Standardized terms and methods have long been recognized as crucial to the reduction of measurement error in anthropometry and for unity of description in anatomical morphology. Classic examples abound, such as establishment of special committees for standardization [1–3] and the production of international agreements for the unification of anthropometry [1, 2]. Speaking volumes to the weight of the subject is the (repeated) publication of the International Agreement for the Unification of Craniometric and Cephalometric Measurements across three major journals within 13 years during the initial consolidation of the discipline: L’Anthropogie (1906) [1], Science (1912) [4], and The American Journal of Physical Anthropology (1919) [5]. Significance in the historical context is further highlighted by Hrdlička’s call in his first entry to the first volume of the American Journal of Physical Anthropology for “definite unification and perfection of anthropometry in its entire range; [and] systematization of the methods of treating and recording data” [6] p.13. Naturally, increased standardization of anthropometric nomenclature found use in anatomy (see e.g., [7] or for more recent examples [8–10]), thereby contributing to the parallel and exemplary efforts in that discipline to standardize human morphology nomenclature—see six editions of the Parisiensia Nomina Anatomica beginning in 1955 [11], now updated by the 1998 Terminologica Anatomica [10], which comprises 5640 entries [12] and including landmarks like nasion, bregma, lambda, inion, asterion, gonion, vertex, basion, and opisthion [10].

In terms of anthropometry standardization, three other events are especially deserving of mention. First is Paul Broca’s [13, 14] initial push for naming and describing “points de repère”, as Howells says, “to make them the property of craniologists once and for all” [15] p.477. Second, von Török’s [16] extensive systemization and formulation of cranial landmarks, with the definition of over 5000 cranial measurements that served as foundations for modern-day craniometry practice [15]. Third, the internationalization of the Frankfurt Horizontal plane (FH), which stands as such an exemplary beacon of standardization success that it deserves special mention in the form of a brief historical review: the German Horizontal [17, 18], originally proposed by Hermann von Ihering [19], was the forerunner to the FH as a German alternative [13, 14, 20] to French methods for orientating skulls after Broca [18, 21]. It was adopted by anthropologists/craniologists in 1884, following discussions held at the Craniometrical Conferences in Munich (1877), Berlin (1880) and Frankfurt am Main (1882) as a consensus method to orient dry skulls in a standard upright position [17, 18, 22]. It is from this latter congress that the plane takes its well-known name and modified implementation [18, 22]. Note the spelling “furt” after the official 19th Century German published in Correspondenz-Blatt [22], not “fort” after Middle Age Old English/Latin fiddling. The FH was not without controversy or heartache on its proposal given already established French protocols [18, 21], but ultimately, it emerged as the global standard above the French school, in part due to advantages such that the plane worked well for both craniometry and cephalometry, producing directly comparable orientations between the two modes of analysis [20, 23].

In biological anthropology, standardization of skeletal landmarks has strived for further improvement with notable works such as Martin’s Lehrbuch der Anthroplogie [24–27], Howells’ The Designation of the Principle Anthrometric Landmarks on the Head and Skull [15], Montagu’s Handbook of Anthropometry [28], Olivier’s Pratique Anthropologique [29], and more recently, Krogman and Sassouni’s Syllabus in Roentgenographic Cephalometry [30], Howells’ Cranial Variation in Man [31], and Buikstra and Ubelaker’s Standards for Data Collection from Human Skeletal Remains [32]—the latter drawing heavily on Moore-Jansen and colleagues’ Data Collection Procedures for Forensic Skeletal Material [33]. With the rise of computing power, computerized morphometrics has also expanded traditional craniometric chords and indices into more powerful multivariate shape tools [34–37], concurrently extending and formalizing landmark “types” first described by von Török as “natural” and “artificial”| (the latter being geometrically determined [15, 16]), to the modern classification scheme of Type I, II, and III landmarks after Bookstein [34].

The success of craniometric landmark standardization and the crossover with cephalometry has encouraged the extrapolation of the craniometric landmarks to the soft tissue context of the face as analogs of their craniometric equivalents. This is especially attractive for craniofacial analyses in regard to growth and forensic identification, where many landmarks of equivalency exist across the soft and hard tissues (e.g., glabella, nasion/sellion, zygion, opisthsocranion, pogonion, etc.), but it should be noted here that not all soft tissue landmarks possess hard tissue equivalents or vice versa, so a specially tailored nomenclature is required. While forensic photogrammetry and craniofacial identification are the targeted beneficiaries of this undertaking, there may be applications to other anthropometry-based contexts such as ergonomics and industrial design [38–40], especially of head-related equipment (see e.g., [41, 42]) and particularly with the extension of sparse landmarks to dense point clouds.

