Journal of

PHYSIOLOGICALANTHROPOLOGYand Applied Human Science

Original

Virtual Anthropology: The Digital Evolution in

Anthropological Sciences

Gerhard W. Weber, Katrin Schäfer, Hermann Prossinger, Philipp Gunz, Philipp Mitteröcker and Horst Seidler

Institute for Anthropology, University of Vienna, Austria

Abstract The discovery and explanation of differencesamong organisms is a major concern for evolutionary andsystematic biologists. In physical anthropology, thediscrimination of taxa and the qualitative and quantitativedescription of ontogenetic or evolutionary change require,of course, the analysis of morphological features. Since the1960s, a remarkable amount of fossil material wasexcavated, some of it still awaiting a detailed first analysis,some of it requiring re-examination by more developedmethods. While the fossil record grew continuously, arevolution in anthropological research took place withadvances in computer technology in the 1980s: a handfulof innovative researchers working in specializedanthropology laboratories or medical departmentsdeveloped the methodological inventory needed to extractcritical information from subjects in vivo and fromfossilized remains. A considerable part of this informationis preserved in the physically heretofore inaccessibleinterior of anatomical structures. Virtual Anthropology(VA) is a means of making them visible and measurable.Thus, VA also allows access to ‘hidden’ landmarks; inaddition, the large number of semilandmarks accessible onthe form enhances the power of Geometric Morphometricsanalysis. Furthermore, the density information in volumedata allows manipulations such as segmentation,impossible with the real, physical object. Moreover, metricbody measurements generally, and cranial measurementsspecifically, are also an important source of informationfor the analysis of the ontogenetic development of theskeletal system, and—last but not least—for clinical use(e .g. , operat ion planning, operation simulat ion,p r o t he t i c s ) . T hu s , th er e de ve l o p ed a f r u i t f u linterdisciplinary cooperation between statistics, medicine,and physical anthropology. J Physiol Anthropol, 20 (2):69–80, 2001 http://www.jstage.jst.go.jp/en/

Keywords: virtual anthropology, 3D-data, paleoanthropology,electronic preparation, geometric morphometrics, CT-scans,

stereolithography, segmentation

The Importance of Virtual Anthropology for Anthropological Research

Virtual Anthropology (VA) provides procedures toinvestigate three-dimensional morphological structuresby means of digital data sets of fossil and modernhominoids within a computer environment. 3D-data isacquired by different computer necessitating reliantprocesses, depending on the needs of further analysis.For surface measurements, a laser-scan can record thecomplete surface. If one is focusing only on landmark orcontour data, simple digitizers based on magnetic fielddependent systems (Polhemus Fastrak) or mechanicalsystems (Microscribe 3D) can fulfill a reliable and time-saving task. More expensive in every sense is theacquisition of volume data; but, once it has beenrecorded, it provides more freedom for many kinds offurther analysis because the real object is converted intoa virtual one which is an exact copy of the original—limited only by the spatial resolution of the scanningdevice. Medical diagnostic radiology is most often usedfor volume recording. This idea is not recent, as onlyseven years after W. Roentgen discovered x-rays, two-dimensional radiographs were used to study thefossilized Krapina Neanderthals (Gorjanovic-Kramberger,1902). But the extension into the third dimensionenhanced dramatically the possibilities of qualitative andquantitative analysis of morphology. ComputedTomography (CT), also based on x-ray technology anddeveloped in the early 1970s, was applied to fossil studiesin the 1980s by Conroy and Vannier (1984), Wind (1984)and Zonneveld and Wind (1985). CT is especially usefulwhen studying fossil skeletal remains because thefossilized material delivers excellent signals. Theresulting output from a CT-scanner is a 3D-data matrix

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(for more details see ‘Electronic Preparation’ section),consisting of small information units, called voxels (cf.pixels in 2D). Dedicated software can visualize thevirtual object on the computer screen and allows formanipulations like scaling, magnifying, rotating, cutting,moving, measuring or imaging (Fig. 1). A related kind ofdata, but acquired with a different method based onradiofrequency pulses, is produced by MagneticResonance Imaging (MRI). In contrast to CT, thistechnique is sensitive to hydrogen nuclei spin orientationand thus best appl icable to specimens in vivo .Mineralized bone delivers none or only weak signals butsoft tissue like brain or other organ tissue is well defined.Morphological investigations can also profit considerablyfrom these methodologies when ontogenetic processesare analyzed, suggesting mechanisms for evolutionarychange. Comparative studies with primates and recenthumans play a key role in this context (Semendeferi et al.,1997). The technical details of diagnostic radiology havebeen reviewed many times (Vannier and Conroy, 1989).Recently , a very readable e lementary technicalintroduction from the paleoanthropologist’s point of viewwas published by Spoor et al. (2000), suggesting the useof radiology in this field.

Most important for the anthropological and clinical useare the striking advantages that we see when comparingVA with traditional methods of analysis: (1) theaccessibility of all—including hidden—structures (e.g.endocranium, sinus, tooth roots, medullary cavity of longbones, etc.); (2) the permanent availability of the virtualobjects; (3) the general accuracy and reproducibility ofmeasurements; (4) the possibility to obtain informationfor advanced morphometric analysis.

