Cranial remains recovered from a fossil site, archaeological field, or crime scene are often incomplete due to taphonomic processes, animal scavenging, perimortem injuries (e.g., gunshot wounds or blunt force trauma) or damage during recovery (Krogman and İşcan, 1986). A reconstruction of the original form is often required important to allow morphological and morphometrical analyses or to apply forensic art techniques for positive identification, such as skull/photo superimposition (Fenton et al., 2008). Furthermore, cranial reconstruction is a fundamental issue for surgical disciplines, including orthodontics and maxillofacial surgery, to restore both form (for aesthetic purposes) and function (articulation, occlusion, and mastication) (i.e., Mehta and Deschler, 2004; Young et al., 2007; Baumann et al., 2011). In the last decade computer-based methods for digital reconstruction of skeletal features have emerged and are now used in bioarchaeology and forensic anthropology (Fantini et al., 2008; Benazzi et al., 2009b, 2009a, 2009c, 2010), paleoanthropology (Ponce De León and Zollikofer, 1999; Neubauer et al., 2004; Gunz, 2005; Zollikofer and Ponce De León, 2005; Gunz et al., 2009a; Grine et al., 2010; Benazzi et al., 2011b; Weber and Bookstein, 2011; Benazzi et al., 2013), and recently emphasis has been given to its potential applications in craniomaxillofacial surgery (i.e., Benazzi and Senck, 2011; Benazzi et al., 2011a). Digital reconstruction techniques include a full documentation of the process, which leads to reproducible results and less error-prone to subjectivity compared to traditional manual approaches.
Despite these advantages, some limitations apply to digital techniques also. In both traditional and digital methods it is true that the larger the missing cranial portion is, the more difficult the reconstruction will be. We still do not know to what degree the accuracy of a reconstruction is affected by the size of the missing part, particularly when we deal with very large skull defects that include the midsagittal region. In fact, the most frequent approach for digital cranial reconstruction exploits mirror imaging techniques, but this approach becomes less useful the further the damage extends into the midsagittal region. Moreover, since methods for digital cranial reconstruction are often based on morphological information gathered by reference to undamaged specimens (i.e., Gunz 2005; Gunz et al. 2009a; Benazzi et al., 2009c), it is unclear how, and to what degree, the final reconstruction is affected by the general cranial morphology, sex, and asymmetry of the reference specimen used.
To answer these questions, we simulated some very large skull defects in a cranium of one individual (we omitted any information from the mandible) randomly chosen from a sample of 26 skulls. All the other specimens were used as reference sample to address the reconstruction. The reference sample was composed to the effect that it reflects the large cranial variability in humans, in order to investigate the effects of reference dependency on the reconstructed shape features.
The defects presented here were arbitrary chosen to exemplify the case in which missing data affects the midsagittal portions of the skull or a bilateral craniofacial bone, thus preventing the employment of mirror imaging or reflected relabeling techniques for reconstruction. In detail, the following two digital destruction-reconstruction scenarios were compared:
In the first knockout simulation, more than two-thirds of the cranium was missing but a small fraction of the midsagittal plane was still preserved.
In the second knockout simulation, even greater parts of the cranium were missing and there was no clue at all to the actual position of the midsagittal plane.
While in the first case we could still use mirror imaging techniques to restore the bilateral symmetry of the specimen, the second case introduced a number of difficulties, which forced us to develop a new approach. That is to say, we needed to estimate the position of the midsagittal plane before we could mirror imaging the preserved cranial portion. The rest of the missing cranial area was estimated using thin-plate spline (TPS; Bookstein, 1991) interpolation functions. To quantify the accuracy of the two knockout simulations, we computed the residuals between (semi)landmarks of the original individual and each reconstruction.
To summarize, we aim to deliver a new method to reconstruct crania characterized by large missing areas and to compare the variability of the reconstructions in both scenarios, and the effect of the general morphology, sex, and asymmetry of the reference specimens on the accuracy of the reconstructions. Finally, merits and pitfalls of our approach for cranial reconstruction are discussed.
MATERIALS AND METHODS
The basic steps in our study are summarized in Fig. 1 and described in detail in the following paragraphs.