Farkas’ Anthropometry of the Head and Face [43] and Kolar and Salter’s Craniofacial Anthropometry [44] already provide foundational work in the sparse anthropometric landmark domain; however, room nevertheless exists for further nomenclature, landmark, and definition improvement. Currently, a plethora of ambiguous and unstandardized lay terms exist in the literature; “chin lip fold,” “fissure,” or “mentolabial sulcus” for supramentale [45–49] is but one example. Further, forensic facial photogrammetry has wielded landmarks in such a way that many masquerade as craniometric analogs when they are in fact nothing of the kind. Farkas forewarned of this mistaken use and against treating 3D soft tissue landmarks as 2D photographic equivalents [43, 50]. His warnings have, however, rarely made it to forensic examinations where these landmarks are misleadingly established as analogous points (see e.g., [51–58]), and in some cases, only to have their reliability criticized post-analyses [58–60].

The aims of this paper are, therefore, fourfold: (i) to provide a brief overview of gaps in current standardization, especially in the facial and craniofacial identification domains of anthropometry; (ii) to clarify some commonly confused craniofacial landmarks (e.g., gnathion/menton); (iii) to provide an improved nomenclature maintaining intent of craniometric analogs but providing at-a-glance differentiation of soft and hard tissue landmarks— including two types of pseudo-landmarks on 2D photographic images; and (iv) to provide a quick reference guide to the most commonly used craniofacial landmarks for adults and subadults.

To facilitate aims (i) and (iv), we introduce three new terms: norma medialis, corpulometry (corp-ul-om-i-tree), and capulometry (cap-ul-om-i-tree). The former is an addition to the five standard attitudes of the skull [61] to complement norma lateralis and describe the medial view of a skull sectioned in the median plane (Fig. 1). Corpulometry and Capulometry are used to enhance the classification of anthropometry into its constituent parts, thereby facilitating systematic description (Fig. 2). It is, for example, clearly apparent that osteometry is not a separate pursuit to somatometry (as traditionally held) but rather one component of the latter: human bodies possess a skeleton that can be readily measured osteometrically as a part of somatometric analysis. This is especially clear in an era of computerized medical imaging where skeletons can be segmented from within living bodies or cadavers, to be extracted and analyzed. The same applies to craniometry under the banner of cephalometry. Consequently, partner pursuits to osteometry and craniometry to describe the soft tissue (only) components of somatometry and cephalometry are in demand. This is readily attained using Latin prefixes, given the pre-established use of Greek for anthropometric labels. For soft tissue measurements of the body we subsequently introduce the term corpulometry and capulometry after the Latin corpus meaning body and caput meaning head (Fig. 2).

Fig. 1
figure 1

Craniometric landmarks for 3D analysis. Definitions are provided in Table 2. a Norma Lateralis; b Norma Frontalis; c Norma Medialis; d Norma Basalis; e Norma Occipitalis; and f Norma Verticalis. Bold line indicates FH

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Fig. 2
figure 2

Anthropometry and its domains. a Traditional binary division of anthropometry into two streams, one dealing with whole bodies and the other skeletons. b Reorganization of anthropometry recognizing that living persons and cadavers both possess skeletons—osteology stream is indicated by dark grey fields and bold flow lines. Note: missing terms in current nomenclature for soft tissue only components of somatometry and cephalometry. c Revised nomenclature, with living person/cadaver stream highlighted (osteology stream of B remains intact), and with soft tissue counterparts to osteometry and craniometry listed

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Weaknesses of current nomenclature

Inconsistency

Current nomenclature suffers from multiple inconsistencies:

  • Otherwise precisely defined landmarks have been misappropriated (and inconsistently so) to neighboring landmarks. For example, the term supradentale has been used for both alveolare [52, 62] and prosthion [62, 63]. Other examples are the use of gnathion for menton [63, 64] and mid-philtrum for subspinale [52].