To understand the potential of these high-techmethods, a brief review of substantial results achieved isessential. For our team, the story began with theTyrolean Iceman, arguably one of the world’s mostspectacular archeological finds of the last decade. Theintensive collaboration between radiologists andanthropologists that was established with this project waslater successfully transferred to evolutionary studies. Inthe case of the 5,300-year-old mummy, a 3D-hardcopy ofthe inaccessible skull was produced to examine theanatomy. This was the first time (worldwide) that a‘stereolithographic model’ was used for anthropologicalinvestigations (zur Nedden et al., 1994). It was solelybased on the CT-data of a rapidly undertaken scan of thefrozen mummy, which could only leave the refrigeratorenvironment for 30 minutes. The non-invasive approachallowed subsequent morphological investigations(Seidler et al., 1992) leading, among other things, to theconclusion that the Iceman was indeed of local origin andnot a translocated fake item from some other place, likeEgypt.

The transparent stereolithographic models turned out

to be also helpful for questions concerning endocranialmorphology in evolutionary studies. CT-scanned fossilscould be recreated physically. The stereolithographicapparatus consists of a laser beam which cures aphotosensi t ive l iquid res in layer by layer , thusconstructing all the internal features, including cranialcavities, sinuses, nerve canals, etc. These are visibleinside the transparent material and accessible if thespecimen is replicated in several disassembable parts.There is a good reason for this expensive procedure:Because a representation on a computer screen is stilltwo-dimensional and the third dimension an opticalillusion, it is quite often necessary to have a tangible realmodel in order to understand the spatial relationships ofstructures. This is the major purpose of such models. Ofcourse, conventional casts of fossil specimens can also beused and do contain some information about texture—butthey do not provide information about internal features.It follows that the stereolithographic models are excellentvisual aides.

Some Homo heidelbergensis specimens are known fortheir extraordinarily pneumatized skulls. Though studieshad been undertaken with radiographs and even withtwo-dimensional CT-data, the true extent could only berealized when stereolithographic models and 3D CT-scanswere available. Moreover, the brain is certainly one of thekey differences between humans and other primates, butunfortunately its development and its endocranialmorphology is still poorly understood. The published

Fig. 1 Daily routine in the Virtual Anthropology Lab. Thereconstruction of a hominid cranium is rendered on thecomputer screen. To investigate the endocranial morphology, thecranium is electronically separated into three parts as perpredefined landmarks. The pieces can then be moved androtated. Coordinate measurements, distances and angles are atthe investigator’s fingertips at any time.

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data suggests that some skulls resemble each otherexternally, yet this does not necessarily mean that theyresemble each other internally. In studying thismorphology using virtual fossils and stereolithographicmodels, some insights could be provided that contributedto the hotly debated origins of Neanderthals and modernhumans (Seidler et al., 1997).

Another brain-related research question is the cranialc a p a c i t y w h i c h , i n a d d i t i o n t o t h e s t r u c t u r a lcharacteristics of the brain, can be an important item oftaxonomic classification. Estimating this volume isrelatively easy—if a skull is almost intact, while the task ismore susceptible to observer errors in the case offragmented skulls. Virtual endocasts of the braincasecould be produced electronically in a highly reproducibleway and helped to visualize and measure the cranialcapacity of Australopithecus africanus specimens orarchaic Homo with a minimal error (Conroy et al., 1998;Conroy et al., 2000; Falk et al., 2000). Basically, everycavity, whether accessible on the original specimen ornot, can be extracted and treated as a separate object.Shape and size analysis of sinuses are just one otherexample for this technique (Rae and Koppe, 2000;Prossinger, 2000b). An excellent contribution tomorphologically important traits distinguishing speciescame from the examination of the labyrinth in thetemporal bone, after Spoor et al. (1994) had shown thatthe relative size of the semicircular canals is very similari n H . s a p i e n s a n d H . e r e c t u s w h e r e a s t h eaustralopithecines show great-ape-like proportions.Furthermore, some intermediate evolutionary stages,attributed to H. habilis, could be distinguished by thistrait. Moreover, labyrinth morphology was used toidentify specimens after the discovery that Neanderthalshave derived features of inner ear morphology (Hublin etal., 1996).

Generally, fossils have many undesirable propertiesstymieing the ambitious researcher. Destruction is aconsequence of the taphonomic processes during thespecimen’s progress from biosphere to lithosphere. Oncediscovered, the idea of paleoanthropologists is that thefinds should begin their return to their original conditionto serve as reliable clues for the morphology of theassigned species, whatever this was. But fossils are notonly frequently fragmented, they can also be highlyinterspersed with sediments. Many times, fossils have toundergo a series of procedures, where all of them areprone to subjective influences. Some specialists haveachieved remarkable results in reconstructing specimenselectronically (Kalvin et al., 1995; Zollikofer et al., 1995).But the re-assemblage of fragmentary fossils—physicallyand/or electronically—is a very delicate problem,involving considerable knowledge about the fossil recorda n d c o m p et e nc e in t ec h n o lo g i ca l i s su e s . T h ereconstructions do not always meet the general scientific

expectation of reproducibility of experiments and aretherefore often hotly contested. The simple mechanicalpreparation of encrustations inherently has the samedisadvantage. Both the physical reconstruction and thephysical preparation tend to have the taste of a ‘final’intervention where later corrections based upon a deeperknowledge are—literally—too late.