Our study included computed tomography (CT) scans of 26 dried skulls from an adult modern human sample (13 females and 13 males) of mixed origin (Europe, Africa, Australia, Asia), ranging in age at death from 18- to 59-years-old (Table 1). The CT scans were acquired at the Radiologie 2 Medizinische Universität Innsbruck, Austria, and at the Ruber clinic Madrid, Spain, via a Siemens Somatom Plus 40 (Innsbruck) and a General Electric, model GE Light Speed 16 (Madrid). All CT scans were recorded in DICOM file format at a reconstruction matrix size of 512 × 512 pixels. Pixel size ranged from 0.42 to 0.51 mm and slice thickness from 0.625 to 1 mm. The half-maximum height protocol (Spoor et al., 1993) was used to reconstruct each cranial surface from the CT scans via the software package Amira 5.3 (Mercury Computer Systems, Chelmsford, MA).
Using the open-source software Edgewarp3D (Bookstein and Green, 2002) and AMIRA 5.3, a 3D-template of anatomical landmarks (n = 79) and semilandmarks (n = 567) was created to capture the geometry of the cranial surface (Table 2, Fig. 2). Because the extensively damaged crania only preserved a minor part of their original form, it was crucial to fully exploit that scarcely preserved morphology. As substantial surface information would be omitted if we would only use traditional anatomical landmarks, we included curve and surface semilandmarks. The template was warped onto each complete specimen cranium by iterative TPS (Bookstein, 1991). This procedure computes a mapping function between two point configurations that maps the landmarks exactly while the space in-between is smoothly interpolated. Note that it is not necessary to align the template and the target during the procedure, because the template and each complete specimen cranium are brought into the same space during the TPS procedure. As part of the digitization process, semilandmarks were allowed to slide along curves and surfaces to minimize the bending energy of the TPS computed between each specimen and the sample Procrustes average. Any TPS has a bending energy, the (idealized) physical energy required to bend an infinite, infinitely thin metal plate into the specified form from an initially flat configuration in which bending energy is a scalar quantity that measures the amount of bending (Bookstein and Green, 1993). Sliding of semilandmarks is an iterative process repeating the following three steps (Gunz, 2005; Mitteroecker and Gunz, 2009): (1) computing the sample Procrustes mean shape and tangent vectors for each semilandmark in each specimen, (2) sliding the semilandmarks along the tangents to minimize the bending energy to the sample Procrustes mean shape (along tangent vectors to the curve or the tangent planes to the surface), and (3) projecting the slid semilandmarks to the nearest point on the curve or the surface, as they may not be directly situated on the curvature after sliding in Edgewarp3D. After these operations, semilandmarks can be considered as geometrical homologous points.
Table 2. List of anatomical landmarks of the template
Digitized on the alveolar process between the teeth.
Landmarks and semilandmarks were converted to shape coordinates by generalized procrustes analysis (GPA) (Rohlf and Slice, 1990). This involves translating, rescaling, and rotating the configurations relative to each other to minimize the overall sum of squared distances between corresponding (semi)landmarks. Rescaling adjusts the landmark coordinates so that each configuration has a unit centroid size (CS; square root of the summed squared Euclidean distances from all (semi)landmarks to their centroid).
For the two destruction-reconstruction scenarios to be tested (knockout regions), the cranium of one individual (Ind1; Table 1) was randomly selected, while the other 25 individuals represented the reference sample used for the reconstruction. Ind1 was oriented with respect to the Frankfurt Horizontal plane (xy-plane) in Rapidform XOR2 (INUS Technology). Then, the midsagittal plane (computed as the best-fit plane of 12 anatomical landmarks: Prosthion, Subspinale, Rhinion, Nasion, Bregma, Lambda, Inion, Opisthion, Basion, Staphylion, Incisivion, Orale) was defined parallel to the y-axis (running anterior–posterior). The cutting plane for the first simulation (mid-sagittal plane preserved) was located by an anticlockwise rotation of −30° from the midsagittal plane using an axis parallel to the y-axis at Nasion. After the rotation, an arbitrary translation of 3 mm along the x-axis (from left to right) towards Zygoorbitale (landmark 13) was performed. As a result, most of the left side of the cranium and significant parts of the right side were deleted, but a small portion of the left side remained which could later be used to establish the midsagittal plane. This first knockout individual (KI-1) still featured 36 anatomical landmarks (Fig. 3a).
The cutting plane for the second case (no midsagittal landmarks preserved) was defined by taking the cutting plane of the first case and translating it further to the right side of the cranium (again along the x-axis) for a distance of 12 mm, and clockwise rotation of 6°. This second knockout individual (KI-2) completely lacks any landmarks from the midsagittal plane and features only 24 landmarks (Fig. 3b).
