Coronal holes can be identified as the regions with magnetic field lines extending far away from the Sun, or the darkest regions in EUV/X-ray images with predominantly unipolar magnetic fields. A comparison between the locations of our determined regions with open magnetic field lines (OMF) and regions with low EUV intensity (LIR) reveals that only 12% of the OMF regions coincide with the LIRs. The aim of this study is to investigate the conditions leading to the different brightnesses of OMF regions, and to provide a means to predict whether an OMF region would be bright or dark. Examining the statistical distribution profiles of the magnetic field expansion factor (f s ) and Atmospheric Imaging Assembly 193 intensity (I 193 ) reveals that both profiles are approximately log-normal. The analysis of the spatial and temporal distributions of f s and I 193 indicates that the bright OMF regions often are inside or next to regions with closed field lines, including quiet-Sun regions and regions with strong magnetic fields. Examining the relationship between I 193 and f s reveals a weak positive correlation between log I 193 and log f s , with a correlation coefficient ≈0.39. As a first-order approximation, the positive relationship is determined to be log I 193 = 0.62 log f s + 1.51 based on the principle of the whitening/dewhitening transformation. This linear relationship is demonstrated to increase the consistency between the OMF regions and LIRs from 12% to 23%.