The electronic preparation of CT-data is in fact a highlysophisticated, but helpful and, above all, reversibleprocess and can be also applied to internal structures.This lead, for example, to the first representation of theanterior cranial fossa and paranasal sinuses of the mid-Pleistocene specimen of Steinheim (Prossinger et al,1998), more than 60 years after its discovery. There isalso a second benefit: Preparators sometimes useartificial material to complete a partly fragmented skull.Occasionally, it is difficult to distinguish (painted) plasterfrom fossilized bone primarily because one fears toscratch the surface. The different gray values in CT-scansoften reveal a clear answer, demonstrated in the case ofthe Neanderthal specimen of Le Moustier I (Thompsonand Illerhaus, 1998); it had, by the way, an unbelievablyturbulent history and is the ultimate monument to theblunders that had been made in the physical preparationand reconstruction of a fossil specimen.

These examples point out the potential of VirtualAnthropology for meaningful morphological analysis,using procedures that are similar to those applied intraditional anthropology. But Virtual Anthropology alsoallows for study programs that are completely novel. Perse, digital 3D-data is a source of information formorphometric analysis, no matter if it was acquired withCT-scans or MRI-scans, with mechanical surfacemeasuring devices or by laser-scanning surfaces.Landmark coordinates, linear and angle measurements,surface areas, and volumes represent quantitative datathat validate and document the evolutionary changes ofspecies with hard numbers and permit statistical analysiso f f o r m a n d s h a p e b y m e t h o d s o f G e o m e t r i cMorphometrics (Bookstein et al., 1985). The possibility toprobe every hidden structure rapidly increases theamount of data. Examples of results that became evidentby morphometric comparison of mid-Pleistocene withmodern hominids are elaborated in the ‘GeometricMorphometric’ section. In summary: we found that theforms of the inner and outer shapes of the human frontalbone are determined by completely independent factors.The morphometric analysis also indicates that anunexpected stability in anterior brain morphology wasevident and this during the time when modern humancognitive capacities emerged (Bookstein et al., 1999).

The accuracy and reproducibility of the measurementsconducted on virtual objects has been well described(Richtsmeier et al., 1995; Weber et al., 1998). Payingattention to several influencing factors, it can be

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concluded that measurements on virtual objects are bothvalid and reliable enough to be used in lieu of physicaldistance and volume measurements; the more so becausethey can also be taken of all physically inaccessiblestructures.

Because so many data points are available with 3D-digitizing methods, completely different approaches tomorphological analysis became feasible. For example,bone thickness is an interesting feature of humanevolution, though most studies fall short of offeringadequate information about the structural details of acranium since only a handful of measurements is taken.In sampling thousands of thicknesses along the surface ofa bone with semiautomatic algorithms from CT-scans(Weber and Kim, 1999), topographical thickness mapscan be obtained. The evaluation of measurements showsthat not necessarily the mean or maximum thicknessdiffers between species but the pattern of thicknessdistribution (Weber et al., 2000a). Or, in anotherexample, the laser-scan based analysis of congruency ofjoints was used to show if a fossil tibia (OH35) and talus(OH8) can be assumed to originate from the sameindividual, which could, in this case, be rejected becauseof the three-dimensional characteristics of the articularsurfaces (Wood et al., 1998).

As mentioned, from the paleoanthropologist’s view the3D-imaging methods are not only valuable for the studiesof fossils. Ontogenetic studies provide the comparabledata for investigating evolutionary constraints likeallometry and heterochrony. MRI is therefore alsoimportant for ontogenetic analysis with respect tophylogeny because it provides detailed visualization ofsoft tissue such as brain tissue (Falk et al., 1991),cerebrospinal fluid or blood vessels. Extending theunderstanding of functional aspects, the possiblecombination of MRI-scans with overlaid CT-scans of thesame extant individual clarify the relation of skeletalelements and soft tissues.

Virtual Anthropology now also supplies tools which arewell applicable to medical use. An increasing number ofquest ions concerning poorly known anatomicalparameters can be answered with the help of the newmethods. For example, a simulation of the cranialcapacity increase entailed by a new surgical interventionin the case of a malignant brain edema (circularcraniotomy) was conducted. The results were based onCT-data of skulls and studies on human cadavers,showing that the goal of a 10% volume increase necessaryfor lowering the intracranial pressure could be achievedby a moderate frontal elevation of the calotte by around1.6 cm—without risking brain damage (Weber et al.,2000b). Similar projects are currently underway, somedealing with the investigation of the medullary cavity oflong bones for adjusting fractures, others with the shapeand volume analysis of the orbitals for plastic surgery.

Reversible, Electronic Preparation Using Segmentation Algorithms

The new techniques available in Virtual Anthropology(VA) environments offer the possibility of solving somelong-standing segmentation problems. Fossilized skullsrarely fossilize in isolation: they are embedded in amatrix of sediment which fossilizes along with them (orthe sediment subsequently fossilizes after the bone hasalready done so). In both cases, the sediment and thefossi lized bone have remarkably similar mineralconstituents (and thus, similar attenuation in an x-raybeam). Segmentation is the methodology used toseparate the two fossilized regions: the fossilized bonefrom the fossilized sediment (the latter usually—but notalways—of little interest in itself). In the followingparagraphs , we descr ibe the d i f f icul t i es o f thesegmentation, but in such a way as to point to amethodology we have developed to overcome theattendant problems (Prossinger et al., 1998).