Missing Data Estimation
Since there is only unilateral information preserved, reflected relabeling (Mardia et al., 2000), a frequently used method to estimate missing data, cannot be applied. Consequently, a mid-sagittal plane is required for the process of data restoration. In the case of KI-1 bilateral symmetry was restored by mirror imaging the right side along a best-fit plane of the seven remaining midsagittal anatomical landmarks (Prosthion, Subspinale, Opisthion, Basion, Staphylion, Incisivion, Orale). In the same step, each of the 36 real landmarks, that are present in the virtually cut cranium, was mirrored along the same plane, leaving out unpaired landmarks. During this procedure, a mirror-imaged model is created.
Restoring bilateral symmetry in KI-2 is a disproportionately harder task. Since there are no midsagittal landmarks, and thus no midsagittal plane to apply mirror imaging, we needed an additional step. The trick we used here derives from the idea of reference-based reconstruction (Weber and Bookstein, 2011). We used the midsagittal planes of all the other 25 individuals of the reference sample to mirror image the remaining right half of KI-2. To be able to implement this information, the individuals in the sample were superimposed via a GPA which only incorporated the 24 anatomical landmarks still preserved in KI-2 (a so called partial GPA). The position of the rest of the landmarks was calculated using the respective translation vector and rotation matrix of each individual that was computed during the GPA. This procedure, which could be referred to as a block GPA, was carried out via the open-source software Morpheus et al. (Slice, 1998) by “demoting” each landmark in the missing area of KI-2. As all the individuals were now superimposed according to the remaining 24 landmarks of KI-2, it is possible to compute the best-fit midsagittal plane of every complete individual and mirror the surface of KI-2 relative to these midsagittal planes using Rapidform XOR2. The 24 anatomical landmarks that were present in KI-2 were included in the mirroring process, unpaired landmarks were not present. Accordingly, during this procedure we gained 28 different versions of the mirrored KI-2 (25 using each individual of the reference sample, and one in each case using the grand mean (GM), the female mean and the male mean). Figure 3c shows the result of mirroring KI-2 according to the midsagittal plane of the Procrustes mean shape. It is worthwhile to note that GPA scales the landmarks configurations to unit CS, so any effect of size was circumvented during the computation of the midsagittal planes. By multiplying the landmark configuration and surface model of each specimen by its respective CS obtained during GPA, the superimposed landmark configurations are brought back to the space of the original specimens. This allows the usage of the original units (mm) to express the accuracy of the reconstruction.
After mirror imaging the knockout individuals to obtain complete forms, we estimated the remaining missing data by TPS interpolation (Bookstein, 1991; Gunz et al., 2009a) (Fig. 3c). The basic idea in the use of TPS algebra for missing data estimation is the warping of a complete reference configuration (reference model or template) onto an incomplete target (target model) based on a subset of (semi)landmarks available in both reference and target model, minimizing the thin plane spline's bending energy between the reference and the target (Gunz, 2005). The interpolation function maps the missing landmarks from the complete onto the incomplete specimen, thereby optimizing the bending energy of the TPS (Gunz et al., 2009a). Missing landmarks are then placed so that the overall bending energy between the reference and the target is at a minimum, consequently generating the smoothest interpolation (Gunz et al., 2009a).
In case of KI-1, the single surface model created during mirroring together with the available anatomical landmarks, served as target. Each complete specimen (25 individuals of the reference sample, plus the GM, the female mean, and the male mean) served as reference model and was warped onto the mirrored KI-1.
The second knockout simulation created 25 individual models plus three models obtained by using the female, male, and GM as references. In this case, corresponding mirrored reconstructions and original individuals represent the target and reference respectively. That means that the complete surface model of, for example, Ind2 (Table 1) was used as reference and was warped onto the mirror reconstruction of KI-2 according to the midsagittal plane of Ind2.
