Geometric morphometric methods for three-dimensional virtual reconstruction of a fragmented cranium: the case of Angelo Poliziano
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The process of forensic identification of missing individuals is frequently reliant on the superimposition of cranial remains onto an individual's picture and/or facial reconstruction. In the latter, the integrity of the skull or a cranium is an important factor in successful identification. Here, we recommend the usage of computerized virtual reconstruction and geometric morphometrics for the purposes of individual reconstruction and identification in forensics. We apply these methods to reconstruct a complete cranium from facial remains that allegedly belong to the famous Italian humanist of the fifteenth century, Angelo Poliziano (1454–1494). Raw data was obtained by computed tomography scans of the Poliziano face and a complete reference skull of a 37-year-old Italian male. Given that the amount of distortion of the facial remains is unknown, two reconstructions are proposed: The first calculates the average shape between the original and its reflection, and the second discards the less preserved left side of the cranium under the assumption that there is no deformation on the right. Both reconstructions perform well in the superimposition with the original preserved facial surface in a virtual environment. The reconstruction by means of averaging between the original and reflection yielded better results during the superimposition with portraits of Poliziano. We argue that the combination of computerized virtual reconstruction and geometric morphometric methods offers a number of advantages over traditional plastic reconstruction, among which are speed, reproducibility, easiness of manipulation when superimposing with pictures in virtual environment, and assumptions control.
KeywordsVirtual anthropology Cranium reconstruction Geometric morphometrics Superimposition techniques
Reconstruction of facial and neurocranial morphology has played an important role in forensic anthropology, paleoanthropology, and medical science. In forensic anthropology, skeletal remains are often the only retrieved parts of missing individuals. As a result, various physical anthropological techniques have been developed to identify a victim from skeletal remains . In this context, cranial remains are frequently used not only in the assessment of an individual's sex and age  but also in dental  and skull–photo superimposition for the purpose of their personal identification [4, 5, 6, 7, 8]. Moreover, plastic craniofacial reconstruction can be performed only on the entire skull of the individual. The plastic reconstruction creates an approximation of the individual's face at the time of death that sufficiently resembles the deceased person to allow recognition [9, 10, 11]. This is true not only for facial reconstruction based on manual methods in which modeling clay or plasticine are applied on a cast of the skull [12, 13] but also for computer-based forensic facial reconstruction [14, 15].
It is obvious that the precision of a reconstruction depends on the completeness of the skull. In other words, the more parts that are missing on the skull, the less reliable the skull–photo superimposition becomes, therefore resulting in an inadequate facial reconstruction. In order to overcome this limitation, recreating the complete skull is often required. Nowadays, there are two different approaches recognized: a “traditional” and a “virtual” one. In the former approach, the reconstruction is carried out by a specialist directly on the bone so that a physical contact with the bone is required. The replacement of missing parts involves reproducing the external integrity of the bony segment by means of dental wax or hot paste made of organic and inorganic components (modeling chalk, raw beeswax, rosin, zinc white). This reconstruction method is highly subjective, and accuracy of the result decreases as the size and complexity of the bony parts under reconstruction increase. The second approach to reconstruction, i.e., virtual techniques such as reverse engineering and geometric morphometrics, has been shown to minimize the effect of the subjective choices of the operator and increase the reliability of the result [16, 17, 18, 19, 20].
Three-dimensional virtual reconstructions have recently been used for planning mandibular reconstruction , modeling of the orbital cavity , and in maxillo-facial surgery [23, 24]. They are also widely used in paleoanthropological research [25, 26, 27, 28], which illuminates the great potential of the new three-dimensional technologies. The problems faced in paleoanthropology are very similar to those found in forensic anthropology because fossil skulls are often heavily distorted and fragmented. Consequently, the methods developed in paleoanthropology in order to solve the problem of deformation  and reconstruction of missing data [18, 27] can be rightfully applied in forensic anthropology for reconstruction of fragmented skulls for identification purposes.