We start our investigations by accessing the CT-scandata file. In a CT-scanner, one or more x-ray tubes revolvearound the sample to be scanned, with a detector arraydiametr ical ly opposi te . The measured angulardis tr ibution of x -ray a ttenuation al lows for thereconstruction of the spatial distribution of the absorbingcenters, resulting in a pattern of image elements, calledpixels. This step in the process is done in a fixed plane;the pixel image plane is called a slice. Moving the tube/detector assembly relative to the fossil by a specifieddistance (the so-called ‘slice thickness’) perpendicular tothis plane for the reconstruction of further slicesgenerates a stack of slices called the CT-scan. In practice,CT-scans rarely have slices that are as thin as thedimensions of the (square) pixels within the slice.Mathematical interpolation can reconstruct ‘isovoxels’,i.e., three-dimensional volume elements with threeidentical dimensions.

The attenuation of the x-ray beam by the fossil materialdepends on the electromagnetic interaction properties ofthe (fossilized) sample material with (medium energy) x-ray photons. These interaction properties are those ofsilicates and similar (in an electromagnetic sense)minerals. In many specimens, the attenuation of thebeam is almost the same for both the fossilized bone andfor the fossilized sediments. To the chagrin of theresearcher, it is then difficult to determine the boundarybetween fossil bone and sediment because the similarityin attenuation results in nearly identical gray values inthe CT-scan data file (Fig. 2a). The segmentationmethodology, therefore, can be described as: find amethod that can identify the boundary. Invariably, themethod (if it exists) will rely on mathematical andalgorithmic techniques. In passing, we would like tostress that one advantage of algorithmic techniques is the

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possibility of applying different algorithm sequences tothe same (virtual) specimen; all segmentation algorithmsare reversible and there is no damage to the (priceless)originals. We have found that manual, conventionalpreparation does not always only remove sediment; therea r e p r e p a r e d f o s s i l s w i t h d a m a g e d s u r f a c e s(Berckheimer, 1933; Thompson and Illerhaus, 1998). Incontrast, electronic preparation in VA cannot damage theoriginal.

In our research of the segmentation problem, we havedevised various such methods; all are based on thestrategy of using mathematically defined filters to extractimage properties of the sediment that are different fromthose of the fossil bone. For example, the gradient filterfinds the direction of ‘steepest descent’ (i.e., the grayvalues in the filter file are proportional to the maximumchange in gray values of CT-scan file). Unfortunately, thesteepest descent is zero in regions where the sedimentand the fossil bone are fused (at least in an x-rayattenuation context). Finding the boundary between thesediment and the fossil bone will, in most cases, not bepossible when applying the gradient filter.

Another filter is the mask filter. It replaces the grayvalue of a specific voxel in the CT-scan file with the localaverage of gray values in a cube of size

(1 + 2 · h) × (1 + 2 · h) × (1 + 2 · h).

The mask filter thus performs a sort of averaging, which‘masks’ local details (where ‘local’ refers to featuresinside the cube). An unmask filter is the differencebetween the file to be masked and the resultant maskalgorithm output. As the name implies, it removes theaveraging, thus accentuating the details and signalfeatures within the cube.

In many fossil specimens where segmentation is achallenging task, the sediment consists of stones andgrains interspersed with mixtures of various materials(Fig. 2a). Needless to say, such mixtures will have arather inhomogeneous attenuation structure. This ratherlarge variation in attenuation density is what we takeadvantage of: the gradient file will have pronouncedfluctuations in regions of inhomogeneity, and the fossilbone will be rather uniform in its attenuation structure;consequently, the bone regions in the gradient file will bealmost constant (and will have very small gray values).Applying the unmask filter to the gradient file willproduce a close-to-zero values in the fossil bone regions,and a rather strong multi-peaked signal in the sedimentregions (Fig. 2b).

If we now convolute the unmask-filtered gradient filewith the original CT-scan file, the difference betweensediment and fossil bone will be quite pronounced(Prossinger et al., 1998).

The next step is simply tedious work: we image-edit theconvoluted file with suitable tools. We can outline the

Fig. 2 An illustration of the segmentation process. (a) One slice ofa mid-Pleistocene cranium with incrustations. The sediment,which also contains small pebbles, can clearly be identified.However, the boundary between sediment and fossil bone is noteverywhere sufficiently distinct. (b) The result of applying agradient/unmask filter to the same slice. The sediment is clearlyisolated, but the ‘probing’ of the filter out to a distance h resultsin the evident ‘jaggedness’ (see text). (c) The electronicallyprepared slice. After removal of the (filtered) sediment image viaimage editing and smoothing with dilate/erode algorithms, theprepared cranium reveals interesting endocranial features.

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sediment region by, for example, setting a ‘seed’ andapplying a contour-detecting algorithm to a suitableregion around the seed. Of course, in our application thesuitability will be defined by the now pronouncedboundary of the multi-peaked sediment region. Imageediting slice-by-slice this way will remove the convolutedsediment structure, albeit with a rather rough surface.Due to the ‘probing’ of the unmask filter out to a distanceh in all three directions, the resultant surface has a‘jaggedness’ in the order of h (Fig. 2b).

