  Aims: We examine the recoverability and completeness limits of the dense core
mass functions (CMFs) derived for a molecular cloud using extinction data and a
core identification scheme based on two-dimensional thresholding.
  Methods: We performed simulations where a population of artificial cores was
embedded into the variable background extinction field of the Pipe nebula. We
extracted the cores from the simulated extinction maps, constructed the CMFs,
and compared them to the input CMFs. The simulations were repeated using a
variety of extraction parameters and several core populations with differing
input mass functions and differing degrees of crowding.
  Results: The fidelity of the observed CMF depends on the parameters selected
for the core extraction algorithm for our background. More importantly, it
depends on how crowded the core population is. We find that the observed CMF
recovers the true CMF reliably when the mean separation of cores is larger than
their mean diameter (f>1). If this condition holds, the derived CMF is accurate
and complete above M > 0.8-1.5 Msun, depending on the parameters used for the
core extraction. In the simulations, the best fidelity was achieved with the
detection threshold of 1 or 2 times the rms-noise of the extinction data, and
with the contour level spacings of 3 times the rms-noise. Choosing larger
threshold and wider level spacings increases the limiting mass. The simulations
show that when f>1.5, the masses of individual cores are recovered with a
typical uncertainty of 25-30 %. When f=1 the uncertainty is ~60 %. In very
crowded cases where f<1 the core identification algorithm is unable to recover
the masses of the cores adequately. For the cores of the Pipe nebula f~2.0 and
therefore the use of the method in that region is justified.