  • Imprecise lay terms have been used for otherwise precisely defined landmarks. This is most frequent in the craniofacial identification literature where “artistic rules of thumb” are common [65], and/or where surface examination of the face is undertaken for ultrasound measurement [47]. Examples include the use of the “upper lip” for an approximation of labrale superius or labiale superius [46, 66]; “beneath chin” for menton [46, 47, 57, 67]; “zygomatic arch” for zygion [68]; “lateral piriform point” for alare [69]; and “lateral nostril” for alar curvature point [45–48]. More grotesque examples include “between the eyebrows” [47] or “the bald spot between the eyebrows” [70] for approximations of glabella—better described as the most anterior midline point on the forehead or frontal bone in the region of the superciliary ridges when the head is orientated in the FH [1].

  • Multiple technical terms exist for the same landmark (e.g., alveolare/infradentale superius), and some terms are named illogically. Infradentale superius, for example, implies a landmark inferior to the teeth that is superior—an unintuitive consequence of establishing a complement of infradentale.

  • Single and common landmark labels (e.g., alare) are used to define non-analogous points on both the hard and soft tissue profiles. In the case of alare, it symbolizes the most lateral part of the nasal aperture on the skull, and the most lateral apex of the wings of the nose (not to be confused with the mid-junction of the ala with the soft face) [43]. A good example of the misappropriated use of alare is in craniofacial identification where soft tissue thickness measurement at these landmarks (see e.g., [71]) would describe awkward measurements of the nose rather than of the junction points of the nasal wings with the cheek as intended [72]. At the opposite end of the spectrum, some craniometrically analogous points are given entirely different names, inconsistent with otherwise typical anthropometric practice (see use of the prime [′] below). For example, hard tissue nasion, which often represents the most posterior point on the bony frontonasal contour (defined by the junction with the frontonasal suture), has a soft tissue equivalent sellion, which frequently falls inferior to nasion.

  • Soft tissue analogs of craniometric landmarks are sometimes designated, in their abbreviated format, by the prime of the craniometric landmark (e.g., g and g′), but inconsistently so. Compare, for example, Swennen [73] versus George [62] and Krogman [30] versus Farkas [43]). The prime has also been used in an entirely different intent by Farkas [43] to label lateral versions of midline landmarks (e.g., labiale superius for the midline landmark vs. labiale superius′ for the lateral landmark). Complicating matters further is the instance mentioned above where some soft tissue analogs possess an entirely different label to their craniometric counterparts (see e.g., nasion and sellion, or the supramentale—also known as Point B in the orthodontic literature [55]—whose soft tissue equivalent can be any one of the following: labiomentale (lm; [70]), inferior labial sulcus (ils; [70]), sublabiale (sl; [43]), chin lip fold [47], mentolabial sulcus (mls; [72]) or chin fissure [74]).

Misappropriation of landmarks to 2D images

Landmarks that, by definition, depend on 3D surface typology have been hijacked to 2D images, such that their labels are used for points that are established without access to the necessary prerequisite information. For example, glabella is routinely established on lateral face photographs, but it is impossible to see unless the brow precisely rises to an apex along the median plane ([43]; Figs. 3, 4, and 5). Where the brow ridges project either side of the median plane, the most anterior point on the brow ridge will not represent the glabella. Similarly, mid-philtrum is hidden by the philtral columns in a lateral view. In an anterior view, alar curvature point cannot be located in most individuals since it falls posterior to, and is tucked behind, the nasal ala. Another prime example is gonion, which cannot be established in frontal photographs for two reasons: (i) as a craniometric homolog, it must be palpated; and (ii) gonion falls behind the curve of the cheeks in the frontal view, such that it cannot be seen (an effect exaggerated by increased perspective distortion at short subject-to-camera distances [24, 75–77]) (see Figs. 3 and 4). Problematic in photogrammetry is also the common practice of establishing landmarks, defined by curvature (commonly Bookstein type II and III landmarks) from texture or shape-from-shading information. This practice depends almost entirely on subjective speculation since curvature detail is conjectured from color or shading—an undertaking further confounded by lighting and exposure. Consequently, these landmarks can only be considered quasi at best and are unlikely to precisely or accurately represent their original anatomical intent.