In this study, we applied a computerized method of reconstructing missing cranial data to the case of a famous fifteenth century Italian humanist, Angelo Poliziano. An entire skull was reconstructed using virtual models and geometric morphometric methods (GMM) starting with a preserved portion of the face. We attempted to use the most reliable methods available, always aware that it is impossible to reproduce the morphology with absolute precision. Moreover, since the Italian humanist had been depicted in numerous paintings, the reconstructed skull will be virtually superimposed onto the paintings of a middle-aged Poliziano in order to verify his identity.
There is a protocol for the skull/painting superimposition that has been proposed and developed in the past [30, 31]. It requires establishing consensus between paintings and, when available, verbal descriptions of the historic character. The challenge, in our case, was that there was little resemblance among several known portraits of Angelo Poliziano. Moreover, it is well known that portraits dated by fifteenth to sixteenth centuries frequently lacked precision and technique characteristic of the later ages. As a result, any attempt of Poliziano's identification would be only as reliable as the painting chosen for superimposition. Nevertheless, we use this opportunity to present the virtual methods of facial reconstruction and superimposition in forensics.
In July 2007, the graves of two important fifteenth century Italian humanists were opened in order to shed light on their sudden deaths that were historically recorded. Angelo Poliziano (1454–1494) and his friend, the humanist Giovanni Pico della Mirandola (1463–1494), died within a short period of time in Florence under mysterious circumstances. They were subsequently buried into two different graves in the S. Marco cloister (Florence). Poliziano's skeleton remains were preserved worse than those of Giovanni Pico, probably due to the more humid condition of the place in which he was buried.
The well-preserved skeletal remains of a tall and robust male were consistent with descriptions of Pico as reported in the historical sources . In contrast, the presumed cranial and post-cranial bones of Poliziano were fragmented and extremely fragile to the extent that the traditional physical anthropological techniques that were applied for identification of Poliziano remains have not yielded an assertive result. Furthermore, given the bad preservation of the bones and the lack of living relatives, DNA could not provide any aid for his identification. No useful verbal descriptions of the facial features of Angelo Poliziano were available, but there were a number of paintings that were made during his life or shortly after his death. As a result, it has been suggested that superimposition of the remains with the paintings should comprise the next step of the identification process.
Materials and methods
The cranium of Poliziano was represented by an extremely deformed parieto-frontal fragment, seven other smaller cranial fragments, and a portion of the face where nearly all of the left maxilla and the entire left zygomatic bone were missing (Fig. 2a). The cranial bones were scanned at the radiology department of Ravenna Hospital by means of computed tomography (CT) performed using a Brilliance 64-slice scanner (Phillips Medical Systems, Eindhoven, The Netherlands) with a slice thickness of 0.9 mm, increment 0.45 mm. At the same time, in the Department of Anatomy, Pharmacology and Forensic Medicine (University of Turin), the skull of a 37-year-old Italian male whose face was morphometrically similar to that of Poliziano was selected for the reference shape and scanned at the Clinic Pinna Pintor of Turin by CT Philips AURA (Phillips Medical Systems, Eindhoven, The Netherlands) with a slice thickness of 1 mm, increment 0.5 mm. The presence of a reference skull in the 3D reconstruction is as essential as in traditional methods of plastic reconstruction. In the present study, the reference skull data are used in the further geometric morphometric manipulations with landmarks and surfaces in order to receive a complete cranium model on the basis of the remains attributed to Angelo Poliziano.