We do not smooth these surfaces with conventionalinterpolation algorithms, because these might (and do)introduce smoothness where there are sharp ridges andpeaks in the fossil skull. Instead, we apply a combinationof dilate and erode algorithms (employing jacks andcubes with suitable connectivities). Dilate algorithmsapply layers to a surface and can fill cracks and smallgaps. Erode algorithms will remove layers, but cannotopen cracks. The attractive feature of using a sequence ofdilate/erode algorithms is their non-commutativity.

How do we know when such a dilate/erode algorithm issuccessful? We store as an intermediate file every resultof an dilate/erode application. We do not worry if theresult of one such operation introduces a difference ofone or two voxels in some neighborhood, but we docarefully ensure that two or more dilate/erode steps donot drift away from the (rough) surface detected by thegradient/unmask filter combination. The result isremarkably satisfactory wherever we can ascertain theresultant surface (for example, where there areanatomically unique features to be detected, such asforamena or sutures) (Fig. 2c). We do note that the partsof the foss i l crania where we have appl ied thissegmentation methodology so successfully has nosediment any more, and the sequence of dilate/erodealgorithms we have applied very, very rarely changed thesurface at all (Prossinger, 1999).

There are some straightforward applications that thesemethodologies (gradient/unmask filter and dilate/erodeoperations) can be used for. Here, we mention one thatwe are currently active in: detecting paranasal sinusesand endocast features. After we having produced asediment-free virtual fossil cranium, we can set a seed insome sinus region or in the brain cavity and use contourdetection to ‘flood-fill’ such a region to a predeterminedgray scale. Thus, we can ‘build up’ slice-by-slice, anyhollow in the cranium (Weber et al., 1998). We canisolate these cavities and either investigate their relationwith the geometry of the fossil cranium (Prossinger et al.,2000b) or apply methods of Geometric Morphometrics.

Furthermore, we can find the volumes of paranasalsinuses or of endocasts (or of the fossil bone itself, for thatmatter) by simply counting the number of voxels havingthe specified gray scale and multiplying the volume ofone (iso)voxel.

Insights Gained with Geometric Morphometrics

Methodological prerequisitesWhenever one needs to compare shapes of organisms or

some of their particular structures, morphometricmethods are needed. Since the proper description andstatistical analysis of shape variation within and amongsamples of organisms and the analysis of shape change asa result of growth and evolution are basis for testinghypotheses in evolutionary theory and presenting newfindings, we are highly dependent on the power of themethods used. The approaches we present here providesuch opportunities to a heretofore unequalled and highlys a t i s f y i n g e x t e n t , a n d a r e t h e r e f o r e u r g e n t l yr e c o m m e n d e d a s s t a n d a r d a p p l i c a t i o n s i nanthropological studies dealing with morphometry. Theyare effective in capturing information about the shape ofan organism combined with powerful statistical methodsfor testing differences in shape. They also offer theresearcher visualizations of shape differences and evensuggest traditional measures that could be used in simplestudies (Rohlf and Marcus, 1993).

The approach commonly used in (paleo)anthropologyis now referred to as traditional morphometrics(Reyment , 1991 ; Marcus , 1990) or mult ivar ia temorphometrics (Blackith and Reyment, 1971), eventhough it is only a few decades old. A summary ispresented in a review (Rohlf and Marcus, 1993, p. 129):“Traditional morphometrics are characterized by theapplication of multivariate statistical methods to sets ofvariables. The variables usually correspond to variousdistance measurements-as well as areas and volumes onan organism, usually captured by calipers as lengths andwidths of structures and distances between landmarks.Sometimes angles and ratios are used. Applications havefrequently been concerned with allometry (change inshape as a function of size) and size correction (to enablethe study of shape differences among samples oforganisms adjusted to a common size). The results aremostly expressed numerically and graphically in terms oflinear combinations of the measured variables. Examplesof the techniques used are principal component analysis,canonical variate analysis, discriminant functions andgeneralized distances.”

The shape of the original form is not recoverable fromthe usual matrices of distance measurements—not even asan abstract representation—even if the data set ofmeasurements records all possible distances between allconsidered landmarks. An investigator may know, forexample, that several distance measurements share thesame landmark, but this information is not included inthe multivariate analysis. The analyses cannot beexpected to be as powerful as if all information wereincluded. Another flaw of the traditional metric approachis that, although it might occasionally be able to

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determine the combination of change in size and shape assomething like a change in form, it certainly cannotproperly distinguish variation in size from variation inshape.