Principal component analysis (PCA) of the matrix of shape coordinates was carried out on the original sample. All reconstructions, obtained during the first and the second knockout simulations, were subsequently projected in the same multivariate shape space as the original sample so that one can evaluate the variability of those two groups in relation to the variability of the sample they originated from. We measured the Procrustes distances (the square root of the sum of squared differences between the coordinates of corresponding landmarks) between the respective reconstruction and the original specimen in order to evaluate geometrical closeness. Our plots of the shape space PCA are enhanced by the static allometric trajectories (smaller to larger adults) of the original and reconstructed samples using quadratic regressions on the natural logarithm of Centroid Size (LnCS). To visualize the shape changes along the static trajectories, we set aside the PCA and instead estimate the average shapes at different size by quadratic regression of the Procrustes shapes coordinates on LnCS. The regression estimates were visualized by TPS deformation (Bookstein, 1991) of the Procrustes mean shape surface, generated from a triangulated scanned surface of a single specimen. Note that the surface areas are interpolated by the TPS also in places where there are no (semi)landmark information.
To investigate the accuracy of the reconstructions based on mirror imaging and geometric (TPS) reconstruction we present the results separately: missing data that were estimated using mirror imaging (MissingDataMIRROR: MD-MIRROR; 131 (semi)landmarks for KI-1 and 113 (semi)landmarks for KI-2) and missing data that were estimated using TPS (MD-TPS; 118 (semi)landmarks for KI-1 and 159 (semi)landmarks for KI-2). Results are expressed in the form of residuals between the (semi)landmarks of the original configuration and the estimated configurations. In addition, an average residual is calculated for each individual. A semilandmark carries only shape-information perpendicular to the curvature, so for the missing semilandmarks only the residual normal to the ridge curve or surface was used. We define reconstruction accuracy as the square root of the mean squared difference between the original and the reconstruction (root mean square: RMS), which has the same units as the data (mm). The RMS was computed for each individual and each landmark separately.
Because the density of (semi)landmarks is high (Fig. 2a), the visualization of the standard error of each point can be confusing. For this reason, surface deviation analysis based on the minimal Euclidean distances between the surface vertices was carried out in Rapidform XOV/Verifier™ (InusTechnology). Results were displayed as a color map onto a model's surface. The color values range from the minimum to maximum deviation between the original specimen and their respective reconstructed forms. For practical reasons, only the color maps between the original specimen and the reconstructions for which the Procrustes mean shape was used as reference (for both knockouts) are displayed. Since, the original and the reconstructed objects are brought into the same space during the TPS procedure, a superimposition step is not mandatory.
Phenotypic Variation—Sexual Dimorphism and Individual Asymmetry
Sexual dimorphism and individual asymmetry were investigated because the outcome of every reconstruction could be influenced by sex and asymmetry of the chosen template. Accordingly, we carried out a permutation test (number of permutations = 10,000) on the Procrustes distances between (semi)landmarks both in shape-space and form-space (shape and size) between males and females in order to analyze whether the group mean shapes and forms differ significantly in our sample of complete modern humans.
To quantify total asymmetry of each individual's face (object symmetry), we applied the Procrustes asymmetry assessment method from Mardia et al. (2000). The computation of total asymmetry for each individual incorporated the following steps: (1) for each individual landmark configuration of the facial bone (Table 2, facial landmarks), a mirrored and appropriately relabeled form is produced; (2) each individual and its mirror are projected into shape-space using GPA; and (3) the total asymmetry is defined as the Procrustes distance between the original landmark configuration and its relabeled reflection. Since after GPA each individual is in shape space, the Procrustes distance between each individual and its mirror is rather small. This asymmetrical variation is not necessarily biologically informative but provides additional information that could help to interpret the outcome of the reconstruction.
Data processing and analysis routines were written in R software (R Development Core Team, 2010).
First and Second Knockout Individual
Figure 4a shows a shape-space PCA of the original sample (red spheres), in which the reconstructions of KI-1 (blue spheres), and KI-2 (green spheres) are projected. Figure 4b displays a magnified view of the above shape-space PCA in the proximity of the original individual (Ind1 = black sphere). Figure 4c shows shape differences in our modern human sample for the first three eigenvectors facilitating the interpretation of the resulting reconstructions in the light of human cranial variation. The first three PCs explain ∼64% of total shape variation. PC1 (40.05%) represents dolicocephalic (negative scores) versus brachycephalic (positive scores) shape differences. Individuals on the left side (negative PC1 scores) of the PCA plot are characterized by a narrow and high vaulted neurocranium with a broader and higher face. In contrast, individuals on the right side of the PCA plot show a broad and stout neurocranium and a narrower and shorter face (Fig. 4c). Negative PC2 (14.78%) scores generally correspond to narrow faces with a lesser interorbital breadth and a narrow nasal aperture. Nasal bones are projected anteriorly and the maxilla is rotated ventrally. Positive PC2 scores are related to a broader face with a higher interorbital breadth, a wide nasal aperture, nasal bones that are less projected, with a maxillary bone that is rotated more backwards. Negative PC3 (8.86%) scores correspond to a flat frontal shape, the neurocranium is more globular and less broad. Positive PC3 scores correspond to a rounded frontal shape and a higher bizygomatic and neurocranial breadth.