Identification of landmarks
List of landmarks and curves identified on the 3D models of the reference skull and Poliziano
Maxillo-naso-frontal suture leftc
Maxillo-naso-frontal suture rightc
Mental foramen left
Mental foramen right
Squamosal suture right
Squamosal suture left
Lower zygomaticotemporal outline left
Lower zygomaticotemporal outline right
Zygomatic edge left
Frontomalare orbitale leftc
Palatine corner left
Zygomatic edge rightb
Frontomalare orbitale rightc
Palatine corner right
Zygomaxillare suture left
Frontomalare temporale leftc
Zygomaxillare suture rightb
Frontomalare temporale right
Zygomatic lateral left
Zygomatic lateral rightb
Posterior palatine edgeb
Supraorbital notch leftc
Supraorbital notch rightc
Total semilandmarks on curves
Lower zygomaticotemporal suture left
Zygomaxillare inferior left
Lower zygomaticotemporal suture right
Zygomaxillare inferior rightc
Due to the extreme flattening of the parieto-frontal fragment of the Poliziano cranium, only the facial fragment was considered for the three-dimensional cranial reconstruction. Consequently, fewer landmarks (14) and curves (eight) could be identified on Poliziano's face than on the reference (Table 1; Fig. 2c). Since some of the identified curves were incomplete, a total of 47 semilandmarks were selected on the Poliziano curves.
Homologous landmarks of the reference skull and the Poliziano facial fragment were exported in two distinct.txt files, with missing landmarks of the second one labeled as “x x x” (x, y, z coordinates). The same procedure was followed for the semilandmarks of the curves. Finally, the external surfaces of the reference skull and the Poliziano facial fragment were selected and exported as point clouds.
Reconstruction of the missing data
Two methods of the missing data reconstruction on the skull have been previously proposed [18, 36]. One of them, the statistical reconstruction, requires a reference population and takes into account variance and covariance within it. Ultimately, this approach yields best results . An alternative approach, geometric reconstruction, uses properties of the thin-plate spline function and the data about one reference and one target specimen. This method provides for slightly less reliable results and has more dependence on the properties of the reference shape when, as in our case, there are a lot of data missing [18, 36]. It is therefore important to match the reference and target at least by such properties as sex and age. In the absence of the reference population, we have chosen the geometric method of reconstruction.
During the process of reconstruction, we had to address the possibility of deformation in the Poliziano facial fragment. The facial fragment appears anatomically congruous, and it is difficult to establish the amount of deformation, if any, present in the face. An experimental attempt of reflecting the right side of the face and fitting it to the left was not successful as the remains of the left orbit and the reflection of the right orbit did not fit together. The mismatch may have occurred as a result of the deformation or as normal bilateral asymmetry of the human face [37, 38, 39]. Given the poor preservation of the left side of the face, there was no possibility to recreate the original facial structure that would account for the natural bilateral asymmetry. Therefore, we proposed reconstruction of a symmetrical face which would approximate the original.
We have considered two reconstruction options. The first one provides a consensus shape between the original Poliziano fragment with missing data reconstructed and its reflection. Ultimately, the information from both right and left sides is preserved in this model assuming that no deformation is present on either side. The second reconstruction was obtained by replacing the left side for the reflection of the right side of the face so that the left facial part is disposed of. In this case, it was assumed that the original lacked deformation only on the right side.
The flow of computation involved a number of procedures applied for reconstruction of the missing cranial data by Gunz . Practically, we used formulae developed by P. Gunz and P. Mitteroeker and described by Gunz  and for Mathematica 5.2 (©1988–2005 Wolfram Research, Champaign, IL, USA).
A reflection for the surface, landmarks, and curve semilandmarks of the Poliziano face was obtained. Paired landmarks and semilandmarks on reflection were re-labeled so that the homology with the original was restored.
Geometric homology for semilandmarks on curves was achieved between the reference skull and Poliziano on one hand and the reference skull and the reflection on the other. This step involved relaxing (sliding along tangent vectors) semilandmarks on the reference against the preserved semilandmarks in Poliziano and its reflection in turn so that the semilandmarks on different models would find themselves in geometrically homologous positions. The relaxation (sliding) procedure and discussion of its biological impact are given by Gunz et al. [36, 40]. Two models have been obtained: (a) semilandmarks on the reference relaxed against Poliziano and (b) semilandmarks on the reference relaxed against reflection. The relaxed semilandmarks were projected back onto the surface of the reference individual for each of the models.
