## 1 Introduction  
The Frankfort Craniometric Agreement of August 1882 is considered a landmark development in anthropometrics. It developed a horizontal plane of reference, referred to as the Frankfort horizontal (FH) plane. The FH plane or the auriculo-orbital plane closely represents the natural head position. Thus, it was rapidly adapted for patient orientation in cephalometric imaging [1]. The use of this plane has been increasingly employed with the advancement of cephalometry in orthodontics. Various analytical parameters and norms are in tandem with the FH plane.  
Cranofacial imaging modalities have undergone a marked evolution. Furthermore, 3D imaging modalities, such as cone-beam computed tomography (CBCT), have gained a large impetus. The ongoing advancement of CBCT imaging is concomitant with its rapid clinical adaptation for craniofacial analysis. The 3D perspective has made CBCT essential for the diagnosis of skeletal malformations, particularly concerning the assessment of facial symmetry [2]. However, the assessment standards have not kept pace amidst the increasing use of CBCT. Moreover, researchers often use variable definitions to describe similar cephalometric reference plane(s) [3]. Studies report on numerous combinations for defining the FH plane. The basic landmarks defining the plane are, namely, the orbitale (Or) and porion (Po). Nonetheless, researchers have used the variability among the choices viz. a four-point plane with bilateral Or and Po [4], a three-point plane with unilateral Po, Or [5], or a calculated median of either Po [6] and Or [7] landmarks.  
All 3D analyses require the orientation of the acquired image. A digital orientation device is used to reproduce the natural head position (NHP) or landmark-based orientation [8]. The popularity of landmark-based orientation can be attributed to its ease of application. This, in turn, adds to the significance of landmark standardization for the reference planes, such as the FH plane [9]. Moreover, the corresponding midsagittal and coronal planes are oriented with reference to the established horizontal plane. In other words, the spatial orientation of the intracranial reference planes is interdependent. Moreover, a similar orientation methodology is applied to reorient the CBCT model to synthesize the cephalograms [8].  
However, a change in the landmarks defining the horizontal reference plane increases the sensitivity of the dependent cephalometric landmark coordinates. Consequently, this influences the accuracy of the metric assessment. Furthermore, there is an inherent variation in Or and Po detection. This can produce notable transversal errors, particularly while using the FH plane to assess cranial symmetry [10].  
The 3D cephalometric analysis draws its significance from the accuracy of the 3D assessment of skeletal deformity and asymmetry. Variable descriptions of reference planes have made the repeatability and reliability of the 3D analysis a challenging area of interest. However, the study design has been highly selective, with either a dry skull model [11; 12] or high-resolution CT [11; 12; 13]. Furthermore, several studies have deployed specialized [9; 14] or custom-coded software [3], factoring the generation of a threshold dependent model for analyses.  
Therefore, we aim to evaluate the impact of changes in the FH plane definition on frontal symmetry analysis using a clinically adaptable protocol, such as one in an orthodontic specialty setup. Our null hypothesis is that geometric deviations between the planes do not significantly impact the diagnostic evaluation of facial symmetry.