The highest variation for the produced reconstructions is along PC1, reflecting the influence of the breadth of the cranium on the outcome of the reconstruction, though the degree of variation is much higher for KI-2 (green line, Fig. 4a). Mean reconstructions for both cases (Fig. 4b) plot close to the original individual (Ind1). Results of each simulation are discussed in the following sections.
First Knockout Individual (KI-1)
Figure 5 shows the static allometric shape variation (regression estimates) within the first knockout sample. Reference crania that are characterized by a relatively higher cranial vault produce reconstructions with (artificially) high vaulted neurocrania (Fig. 5). On the other hand, reference craniums that are broader produce less vaulted neurocrania. Facial differences are less influenced by the reference crania because facial breadth of KI-1 is determined during mirror imaging; the missing facial area is small compared to the missing area of the cranial vault. Besides the height of the neurocranium, shape changes related to the orbital shape and the height of the nasal aperture are most obvious.
While dolichocephalic individuals produce reconstructions that are characterized by supero-inferiorly elongated orbits and nasal apertures (negative PC2 scores; Fig. 4c), brachycephalic templates produce orbits and nasal apertures that are less high (positive PC2 scores). The mean shapes (female, male, and GM) produced reconstructions that showed together with Ind2 and Ind14 the least distance to the original Ind1, both in terms of accuracy as well as Procrustes distance (Table 3). The RMS from the original individual to each reconstruction after missing data estimation ranges from 2.39 to 2.81 mm for the mirroring and 2.13 to 9.75 mm for missing data estimated by TPS (Table 3). The variation in the values for MD-MIRROR is due to the TPS procedure. Semilandmarks on MD-MIRROR slide during the estimation of the MD-TPS, so different templates produce slightly different landmark configurations on MD-MIRROR as well.
Table 3. KI-1: accuracy of the reconstruction (RMS, in mm)
The RMS of landmarks in the MD-MIRROR area vary between 0.05 mm for landmarks positioned on the nasal clivus and 8.21 mm for landmarks on the lateral alveolar process. The RMS of landmarks in the MD-TPS area varies between 0.24 mm for landmarks in the supraorbital region just above the orbits and 9.73 mm for rhinion.
Using a color-coded deviation map (Fig. 6), we highlighted the shape differences between the original individual 1 and the reconstruction (using the GM as reference specimen). In this case the accuracy of MD-MIRROR was 2.48 mm and 2.65 mm for MD-TPS. The highest negative values (i.e., when the reconstruction is smaller than the original) were found in the infraorbital region, the orbital wall, and cranial vault. Positive values were associated with landmarks in the maxillozygomatic area, supraorbital margin, on the lower portion of the parietal bone, and in the temporal region. Landmarks that are situated on the mirror image generally show a smaller RMS than landmarks that were estimated using TPS. Nevertheless, landmarks estimated by TPS, which are situated in the immediate vicinity of remaining “bone” have a small RMS comparable to MD-MIRROR.
While male and female mean shapes do not differ significantly (P-value = 0.82), their mean forms (form is shape and size) do differ significantly (P-value < 0.001). That underscores a long known fact, namely that size is an important factor for sexual dimorphism. Sexual size dimorphism was confirmed by a permutation test on male and female CS (P-value < 0.001). Nevertheless, our results suggest that sex of the reference cranium has not much influence on the accuracy of the reconstruction. Figure 7a,b illustrates the distribution of reconstructions obtained by templates of different sex in terms of accuracy and Procrustes distance. Permutation tests show that there is no significant difference in the mean of the female and male reconstructions in terms of accuracy or Procrustes distance (P-value > 0.92).
Table 4 contains the values of object asymmetry for each individual in the sample. Smallest values can be found for the Procrustes mean shape (GM) and for the sex specific mean shapes.