The third step involved reconstruction of the missing data in the original Poliziano and its reflection. In order to do so, the relaxed reference shapes were warped (see below) onto the preserved landmarks and semilandmarks in Poliziano and its reflection accordingly. The warping procedure utilizes properties of the thin-plate spline function. In this case, the existing homologous landmarks are superimposed, whereas data between them are estimated so as to minimize the bending energy matrix of the shape [36, 40, 41]. The resulting estimations for Poliziano and its reflection contained a complete set of landmarks and semilandmarks for the whole cranium. To achieve a better fit for the estimated surface, semilandmarks whose position fell onto the preserved surface in Poliziano and its reflection were projected onto the respective surfaces. At the end of this step, we have obtained two maximally fitted datasets of the landmarks and semilandmarks for the complete Poliziano skull and its reflection.
A consensus shape between Poliziano and its reflection was calculated. In order to do so, we first achieved geometric homology of semilandmarks between the complete Poliziano dataset, its reflection, and the reference model by relaxing semilandmarks on both Poliziano and reflection against the reference. After this step, a consensus shape was obtained as an average between the complete skulls for Poliziano and its reflection after Procrustes superimposition without removal of the size variable. Ideally, the consensus shape between the original and its reflection corrects for the bilateral asymmetry in the object [42, 43]. The possibility of an error introduced in this reconstruction due to the properties of the thin-plate spline function is discussed below [18, 36].
The second reconstruction of the complete cranium is received by means of Procrustes superimposition of the Poliziano model and its reflection followed by the replacement of the left paired landmarks and semilandmarks in Poliziano by their counterparts in the reflection. The full size is then restored to the centroid size of the original Poliziano model.
All of the 314 landmarks and semilandmarks of the reference skull were thus transformed into the corresponding landmarks and semilandmarks for the two complete models of Poliziano's skull, whereas the surface of the reference skull was automatically warped so as to minimize the bending energy of the according transformation . Two final surface models were obtained by the warping procedure: Model A represents a symmetric version of the Poliziano skull achieved as a consensus between the original warped shape for the complete Poliziano and its reflection. This reconstruction, therefore, averages information on both sides of the face diminishing the amount of deformation, if present on either side (Fig. 3c); model B, a symmetric model of the Poliziano skull, in which the potential deformation on the right has not been removed and the left side is reconstructed as reflection of the right with the loss of all information on its original configuration.
In both models (A and B), a good correspondence was displayed in the frontal bone as well as in the right frontal process of the maxilla (Fig. 4b, d). In model A, the portion around the zygomatic-maxilla suture was more divergent, where a deviation of about 3–4 mm was detected (Fig. 4b). In model B, a large difference was found in the left lateral orbital process of the frontal bone, where the real facial fragment of Poliziano deviated by about 6 mm (Fig. 4d).
Both models (A and B) have been compared with the paintings of the historical character by means of virtual superimposition. Given that Poliziano died at the age of 40, the portraits of a middle-aged Poliziano depicted by Domenico Ghirlandaio (1449–1494) and Theodor de Bry (1528–1598) were chosen (the first one form the Tornabuoni Chapel, in the church of Santa Maria Novella, Florence; the latter from the Bibliotheca Calchographica di Jean Jacques Boissard). It is worthwhile to note that since Ghirlandaio worked when Poliziano was still alive, his paintings are considered more reliable than the portrait depicted by de Bry about 50 years later. Furthermore, in contrast to some other paintings of Poliziano that show him in lateral view (i.e., a painting of Domenico Ghirlandaio, “Storie di San Francesco”, from Sassetti Chapel in Santa Trinità, Florence, and Sandro Botticelli (1445–1510) “Adorazione dei Magi”, Galleria degli Uffizi, Florence), the portraits of Ghirlandaio and de Bry that we have chosen for the cranium/painting superimposition painted a fronto/lateral view of Poliziano's face, therefore providing better conditions for the superimposition method. Unfortunately, the two portraits present substantially different physiognomic features of Poliziano's face (mainly in the forehead and in the zygomatic bones) so that we could not presume to reach a positive identification with certainty.
