This paper presents a comparison of local descriptors for a set of 26 craniofacial landmarks annotated on 144 scans acquired in the context of clinical research. We focus on the accuracy of the different descriptors on a per-landmark basis when constrained to a local search. For most descriptors, we find that the curves of expected error against the search radius have a plateau that can be used to characterize their performance, both in terms of accuracy and maximum usable range for the local search. Six histograms-based descriptors were evaluated: three describing distances and three describing orientations. No descriptor dominated over the rest and the best accuracy per landmark was strongly distributed among 3 of the 6 algorithms evaluated. Ordering the descriptors by average error (over all landmarks) did not coincide with the ordering by most frequently selected, indicating that a comparison of descriptors based on their global behavior might be misleading when targeting facial landmarks.