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Bredart (2003) discusses your exact hypothesis and reports the results of a couple of studies. I'd recommend having a read of the article.

The authors acknowledge that in contrast to familiar others the experience of our own face typically comes through self-inspection in mirrors.

They summarise some relevant literature:

Troje and Kersten (1999) showed that participants were faster when naming frontal views compared with profile views of their own face, and that this advantage for frontal views disappeared when naming familiar colleagues’ faces. In addition, Laeng and Rouw (2001) showed that the full-frontal view is superior to other views for facial self-recognition but not for the recognition of other people’s faces. A pose corresponding to 22.5 degrees from the frontal view seems to be optimal for other people’s faces. However, for highly familiar faces (e.g. faces of close friends or partners), the frontal view could be recognised as quickly as the 22.5 degrees view. In short, because of ecological constraints on visual experience, self-recognition is easier from frontal views than from other views. This superiority of frontal views was not observed for other highly familiar faces.

They also discuss one methodology that involves "searching for a target face among a set of other faces". Thus, the speed of finding the face is one way operationalising familiarity.

With regards to their findings, the following quotes the abstract:

Experiment 1 examined our ability to recognise the usual horizontal orientation of our own face (mirror orientation) as compared with another very familiar face (normal orientation). Participants did not use the same kind of information in determining the orientation of self-face as in determining the orientation of the other familiar face. The proportion of participants who reported having based their judgement on the location of an asymmetric feature (e.g. a mole) was higher when determining their own face’s orientation than when determining the other familiar face’s orientation. In experiment 2, participants were presented with pairs of manipulated images of their own face and of another familiar face showing conflicting asymmetric features and configural information. Each pair consisted of one picture showing a given face’s asymmetric features in a mirror-reversed position, while the facial configuration was left unchanged, and one picture in which the location of the asymmetric features was left unchanged, while the facial configuration was mirror-reversed. As expected from the hypothesis that asymmetric local features are more frequently used for self-face judgements, participants chose the picture showing mirror-reversed asymmetric features when determining the usual orientation of their own face significantly more often than they chose the picture showing normally oriented asymmetric features when determining the orientation of the other face. These results were explained in terms of competing forward and mirror-reversed representations of our own face.

Reference