The first important merit of the new morphometricmethods is that the method of data recording allows tocapture the geometry of the structure being studied. Thisis achieved by digitizing two-dimensional (2-D) or three-dimensional (3-D) coordinates of the landmarks (aspoints), from which traditional distances may still becomputed, by the way. These landmarks, as described byBookstein (1991), reflect a biological homology in tissues,anatomical locations and coordinates, and these versionsof data are very attractive to anthropologists interested inevolutionary questions. The so-called Type I landmarksare points whose claimed homology is supported by thestrongest biological evidence, such as a local pattern ofjuxtaposition of tissue types or a small patch of someunusual histology (Slice et al., 1998). They don’t onlypermit the description of shape changes but do specifywhich structure has moved relative to others. When TypeI landmarks are impossible to locate, pseudolandmarkscan be used, as they are either mathematical pointswhose claimed homology from case to case is supportedonly by geometric—rather than (fossilized or in vivo)histological—evidence. Examples are: the position ofextremal curvature on a tooth (a Type II landmark), orpoints which have at least one deficient coordinate, likeeither end of a longest diameter, or the lowest point of aconcavity (a Type III landmark), characterizing morethan one region of the form. Finally, surfaces or outlinesof a structure can be captured by sequentially digitizingalong the respective curve in order to either apply routineoutline methods (like Elliptical Fourier analysis) or togenerate so-called semilandmarks which are allowed tochange their spacing along curves according to the shapedeviation from a respective reference shape. Themultivariate toolkit of geometric morphometrics permitsthese points to be treated as landmark points in someanalyses, but any possible shortcoming they embodymust be kept in mind in the course of any geometric orbiological interpretation (Slice et al., 1998).

As, evidently, geometrical relationships among thelandmarks are not inherent in the raw coordinatesthemselves, functions have to be fitted to them and theestimated parameters subjected to statistical queries.Here, a major achievement of geometric morphometricsbecomes evident, namely, the synthesis of coordinateimportance and landmarks as manageable data,developments in shape theory, and analysis usingstandard univariate and multivariate statistics. From thevarious methods that have been developed, some are ofspecific significance for our own research (Seidler et al.,2000; Bookstein et al., 1999; Schäfer et al., 1999).

Superimposition (Procrustes) methods superimpose a

sequence of specimens so that corresponding landmarksmatch as closely as possible according to an optimalitycriterion. In this process, size, position and orientationare partialed out and differences in shape are recorded asresiduals from the reference shape. The residuals canalso be graphed as displacement vectors at eachlandmark. In numerous software packages there are leastsquares and resistant-fit methods available.

Thin-plate splines compare the shape differencesbetween two landmark configurations. Bookstein (1991)proposed the thin-plate spline interpolation formalism tovisualize the differences in the positions of the landmarksby modeling the deformations taking place between thelandmarks; i.e., in all regions without landmark points.Imagine a combination of landmarks printed on a thinplate and compare it with a second combination oflandmarks, supposing that the differences in coordinatesare taken as vertical displacements of this plateperpendicular to itself, one Cartesian coordinate at atime. The energy necessary to deform the plate at eachlandmark is the so-called bending energy. And, as theb e n d i n g e n e r g y i s h i g h e s t f o r t h e m o s t l o c a ldeformations, its minimization in all the non-landmarkareas models their position. Interpolants modeling suchplate deformations are called thin plate spline functions.They are, first, a convenient solution to the problem ofinterpolation by constructing continuous deformationgrids for data in the form of two landmark configurations(which could be the consensus configurations of the twopopulations under discussion) and, second, the basis forsophisticated analyses of shape difference like Partial orRelative Warps Analysis of these two configuration.

Relative Warp Analysis is applied to the thin platespline interpolation, because it yields the general shapedeviation between two landmark configurations. Theshape deviation consists of different components whichcan be distinguished: the uniform component (the affinepart) and the non-affine part. The affine part describesdistortion and shear-uniform displacements for alllandmarks with zero bending energy. The non-affine partcomprises all non-uniform, local changes, generally with ap os i t i ve bending ene rgy . In o rder to o bta in adifferentiation of these local changes, one can carry outprincipal component analysis (PCA) from the coefficientsof the eigenvectors of the bending energy matrix. ThePCA lists the partial warp scores, ordered in decreasingbending energy (which is analog to a decrease in localshifts of the landmarks). “Relative warps may be thoughtof principal components of the set of all partial warps for acomplete sample of forms as each is derived by thedeformation of the mean shape” (Bookstein, 1997, p. 344).

Two case studiesWe have recently succeeded in finding answers to some

long pending questions concerning the cranial shape

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changes during human evolution.The first study (Bookstein et al., 1999) deals the

hypothesis that the shape change of the inner frontalregion does not simply reflect that of the outer one, sincethe endocranial shape is a response to brain morphologyevolution, whereas the ectocranial morphology respondsto the changing attachment geometry for the muscles ofthe masticatory apparatus (Prossinger, 2000a). To clarifythe relationships between hominid internal and externalfrontal profiles, we examined the profiles using CT scansof 16 modern human crania and five mid-Pleistocenefossil ones. These included three Homo heidelbergensis,one proto -Neanderthal , and one ‘c lass ic ’ Homoneanderthalensis specimen.

Traditional landmarks were located on each specimenin three dimensions. The median sagittal sections werethen processed using a software package with a thin plates p l i n e i m p l e m e n t a t io n . S e m i l a n d m a r k s w e r eadditionally located along the internal curve of thefrontal bone in this plane, and also along the outersurface of the frontal bone. For each fossil, thesesemilandmarks were matched to a typical H. sapiensspecimen along and across the curves in such a way as tominimize the bending energy of the thin plate spline (Fig.3).

The landmarks along the inner arc of the archaic skullprofiles were then Procrustes fitted to the same points ofthe modern ones. These profiles fit so well that they aree s se n t i a l l y i n d i s t i n g u i s h a b l e i n a n o p t i m a l l ysuperimposed scatter. The five archaic and the moderninner profiles are visually and statistically homogenousbut the outer profiles differ markedly. Relative warpsanalysis of the outer and the inner curve separately yieldsexactly the same conclusion. For the outer table, analysisof the first relative warp score separates the two samplesperfectly, while the relative warp scores of the innerfrontal table shows that there is substantial overlap andno significant differences between them.