Fig. 3
figure 3

Example of landmarks positioned using a 2D anterior view only (lateral view of this result is illustrated at the right) and b 2D left lateral view only (anterior view of this result is illustrated at the right). White filled dots represent landmarks positioned by different observers. Black filled dots represent ground truth positions. Light grey dots represent landmarks obscured by the soft tissues

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Fig. 4
figure 4

Example of landmark clustering in a male and female subject: a an anterior view of landmarks placed in a left lateral view and b a left lateral view of landmarks placed in an anterior view. White filled dots represent landmarks positioned by different observers. Black filled dots represent ground truth positions. Light grey dots represent landmarks obscured by soft tissues

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Fig. 5
figure 5

Anterior most points (white fill) mathematically calculated from the point cloud of the 3D photograph for the subject depicted in Fig. 3 using R [55]. Note equal projection bilaterally in some regions

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To demonstrate limits of placing capulometric analogs of craniometric landmarks on 2D images, we took two 3D head scans of ten living subjects (five males, five females; >18 years) using a non-contact Di3D™ stereophotogrammetry system. The first 3D photo was acquired with the subject in a standing position and with neutral expression. The second 3D photograph was taken in the exact same manner, but after landmarks determinable by palpation (zygion and gonion) had been marked on the face ahead of time with a small dot of water-based ink.

Following 3D photo acquisition, each subject examined every unmarked 3D face scan in frontal and left lateral views to position ten well-known anthropometric landmarks: glabella, sellion, pronasale, mid philtrum, sublabiale, pogonion, alar curvature point, cheilion, zygion, and gonion (see Fig. 3). Written definitions of each anthropometric landmark, after Farkas [43], were provided to participants as a reference. Ground truth landmark positions were determined using the palpation marks (by superimposition of images) and, for other landmarks, rotational viewing of the face in 3D. These ground truths were then compared to landmarks established in 2D single views and the millimeter Euclidean distances between the two calculated using the Pythagorean theorem:

$$ d=\sqrt{{\left({x}_2-{x}_1\right)}^2+{\left({y}_2-{y}_1\right)}^2+{\left({z}_2-{z}_1\right)}^2} $$

Results are visually displayed in Figs. 3 and 4 and are numerically summarized in Table 1. Mismatch between the placement of glabella, mid-philtrum, and pogonion in 2D equivalent lateral face views and gonion in frontal views (up to 11.2 and 25.7 mm respectively) was readily observed, simply because the ground truth position cannot be visualized in 2D. Figure 5 shows an example of mapping the most anterior coordinates of a 3D face point cloud in one of the ten subjects. This demonstrates how the profile line does not extend precisely down the midline of the face, even when the head is captured orthogonally and at infinite subject-to-camera distance. The invalidity of unwittingly or generically labeling landmarks on 2D facial images as craniometric analogs is thereby demonstrated. When determined on insufficient anatomical grounds [see 59, 60], it is not surprising therefore that landmarks like gonion, zygion, glabella, and pogonion display high levels of dispersion unacceptable for forensic examination [see again 59, 60].

Table 1 Average Euclidean distances and standard deviations (mm) between precisely located 3D landmarks and those located in anterior-only or and lateral-only face views
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A new nomenclature

An improved craniofacial landmark nomenclature is consequently in demand to boost standardization and limit (unnecessary) errors in comparison of non-homologous landmarks. The new nomenclature must be simple, compact, and should communicate meaning at-a-glance without possibility for confusion. For craniofacial analysis, retaining capulometric analogs of craniometric landmarks where possible would be an advantage. This extends to 2D image analysis where type II/III soft tissue landmarks that approximate craniometric equivalents (e.g., “pogonion” established from lateral view photographs) should be designated as such and should be differentiable from even less reliable points established from shape-from-shading information (e.g., “pogonion” in frontal view photographs). Our solution is the following:

  • Traditional craniometric names, abbreviations, and definitions stand (e.g., glabella = g; Fig. 1).

  • All soft tissue capulometric landmarks are designated by a prime (′), irrespective of their position (medial/lateral) or whether or not they possess a craniometric counterpart (e.g., soft tissue glabella = g′; sellion = se′; Figs. 6 and 7).