Table 4. Total asymmetry for each individual in the sample (*10−3)
In KI-1, asymmetry did not influence the final outcome. There is no correlation between the values of facial asymmetry of the individual used as reference for the reconstruction (Table 4) and the accuracy (r = −0.03, P-value < 0.01) or Procrustes distance (r = 0.06, P-value < 0.01) from the respective reconstruction to the original Ind1 (Fig. 7c,d). This means that less asymmetric templates did not yield better results than more asymmetric individuals and vice versa. In general, the symmetrized male, female, and GM shape produce reconstructions with the highest accuracy.
Second Knockout Individual (KI-2)
In contrast to the first case, KI-2 reconstructions vary in direction of the first three PCs, reflecting that the shape variability in the second simulation is higher. Using the midsagittal plane of different individuals during the first step of the reconstruction (mirror imaging) produced 28 different models that vary considerably in facial and neurocranial size. Even though the variation in cranial shape is considerable, especially along PC1, all reconstructions are within the 95% confidence interval of the human sample (Fig. 4a). Figure 8 shows the static allometric shape variation (regression estimates) within the second knockout sample.
Even though we used the shape space configurations of the templates to circumvent problems that would have been imposed by the templates' size, differences in the breadth of the resulting reconstructions can be observed. Templates characterized by a less broad cranium (dolichocephalic) produce reconstructions that are also narrow (Fig. 8). Individuals with a broader neurocranium (brachycephalic) and a broader face produce broader reconstructions. Generally, the most obvious shape differences involve facial breadth and neurocranial height, which nevertheless do not exceed the shape differences observed in KI-1.
Reconstruction accuracy of the missing facial area for each individual ranged from 2.28 to 10.36 mm for MD-MIRROR and 2.65 to 9.48 mm for MD-TPS. Variation of the values for MD-MIRROR is much higher than in the first knockout simulation (Table 5). The RMS of MD-MIRROR landmarks varies from 1.25 mm for landmarks positioned on the zygomatic bone including the lateral orbital rim to 11.3 mm for landmarks on the alveolar ridge. The RMS of MD-TPS landmarks varies from 0.62 mm for landmarks in the supraorbital region to 10.42 mm for rhinion.
Table 5. KI-2: accuracy of the reconstruction (RMS, in mm)
The color-coded deviation map in Fig. 9 illustrates the shape differences between the original knockout individual and the reconstruction of KI-2 using the GM as reference. The accuracy for MD-MIRROR was 2.46 mm and 2.78 mm for MD-TPS (Table 5). Negative deviation values (i.e., the reconstruction is smaller than the original) are found in the infraorbital region, medial orbital wall, and cranial vault, while positive deviation values occur both in the mirrored side and in a portion of the left parietal bone.
The landmark configurations for reconstruction created from female and male references do not differ significantly in terms of accuracy or Procrustes distance (P-value > 0.21). Likewise, reconstructions based on female and male mean are not significantly different (P-value > 0.43). The female mean provides a reconstruction that is as close to the original knockout individual as the one reconstructed by the male mean. In general, the GM performs better than any single reference specimen itself, reflected by low values for the accuracy and Procrustes distance (Fig. 10a–c).
We found a low correlation between the values of individual asymmetry of the reference (Table 4) and the accuracy values of the respective reconstruction (MD-MIRROR: r = 0.146, P-value < 0.01, Fig. 10d; MD-TPS: r = 0.203, P-value < 0.01, Fig. 10e). Low correlation was also observed for the Procrustes distance of the respective reconstruction to original Ind1 and the corresponding values for asymmetry (r = 0.37, P-value < 0.01, Fig. 10f). As for case 1, less asymmetric templates did not necessarily yield better results than more asymmetric individuals and vice versa. In general, the male, female, and GM shape produce reconstructions with the highest accuracy.
