We study a sample of 16 bright and well-resolved late-type stars (10 O-rich giants, 2 red supergiants, and 4 C-rich giants) using the ESO VLTI/AMBER facility at medium resolution (R=1500}) in the K band to detect and measure the deviation from centrosymmetry of their resolved surface brightness distribution. As indicator for departure from centrosymmetry, we use the centrosymmetry parameter (CSP). We observe that CSP increases along the asymptotic giant branch, reaching values as large as 30°. These large CSP values are likely attributable to a few large photospheric convective cells. Carbon stars like W Ori and R Scl, being close to the AGB tip, have the second largest CSP values (17.6° and 22.3°, respectively), being only surpassed by the M5.5Ib/II supergiant T Cet (with CSP of 30.4°.). For K and early M giants, CSP values are smaller, never exceeding 10°, with a clear tendency to increase with the atmospheric pressure scaleheight. This supports the hypothesis that the observed deviations from centrosymmetry are somehow related to convective cells, whose size depends upon the atmospheric pressure scaleheight.