This result implies that mid-sagittal vault morphologyhas remained remarkably conservative since the mid-Pleistocene, despite significant increase in size. Thisconfirms that the forms of the inner and outer aspects ofthe human frontal bone are determined by entirelyindependent factors.

The second study deals with the idea that exo- andendo crania l bone morp holo gy ar e fu nctional lyindependent; we hypothesized in a follow-up study(Schäfer et al., in press) that in the median sagittal planethe whole exocranium is predominantly involved inshape changes and the endocranium in size changes.Here, our sample comprises 21 crania of modern humans,and stereol ithographs of Kabwe, Petralona, andAtapuerca SH5. We measured 3D-coordinates of the mainendo- and exocranial Type I landmarks in the mid-sagittalplane. A Procrustes fit over the set of all landmarks

shows that the largest differences between the modernsand the fossils are in the external frontal and occipitalregions. Fitting all landmarks except nasion and inion,but co-moving them, separates the mid-Pleistocenes evenmore clearly from the moderns. A permutation testconfirms highly significant differences between the twogroups at nasion and at inion with no such differences inthe other landmarks. Additionally, we find that there is asignificant change in exocranial Centroid Size from mid-Pleistocene to moderns, but not in endocranial size.(Centroid Size (Dryden and Mardia 1998), the square rootof the sum of squared distances of the landmarks from thecenter-of-mass of all the landmarks, is a good surrogatefor the intuitive assessment of size of the object underinvestigation.)

The discovery of invariance in internal vault curvatureand the temporal stability in the overall size and shape ofthe endocranium in the mid-sagittal plane encouragesfurther analyses using these methods.

T h e p o w e r a n d n e c e s s i t y o f s e m i l a n d m a r kmethodology for statistical analysis

One purpose of geometric methods is—evidently—tomake coordinate data accessible to statistical analysismethods. The power of these methods is based on theassumption of the homology of landmarks betweendifferent specimens. However, analyzing landmarks—astraditionally defined—restricts the information available

Fig. 3 An example of a thin-plate spline deformation grid.A typical Homo sapiens cranium (not shown) ismapped to the Homo heidelbergensis specimenAtapuerca SH5 (shown), using the complete set oflandmarks (solid circles, numbered 1–26) Landmarks1–17 are Type I landmarks; the semilandmarks (18–26) are on the profiles. The grid lines show thedeformation map as dictated by the bending energyminimization.

77Weber, GW et al.

for each specimen, since the number of points that can bedefined unequivocally on every specimen is limited.

Landmarks function primarily as placeholders for theshape changes occuring in the regions between them.Shape information that is encoded in curvatures is lostwhen the statistical analysis is based on landmarks (i.e.,points) alone. Many biological forms possess only a smallnumber of defined landmarks, while others lack thementirely, thus rendering the morphometric toolkit almostuseless. Recent research is therefore trying to developmethods to include information about curving intomorphometric analysis.

While in many cases it may be easy to define a curve onthe surface of an object, for example the edge of astructure, it is difficult to describe curves reliably withr eference to landmarks , becau se , a l thou gh theuncertainty of the position of a landmark perpendicularto the curve is negligible, defining its position along thecurve is uncertain. In order to include information aboutcurvature, the concept of semilandmarks was introducedby Bookstein (Bookstein, 1991). A semilandmark isallowed to slide along a curve or a surface until all thecorresponding semilandmarks on different specimens arehomologous in a statistical sense (Bookstein et al., 1999)(Fig. 4). The position along the curve/surface of asemilandmark is dependent on the position of thesurrounding “true” landmarks that constrain its shiftwhile its position in the direction perpendicular to thecurve is defined by the properties of the specimen’ss h a p e . W e s e e k t h e o p t i m a l p o s i t i o n o f t h esemilandmarks for subsequent statistical investigations,decreasing the variance along tangent directions (due tomeasurement error) and preserving the variance that is aresult of shape difference. The process described above iscalled spline relaxation and combines the essential toolsof Geometric Morphometrics: the thin plate spline andt h e P r o c r u s t e s r e g i s t r a t i o n . B y r e l a x i n g a l lsemilandmarks against the mean form (computed as aProcrustes average of all forms), the semilandarks

Fig. 4 Semilandmarks on curves. The twothe tangent to the curve so as to minimand target specimen. After relaxation,projected onto the curve. The sliding mthree ‘true’ landmarks (solid circles).

acquire geometric homology within the data set. Thesemilandmarks are not ‘true’ landmarks in that theycannot be defined on a single, isolated specimen—theyexist only in the context of some group average. Only thecoordinate normal to the outline carries informationabout dif ferences between specimens or groups(Bookstein, 1996).

The ability to describe curves and surfaces while notrestricting oneself to ‘true’ landmarks opens a wide fieldof future research. Bookstein (1996) has successfullyapplied semilandmarks on curves to describe shapedifferences in the human brain by comparing the corporacallosa of schizophrenics with those of their physicians.His f ind ing s suppl ie d a va luab le inves t ig at ivemethodology, as subsequently documented by Gharaibehet al. (2000).