Computer-based methods have been extensively used in the last years to overcome the limits of manual cranial reconstructions (Ponce De León and Zollikofer, 1999; Neubauer et al., 2004; Zollikofer and Ponce De León, 2005; Benazzi et al., 2009a,2009b,2009c; Grine et al., 2010; Benazzi et al., 2011a,b; Weber and Bookstein, 2011; Benazzi et al., 2013). Nonetheless, even though digital methods allow to reproduce missing parts and increase the reproducibility of the results, our study is the first one documenting the quantification of the accuracy for restoring very large missing portions of a human cranium. We quantify the outcome of cranial reconstructions in which (1) approximately two-thirds of the cranium are missing and the midsagittal plane is only preserved to a minor extent (KI-1), and (2) more than two-thirds of the cranium are missing as well as the whole midsagittal plane (KI-2). We introduce a technique to estimate a midsagittal plane by means of a human reference sample of known sex, which requires the alignment between the remaining bone and the reference sample based on a subset of corresponding landmarks (block GPA). This way, we exploited the symmetry information of complete specimens but losing information about asymmetry in the original individual by producing a perfectly symmetric reconstruction. Since crania are never perfectly symmetric, important individual information is irreversible lost, but this is an essential problem inherent in reconstructions using mirror imaging. For both knockout simulations, the rest of the missing cranial area is estimated using TPS interpolation functions (Bookstein, 1991). Using the TPS algorithm the remaining missing area between the original and mirrored hemiface is estimated by mapping complete individuals to the specimen with missing bone. It is not possible to restore the symmetry of the skull using TPS since it is only applicable in a meaningful way if the area to be reconstructed is within the point-cloud of landmark data, that is surrounded by preserved morphology. In our knockout simulations bilateral symmetry was restored before applying the TPS interpolation, hence the symmetry of the reconstruction generated by mirror imaging is preserved.
As expected, the second simulation shows a larger variability in terms of cranial shape (dolicocephaly vs. brachycephaly) along the first principal component than the first one. The reconstructions that use the symmetry information of reference individuals produced a continuous sequence of reconstructions, from narrow to broad cranial shape. In contrast, the reconstruction that uses the original midsagittal plane to mirror image the preserved hemiface, produced, to some extent, artificially high vaulted cranial reconstructions. This shows the effects of the reference specimen onto the reconstruction of cranial features. However, it is worth noting that the GM shape of our reference sample produces results that are very similar to the original individual for both simulations, with an average accuracy of about 3 mm (Tables 3 and 5).
As in every reconstruction process, we have to accept that it is impossible to arrive at the original state. Any reconstruction is an approximation towards the original because missing data has to be estimated using assumptions and external information derived from other individuals or samples. One such assumption in our process, symmetry, neglects information about asymmetry in the individual. Other small-scale characteristics of the facial skeleton, for example the form of the nasal bones, that could influence the positive identification of a missing person in a forensic case, are omitted as well.
As shown in Figs. 6 and 9, the overall deviation from the original specimen to the reconstructed in the middle and upper face (based on the GM) is rather moderate. The highest deviation always appeared at the apex of the cranium (thus in the region farthest from the preserved parts in our experiments). In forensic cases this might be of minor importance (during facial approximation, the individual hair style will mask this region in many cases), but could be more influential in other applications, for example in paleoanthropology. Obscuring individual traits of the fossil that is reconstructed may be circumstantial (e.g., facial asymmetry), but producing artificially high vaulted neurocranial reconstructions may strongly influence the outcome of subsequent analyses, for example in studies of ontogeny (Gunz et al., 2010), phylogeny (Gunz et al., 2009b) and biomechanics (Strait et al., 2009). However, since for both simulations the GM shape produces results that are very similar to the original individual, we argue that for scientific problems at large spatial scales, for example for phylogenetic comparisons in paleoanthropological contexts, the accuracy of our approach might be sufficient when applied to the reconstruction of fossil specimens.
Human craniofacial shape ranges from dolicocephaly (long and narrow cranial shape) with a leptoprosopic (long, narrow, and protrusive) face to brachycephaly (wide and short globular cranial shape) with a euryprosopic (broad, flat, and less protrusive) face (Enlow, 1990). We investigated patterns of normal phenotypic variability in our sample in order to evaluate, which reference individuals produce reconstructions that are geometrically closest to the original individual. A shortcoming of this approach is that there is no ultimate rule for an a priori choice of the template to be used during reconstruction. Interestingly, reference individuals that show the smallest Procrustes distance to the specimen to be reconstructed (comparing only the small part of the preserved face in the knock-out individual) do not necessarily deliver the closest over-all reconstruction.
