point, in zylindrical coordinates (galaxy viewed as a disc) it is any vector going through the rotation axis of the disc.