Three-dimensional stereophotogrammetric analysis of 50 smiles: A study of dento-facial proportions

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The purpose of this study was to analyze 50 smiles using 3D stereophotogrammetry (3D-spg)-based facial reconstruction, to calculate ratios involving measurements of the distances between dental and facial landmarks and to compare these ratios with the golden ratio φ (1.618).

Materials and Methods:

Fifty subjects with no obvious malocclusion participated in this study. For each subject, 4 photographs were acquired using the LifeViz Mini™, an absolute calibration 3D-spg system. Facial and dental landmarks (based on Farkas' definitions) were fixed, and 8 distances were measured. Four ratios were then calculated and compared with the value of 1.618.


The ratio “incisal edge of the maxillary central incisor—lower border of the chin/subnasal point—incisal edge of the maxillary central incisor” (IE-Me/SN-IE) was 1.693 ± 0.190, the ratio “right endocanthion—left endocanthion/right exocanthion—right endocanthion” was 1.582 ± 0.173, the ratio “incisal edge of the maxillary central incisor—distal edge of the right canine/distal edge of the right canine—right labial commissure” was 1.670 ± 0.355, and the ratio “right labial commissure—left labial commissure/distal edge of the right canine—distal edge of the left canine” was 1.602 ± 0.136. In contrast, the vertical ratio IE-Me/SN-IE significantly differed from the golden ratio (1 sample t test, P = .009).


This study revealed that the observed ratios were surprisingly close to the golden ratio. Only the vertical ratio differed from the golden ratio, whereas the horizontal ratios appear to be adequately approximated by φ.


If the distances from reference points of the face to teeth within a harmonious smile exhibited recurring esthetic proportions, knowledge of such ratios would provide an additional tool for the elaboration of esthetic treatment plans. In addition, this knowledge could provide guidance when planning tooth positions and dental proportions by encouraging consideration of the global nature of the oro-facial sphere.

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