We apply Procrustes mean shapes of females and males, on the one hand to take sexual dimorphism into account and on the other hand to circumvent population biases. Differences between male and female skulls become discernible at puberty when male skulls develop features that reflect sites of increased muscle attachments, whereas the female skull tends to retain more gracile features, though inter-population differences make general descriptions complicated (Ascadi and Nemeskery, 1970; Ferenbach et al., 1980; Buikstra and Ubelacker, 1994). Therefore, we might assume that the outcome of every reconstruction could be affected by the sex of the chosen template. However, we showed that using a template that is of the same sex as the individual to be reconstructed does not provide better results than the GM shape. Furthermore, we found no differences between reconstructions using the male or the female mean (MM and FM, respectively), which yield results very similar to the GM shape. This may be due to the fact that our sample comprises individuals of various origins. The reference sample was composed so that it covers a large range of cranial variability, ignoring patterns of sexual dimorphism that vary between human populations. Therefore, pooling the specimens of the same sex in our sample may have deleted these population affinities. Nevertheless, in cases where sex cannot be determined, the GM shape may be an effective substitute. Further studies are needed to investigate the consequences of the choice of the reference on the reconstructed shape features concerning sexual dimorphism and population affinity in a larger sample.
We consider facial asymmetry because it is well known that neither skulls nor faces are perfectly symmetric (i.e., Schaefer et al., 2006; Gawlikowska et al., 2007). However, we found no correlation between asymmetry and accuracy of the reconstruction: asymmetric crania provide RMS as high or low as more symmetric individuals. Nevertheless, some further considerations are required. First, no mirroring approach can perfectly reconstruct the original cranium since asymmetry is omitted by definition (we remind the reader that we are dealing here with cases where about two-thirds of the cranium are missing). Secondly, a technical problem arises using a midsagittal plane defined only by a limited number of midsagittal points. The resulting reconstruction will be directly affected by the deviation of this plane, the consequence is a narrower or broader face or cranium, depending on the magnitude of the deviation. The resulting mirror image for KI-1 highlights this situation. Mirror imaging the right side using the midsagittal plane of only inferiorly situated landmarks yields a deviation of about 2.5 mm (Table 3), remarkable for the fact that two-thirds of the cranium were absent. But even if more superiorly situated landmarks could be incorporated in the computation of the midsagittal plane, they would not consider the intrinsic asymmetry of the individual. This shortcoming becomes even more obvious for the second simulation. The error of mirroring is magnified by superimposing individuals based only on the anatomical landmarks that are still preserved in KI-2. The asymmetry of the reference individual is added to or subtracted of the asymmetry of KI-2, which can result in reconstructions that are artificially narrow or broad. In spite of these limitations, some combinations yielded results that are within the range of the outcomes obtained using the individuals' own mirroring plane. The Procrustes mean shape is naturally less asymmetric than any individual in the sample, thus reducing one source of error. It also averages out form differences of groups such as geographic population or sex. Therefore, the Procrustes mean can be suggested in general as a preferable reference specimen, leading to quite comparable results for both simulations.
Uncertainties in the reconstruction due to the references asymmetry could be further decreased by including an existing mandible into the reconstruction process. The bicondylar breadth of the jaw could be employed as a guide as to how far apart the temporomandibular joints should be positioned relative to each other. Also the orientation of the mirrored model could be verified in this way, overcoming even the problems that are imposed by a midsagittal mirror plane that is affected by asymmetry. Furthermore, even the midsagittal plane of the mandible itself could be used to correct for deviations of the cranial midsagittal plane, as far as it is possible to align the mandible with the cranial remains, that is by centric occlusion of the upper and lower dentition.
Computer-based methods for cranial reconstruction are employed to overcome limits of manual methods, but cranial reconstruction remains challenging when large portions should be restored. We introduce a new combination of tools from Virtual Anthropology and geometric morphometric methods for the reconstruction of severely damaged crania in which the midsagittal cranial plane was missing to a large extent or was completely absent. Even if the variability of these reconstructions is larger compared with those obtained using the original midsagittal plane, we have demonstrated that the Procrustes mean shape provides similar results in terms of accuracy for both simulations. Using the mean shape of the reference sample is therefore a good resource for the reconstruction of the entire cranium, circumventing negative effects introduced by the asymmetry or group-related form deviations of a single reference specimen.
The authors thank Antonio Rosas González (Museo Nacional de Ciencias Naturales, Madrid, Spain) for access to CT data via the NESPOS database (https://www.nespos.org/display/openspace/Home). They are also grateful to Abby Drake for providing very helpful comments and suggestions. Finally, they thank Colin N. Shaw and Fred L. Bookstein for general discussion and scientific input.