Since on the portrait Poliziano's face is turned to the right, points were selected on the right side of the models in order to guide the subsequent cranium/painting superimposition process (midsagittal points: ophryon, glabella, nasion, rhinion, subnasale; points on the right: lateral forehead, lateral orbit, orbitale, canine fossa, lateral zygomatic).
Then, cylinders were constructed from vectors, reproducing tissue depth markers regularly used in forensic facial reconstruction  (Fig. 5b). Each cylinder was edited so that its axis is formed by a corresponding vector and the length calculated in accordance with the mean flesh thicknesses in an adult white European male of 40–49 years of age .
Using transformation editor options, the cranium was translated directly onto the pictures, and dynamic orientation and uniform sizing processes were used to arrive at the best possible alignment of the cranium and the portraits of Poliziano. The visualization was set to orthographic camera in order to exactly align objects in 3D space. Following suggestions by Fenton et al. , particular attention was paid to aligning the left and right Whitnall's tubercles of the cranium with the left and right ectocanthion points of the face. Alignment of the tip of the tissue depth marker at the subnasal point and the tip of the nose were also considered. Given the particular orientation of the face on the portrait, further adjustments of the cranium position were necessary so that landmarks on the cranium would align with “corresponding” landmarks on the face. The points identified on the left orbit of the portrait have been located in positions approximately corresponding with the equivalent points on the skull. Although they cannot be considered proper anatomical landmarks, they aided the process of cranium orientation and sizing.
With respect to model Ac, the four cylinders on the midsagittal plane of the cranium correspond well with the landmarks of the portraits (Fig. 7). In detail, the correct size of the left orbit has been recognized mainly in the portrait of de Bry (Fig. 7a, b), an accurate face/cranium proportion has been achieved in both the portaits from the ophryon to the tip of the nose, and the incisors are contained behind the upper lip so that the incisive edge reaches the upper part of the lower lip. Nevertheless, some inconsistencies were observed due to mismatch between the two portraits. In fact, the orthognathic frontal bone of model Ac fit properly with the forehead profile of de Bry's portrait (Fig. 7a, b), unlike the flatter receding forehead painted by Ghirlandaio (Fig. 7c, d). On the other side, the high position of the zygomatic bones of model Ac is more consistent with the depiction made by Ghirlandaio.
Apart from some features also recognized in model Ac, i.e., the orthognathic frontal bone (similar to de Bry'painting) and the high position of the zygomatics (as Ghirlandaio's painting), when model Bc was superimposed onto the portraits (Fig. 8), some other features emphasized that model Bc is less successful than model Ac. For example, the left orbit is too large, the right zygomatic bone runs out of the border of the face mainly in Ghirlandaio's painting (Fig. 8c, d), and the lateral border of the right orbit is pushed too far backward (Fig. 8a, b).
It is well known that human remains recovered from the ground could miss important portions of the skull so that the identification procedure based on skull/photo superimposition [4, 5, 6, 7, 8] and facial reconstruction [9, 10, 11, 12, 13] could be significantly compromised. The reconstruction of damaged skulls is usually performed by means of physical replacement of missing portions. An accurate reconstruction relies on the characteristics of the available part such as its morphology, size, and deformation. Usually, the smaller and fewer fragments that are available, the less reliable the reconstruction result is. A plastic reconstruction of the lost and fragmented bones of an individual's facial features carried out by an expert is normally the most reliable and frequently applied approach. Unfortunately, depending on the difficulty of the case, the plastic reconstruction can take considerable time. This limitation can be partly overcome with the help of the three-dimensional digital models and GMM if those are applied in conjunction with the traditional morphological assessment of the original and the resultant reconstruction. Moreover, the computerized approach provides with a benefit of easy manipulation of the reconstruction and, for example, the picture of the identified individual in virtual environment. The assumptions behind the geometric morphometric approach are known, and therefore, the reliability of the final result may be predicted.