    Fig. 6
    figure 6

    Major 3D capulometric landmarks listed in Table 3: a anterior view and b right lateral view. Grey crosses represent landmarks obscured by soft tissues in the depicted view. Bold line represents the FH

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    Fig. 7
    figure 7

    Supplementary 3D capulometric landmarks for the major facial features: a eye, b nose, c mouth, and d ear. Definitions are listed in Table 3

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  • Two superscripts are used to differentiate the less than ideal quasi-landmarks on photographs, either for skulls, faces, or both:

    • Superscript “p” (for pseudo) to denote 2D extrapolations of type II/III 3D landmarks to particular photographic views, such as gp′ for pseudo-glabella in a lateral face photograph, or gp for pseudo-glabella in a lateral skull photograph (Fig. 8).

      Fig. 8
      figure 8

      Capulometric landmarks positioned on facial photographs using the new nomenclature: a anterior view and b right lateral view. In most cases, similar nomenclature would apply to photographs of skulls with the major exception that the prime is dropped from the landmark label. Bold line represents the FH

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    • The German scharfes S, or eszett, “ß”, to denote estimations based on shape-from-shading information, such as pgß′ for pseudo-pogonion in a frontal face photograph (Fig. 8). Note: the eszett is a convenient and compact representation of the double “s” drawn from the leading letters in “shape-from-shading,” and its derivation from the German language pays tribute to extensive German influence on anthropometry. The eszett should not be confused for the Greek beta (β).

The single additional superscript preserves compact notation, practicality, and efficiency of effort, while boosting descriptive power. The beauty of this system is that all four types of landmarks are easily differentiable, but their identical base labels maintain their original intent of approximations of the ground truth 3D craniometric landmark, e.g., pg ≠ pg′ ≠ pgp′ ≠ pgß′ (see Figs. 1, 8, and 9 for illustration of these terms). Below, we provide a summary of the major craniofacial landmarks using this terminology and some insights to their derivation.

Fig. 9
figure 9

Analogous 3D craniometric and capulometric landmarks illustrated together as useful for craniofacial analyses: a anterior view and b right lateral view. Circles indicate craniometric landmarks; crosses represent capulometric landmarks. Grey crosses represent capulometric landmarks obscured by soft tissues in the depicted view. Note that these landmarks/labels do not apply to photographic overlay of skulls and faces—for soft tissue nomenclature pertaining to photographs see Fig. 8. Bold line represents the FH

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A standardized craniofacial reference set

Craniometric landmarks (3D representation)

If a standard set of soft tissue landmarks for the head is to be constructed, using craniometric analogs where possible, then it is important to start with a well-defined craniometric list. This was heavily constructed herein on sets provided by Martin [25, 27], with supplementations from White [78], Krogman and Sassouni [30], Buikstra and Ubelaker [32], Howells [15, 31], and others where indicated (Table 2). Bookstein types (I, II, or III) accompany these landmarks (Table 2) helping to elucidate their character and degree of reliability [34]. As described by Bookstein [34], Type I landmarks are the most favored as they tend most toward being biological homologous points across individuals, are locally defined, and can often be located with precision. Type II landmarks are defined by geometric criteria and lack information in at least one direction. Type III landmarks are extremal points (often corresponding to instrumentally determined anthropometric points [15]), and while measurements using them are reliable and easy to conduct, they are often difficult or impossible to establish independently [15, 34]. Furthermore, Type III landmarks depend on surrounding structures and/or the overall object orientation, whereas Type II landmarks are locally defined. In some cases we note ambiguity of whether landmarks should be defined as Type II or Type III.

Table 2 Craniometric landmarks including their abbreviations, definitions, and various classifications
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Figure 1 depicts the anatomical location of each of the landmarks defined in Table 2. Note here that we use hand-drawn illustrations to depict landmarks in their 3D state, as they would naturally be determined from the skull by visual inspection. Two-dimensional photographs are specifically reserved to illustrate landmarks of a 2D nature as applicable to 2D photographic conditions (see, e.g., Fig. 8).

It is important to further note that many anthropometric landmarks stray from perfection since they possess intrinsic limitations. For example, glabella (g) is not always well-manifested in younger individuals—metopion (m), for example, often presents as the most anterior position on the frontal bone in the median plane in subadults due to pronounced frontal bossing, but notice that it is not in the region of the superciliary ridges. Additionally, when sutures are obliterated in older individuals, sutural landmarks must be either speculated, or in the case of partial obliteration, projected from residual traces of suture lines, usually at their extremities [25]. Asymmetry or dysmorphology may further obscure or obfuscate some landmarks.