Th e me th od o f sp l ine r e lax a t io n i s ba sed o nfundamental properties of the thin plate spline. The thinplate spline was originally used in physics to model thebehavior of a thin metal plate under pressure. Inmorphometrics, it is used as an interpolation function ofthe deformation of one landmark configuration intoanother. Using both configurations (template and target)as input parameters, the spline interpolates the positionof all points between these landmarks (Fig. 5). The thinplate spline seeks to minimize the sum of secondderivatives of the interpolation function (correspondingto the minimal bending/deformation energy of aninfinitely thin plate). This minimum value is commonlyreferred to as bending energy. Localized deformationsresult in a higher contribution to bending energy than dolarge scale deformations, and the minimization conditionresults in the bending energy of affine transformations(stretching and shearing of all landmarks) being zero.The spline helps to visualize statistical summaries basedon the Procrustes fits. Any vector computed in the courseof multivariate analysis—often the difference of means—can be visualized as a deformation. During relaxation thethin plate spline is not used as a visualization tool; rather,

semilandmarks are allowed to slide alongize the bending energy between template

the new position of the semilandmark isovement is constrained by the presence of

Virtual Anthropology78

its properties are used to find the optimal position of thesemilandmarks, where optimal means “minimal amountof deformation.”

The parametric representation of the deformation viathin plate spline offers possibilities to estimate missingv a l u e s , a p r o b l e m o f t e n e n c o u n t e r e d i npaleoanthropology, because fossils are broken andusually incomplete and therefore landmark coordinatesare missing.

While it is difficult to describe landmarks on curveswithout semilandmarks, it is virtually impossible todefine landmarks on a smooth surface such as theexterior of the human cranium. Here, the combination ofspline relaxation and Procrustes averaging leads topromising results. Figure 6 shows semilandmarks on ahuman cranium after spline relaxation against theaverage configuration computed as the mean ofProcrustes coordinates. The vectors show the shapedifference between a two year old child and an adulthydrocephalic cranium. A shape analysis of two formswith such a distinct size difference shows the advantageof the methodologies described here.

The combination of spline relaxation and Procrustesmethods to obtain homologous landmarks on curvingforms allows us to analyze them as a whole, using all themultivariate statistical methodologies the presentmorphometric literature offers. Although there is nostat istical distribution known for data as highlynonlinearly processed as these slid spline residuals, thepermutation stat ist ic (Good, 2000) offers manypossibilities to test for significance. Indeed, permutationtests are valid under minimal assumptions, so they offer anovel, distribution-free suite of hypotheses tests. Fisher(1935) had already pointed out that every parametric testis (at best) a surrogate for a permutation test. With theavailability of adequately powerful desktop computers,permutation tests will become more and more the methodof choice.

The semilandmarks on surfaces could prove to be thenecessary toolkit for many questions investigating shape

Fig. 5 A thin-plate spline interpolation example. Themapped via the interpolation grid—as defined by th(right).

variation that had previously remained unresolvedbecause of the limitations that are imposed by a two-dimensional representation of three-dimensional forms.

The Future

This undoubtedly incomplete list of meaningfulapplications of Virtual Anthropology demonstratesclearly that anthropological research profits substantiallyfrom methods enabling views into the interior ofstructures. In the near future, an essential part of ourstudies will be carried out not on the real object but in acomputer lab, using various kinds of digital data. Someparticular questions will, of course, remain within thepredominance of the classical research approach. Fort h o se w h o w a n t t o e nt e r t h e w o r l d o f V i r t u a lAnthropology, however, good news is within reach, asadequately powerful desktop computers are nowavailable which can handle the large data files, whilesoftware developers are more often programming in aWindows NT or Linux environment. At the forefront of

quincunx with one point on both diagonals (left) ise minimum bending energy—to the changed quincunx

Fig. 6 Semilandmarks on a surface. The vectors show theshape difference between a two-year-old child and ahydrocephalic adult. The semilandmarks have been relaxedand the vectors are Procrustes residuals (differences inshape after partialing out size).

79Weber, GW et al.

VA developments, some major directions for the futureare:

First, the enhancement of the resolution using micro-CT scans, which allows for a spatial resolution as small as5 µm so that more kinds of analysis (including microstructures) can be undertaken with the same datamaterial.

Second, the reconstruction of fragmented skulls usinghighly reproducible electronic re-assembly tools whichallow for repeated attempts and which are based onstatistical knowledge of object form and shape and theelectronic preparation and correction for deformations.

Third, the exchange of 3D-digital data betweencooperating research institutions with the goal ofextended analysis of morphological variation inhominoids. A first step in this direction is the publicationof the first CD-ROM with 3D-data of a fossil cranium, theBodo specimen (Seidler et al., 1999).

However, we need to keep in mind that we have onlyacquired a plethora of new tools; their application tofossil material does not guarantee meaningful results;interpretation is still the paramount obligation of aresponsible scientist. Nevertheless, because the amountof information has enormously increased, prospects fornovel insights are offered by Virtual Anthropology.

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Received: February 3, 2001Accepted: March 10, 2001Correspondence to: Gerhard W. Weber, Institute forAnthropology, Althanstrasse 14, A-1090 Vienna, Austriae-mail: gerhard.weber@univie.ac.at