The fragmentation and unconfirmed partial deformation of the cranial remains attributed to Angelo Poliziano provided the pretext to employ GMM to reconstruct the cranium. Since attribution of the skeleton remains to Angelo Poliziano was questionable, it was needed to confirm his identity by means of cranial/painting superimposition method that would be analogous to the skull/photo superimposition technique generally used in forensic anthropology.
Both obtained virtual reconstructions performed well in superimposition with the surface of the preserved facial fragment and partially with the paintings. However, both of them have intrinsic imperfection related to the properties of the thin-plate spline function. The thin-plate spline function bends the spline in the vicinity of the existing landmarks and is best at prediction of the missing data in the proximity of the preserved parts. However, if there are no landmarks preserved to bend the spline in the vicinity of the missing landmarks, i.e., if the estimation occurs some distance from the preserved part, then the thin-plate spline grid is almost square . In other words, the further the location of the estimated landmarks from the preserved surface, the closer they resemble the reference shape. As a result, the reconstruction of the neurocranium, however practical in the sense of the further application for the facial features reconstruction, is not reliable in our case. For the same reason, the mandible was removed and was not considered in the skull/picture superimposition.
Further characteristics of the received models include removal of the natural bilateral asymmetry of the face. Moreover, the face of model A ultimately incorporates information not only about the remaining parts of Poliziano and the reliably reconstructed portions of the face in the vicinity of the existent landmarks and semilandmarks. This face also includes information about the relatively remote lateral part of the left zygomatic, which is already less reliable and resembles the reference shape. In addition, the method of finding a consensus between the skull and its reflection is not a remedy for deformation. If present, the deformation is averaged across the sides, and the final outcome is largely dependent on the magnitude and direction of the deformation. However, in the case of Poliziano's face, we found that the consensus method was useful due to the subtlety of the deformation if at all present.
Model B is free of the problems that arise with the calculation of a consensus shape. However, it preserved the original geometry only of the right side of Poliziano's face. This model turned out to have a broader left orbit than model Ac and an even more protruding zygomatic bone as it has been shown in the superimposition with the paintings.
The step of the cranium/painting superimposition has been relatively simple in the virtual environment. The usual technique of the computer-based skull/photo superimposition requires standard equipment such as two video cameras, an electronic mixing device, and a standard monitor of high resolution for viewing [8, 46]. In our case, the orientation and sizing of the two cranial models (Ac and Bc) in comparison with the portraits of Poliziano by Domenico Ghirlandaio and Theodor de Bry as the references were carried out in fully virtual environment. A better fit with the portraits has been shown by model Ac. This result may be due to the presence of some deformation on the right side of the preserved fragment that was averaged out in the consensus shape (model Ac) but led to the failure of model Bc to fit the portrait perfectly.
Since the uncertainty regarding the reliability of the different portraits and the mismatch among them, we cannot claim to provide a positive identification of Angelo Poliziano. Nevertheless, given that a good correspondence was observed between the tissue depth markers (represented by cylinders) and the points identified on the portrayed face, the probability that the facial fragment discovered in the S. Marco cloister (Florence, Italy) in July 2007 actually belongs to the Italian humanist Angelo Poliziano cannot be excluded.
In conclusion, the presented attempt at reconstruction of the cranium and its superimposition with paintings for the identification of Angelo Poliziano is an example of the multi-disciplinary integration of anatomical and morphological expertise with virtual computer modeling techniques. We suggest that the application of this approach can become a valuable tool in forensic anthropology.
We thank Philipp Gunz for providing the formulae that he developed in order to reconstruct missing data in Mathematica. We wish to express our thanks to the staff of the Radiology Department of Ravenna Hospital (Ravenna, Italy) and Clinica Pinna Pintor (Turin, Italy), in particular to Dr Gino Carnazza, for support in this project on the technical aspects of CT scanning. Thanks to Prof. Giacomo Giacobini for help in the choice of the reference skull. Many thanks to Stephanie Kozakowski for copy editing our manuscript. This work was supported by EU Marie Curie Training Network MRTN-CT-2005-019564 EVAN.
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