To clarify some commonly confused landmarks that are not the same, we follow the recommendations of Krogman and Sassouni [30] for menton (me) and gnathion (gn): menton being the most inferior median point on the mental symphysis, while gnathion is the median point located halfway between pogonion and menton (Table 1). Similarly, ophryon (on) should not be confused for supraorbitale (so): ophryon is the median point that intersects the smallest frontal bone chord width [25], while supraorbitale is the median point at the intersection of a line joining the most superior margins of the orbital rims. Lastly, subspinale (ss) should not be confused with acanthion (a)—the former is inferior to the latter (Table 2).

Capulometric landmarks (3D representation)

These landmarks are drawn primarily from Kolar and Salter [44], with additional landmarks from Farkas [43] and some other authors where noted (see Table 3). These landmarks have been supplemented with other points commonly used in the craniofacial literature, for example, soft tissue thickness research [71, 72], and where sparse, new additional landmarks have been added (e.g., at the eyebrows and ear). The capulometric landmarks can be visualized in Fig. 6, and can be found, together with their definitions, in Table 3. Major capulometric landmarks embodying facial feature detail are illustrated in Fig. 7.

Table 3 Capulometric landmarks including their abbreviations, definitions, and various classifications
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As with the craniometric landmarks, capulometric landmarks possess inherent limitations that must be recognized. For example, midramus (mr) is dependent on its hard tissue equivalent, which can prove difficult to palpate through the buccal soft tissues and is, thereby, most readily identified by radiographic cephalometry. Here, it should be noted that landmark establishment on 2D computed tomography orthoslices without multislice 3D reconstruction retains its own set of problems and so should be avoided in favor of multislice reconstruction [79]. Similarly, sM2′ and iM2′ depend on locating the second molars, which can be difficult without undertaking multislice reconstruction mentioned above. It is also worth noting that ophryon’s (on′) utility in the soft tissue context is questionable for individuals possessing artificially shaped eyebrows.

Paired landmarks in craniofacial analysis

As indicated above, craniometric and capulometric landmarks are often used jointly in craniofacial analysis. Radiographic cephalometrics are a good example where standardization is already high; however, even there, problems exist with inconsistencies between authors on how soft tissue and hard tissue landmarks are differentiated [56]. In craniofacial identification, craniometric and capulometric landmarks are again used in a paired fashion, but with minimal standardization that is widely known to be problematic [72, 80]. For instance, facial soft tissue thickness measurements taken at hard tissue nasion have been measured in at least six different ways: (i) directly anteriorly; (ii) to sellion; (iii) to a point between the eyes; (iv) to basion; (v) to a point in the plane of the superior limits of the folds of the two upper eyelids; and (vi) additional variations (for more details, see [72]). To provide another example, the depth of tissue at the cheek and at a point in the vicinity of the mandibular ramus has been taken: at the level of the occlusal plane [52, 66], the level of the lips [45, 47, 48], and at the midramus height [64, 81].

A standard reference set of paired craniofacial landmarks thereby holds value, and the set provided here has been drawn together cognizant of past cephalometric practice and craniofacial identification literature, e.g., [46, 47, 52, 57, 64, 67, 82, 83]. The recommended landmark pairings are listed in Table 4 and illustrated in Fig. 9. It is worth noting that Farkas’ alar curvature point (ac′) is used to designate the mid-junction of the alar wing with the cheek, and we reserve alare (al′) for the most lateral point of the nasal ala following prior recommendations by Farkas [43] and prior usage by Stephan and Simpson [72, 84].

Table 4 Recommended landmark pairings for craniofacial analysis
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Conclusion

This paper provides an improved classification scheme for anthropometry and an improved nomenclature for craniofacial landmarks that enables their class to be clearly differentiated and communicated at-a-glance, in compact format, for both soft and hard tissues. Besides facilitating unity of description, this nomenclature holds special importance for facial photogrammetry where soft tissue landmarks are ill defined and are often misrepresented as craniometric analogs. Using the new notation, a standardized suite of craniometric (skull) and capulometric (soft tissue face) landmarks are provided that enables current confusions to be avoided.