Context :

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 .
We study how the selection of core extraction parameters affects the accuracy and completeness limit of the derived CMF and the core masses , and also how accurately the CMF can be derived in varying core crowding conditions .

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 the mean diameter of the cores ( f > 1 ) .
If this condition holds , the derived CMF for the Pipe nebula background is accurate and complete above M \gtrsim 0.8 \dots 1.5 M _ { \odot } , 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 also show that when f \gtrsim 1.5 , the masses of individual cores are recovered with a typical uncertainty of 25 \dots 30 % .
When f \approx 1 the uncertainty is \sim 60 % .
In very crowded cases where f < 1 the core identification algorithm is unable to recover the masses of the cores adequately , and the derived CMF is unlikely to represent the underlying CMF .
For the cores of the Pipe nebula f \approx 2.0 and therefore the use of the method in that region is justified .

Conclusions :