A Decision Tree for Nonmetric Sex Assessment from the Skull

What we see is what we touch? Sex estimation on the skull in virtual anthropology

BACKGROUND

The increased use of virtual bone images in forensic anthropology requires a comprehensive study on the observational errors between dry bones and CT reconstructions. Here, we focus on the consistency of nonmetric sex estimation traits on the human skull.

MATERIALS AND METHODS

We scored nine nonmetric traits on dry crania and mandibles (n = 223) of archaeological origin and their CT reconstructions. Additionally, we 3D surface scanned a subsample (n = 50) and repeated our observations. Due to the intricate anatomy of the mental eminence, we split it into two separate traits: the bilateral mental tubercles and the midsagittal mental protuberance. We provide illustrations and descriptions for both these traits.

RESULTS

We obtained supreme consistency values between the CT and 3D surface modalities. The most consistent cranial traits were the glabella and the supraorbital margin, followed by the nuchal crest, zygomatic extension, mental tubercles, mental protuberance, mental eminence, mastoid process and ramus flexure, in descending order. The mental tubercles show higher consistency scores than the mental eminence and the mental protuberance.

DISCUSSION

The increased interchangeability of the virtual modalities with each other as compared to the dry bone modality could be due to the lack of tactility on both the CT and surface scans. Moreover, tactility appears less essential with experience than a precise trait description. Future studies could revolve around the most consistent cranial traits, combining them with pelvic traits from a previous study, to test for accuracy.

A morphoscopic exploration of cranial sexual dimorphism among modern South Africans using computed tomography scans

Continual re-evaluation of standards for forensic anthropological analyses are necessary, particularly as new methods are explored or as populations change. Indian South Africans are not a new addition to the South African population; however, a paucity of skeletal material is available for analysis from medical school collections, which has resulted in a lack of information on the sexual dimorphism in the crania. For comparable data, computed tomography scans of modern Black, Coloured and White South Africans were included in addition to Indian South Africans. Four cranial morphoscopic traits, were assessed on 408 modern South Africans (equal sex and population distribution). Frequencies, Chi-squared tests, binary logistic regression and random forest modelling were used to assess the data. Males were more robust than females for all populations, while White South African males were the most robust, and Black South African females were the most gracile. Population differences were noted among most groups for at least two variables, necessitating the creation of populations-specific binary logistic regression equations. Only White and Coloured South Africans were not significantly different. Indian South Africans obtained the highest correct classifications for binary logistic regression (94.1%) and random forest modelling (95.7%) and Coloured South Africans had the lowest correct classifications (88.8% and 88.0%, respectively). This study provides a description of the patterns of sexual dimorphism in four cranial morphoscopic traits in the current South African population, as well as binary logistic regression functions for sex estimation of Black, Coloured, Indian and White South Africans.

Wilhelm Waldeyer as an object - Anatomists as body donors

INTRODUCTION

Berlin anatomist Wilhelm von Waldeyer-Hartz (1836-1921) donated his skull, brain, and hands to his institute. Only the skull survives in the present-day collection. This study investigates the skull itself as much as the historical context of Waldeyer's donation.

METHODS

Physical-anthropological investigation of the remains and historical research.

RESULTS

Waldeyer's main motivation was the donation of his brain to science. While this was the first ever recorded body donation in Berlin, it was not unusual for scientists of his time to donate their brains and/or to investigate brains of fellow scientists to correlate brain morphology to individual traits. Nevertheless, Waldeyer's pupil Hans Virchow expressed reservations dissecting his former boss, reservations that were unknown to him when dissecting others. Waldeyer's brain was never investigated and not preserved, likely due to damage by stroke and poor anatomical fixation. Waldeyer's skull shows the common features of a male European of senile age with some notable anatomical variation including a "trigeminus bridge".

DISCUSSION

Waldeyer's donation is embedded in a tradition of research looking, if in vain, for traceable signs of intelligence or geniality in brains of well-known individuals. Reservations of anatomists to dissect other anatomists and to donate their own bodies persist until today.

Artificial intelligence-based forensic sex determination of East Asian cadavers from skull morphology

Identification of unknown cadavers is an important task for forensic scientists. Forensic scientists attempt to identify skeletal remains based on factors including age, sex, and dental treatment remains. Forensic scientists commonly consider skull or pelvic shape to evaluate the sex; however, these evaluations require sufficient experience and knowledge and lack objectivity and reproducibility. To ensure objectivity and reproducibility for sex evaluation, we applied a gated attention-based multiple-instance learning model to three-dimensional (3D) skull images reconstructed from postmortem head computed tomography scans. We preprocessed the images, trained with 864 training data, validated the model with 124 validation data, and evaluated the performance of our model in terms of accuracy with 246 test data. Furthermore, three forensic scientists evaluated the 3D skull images, and their performances were compared with those of the model. Our model showed an accuracy of 0.93, which was higher than that of the forensic scientists. Our model primarily focused on the entire skull owing to visualization but focused less on the areas often investigated by forensic scientists. In summary, our model may serve as a supportive tool to identify cadaver sex based on skull shape. Further studies are required to improve the model's performance.

Resolving network clusters disparity based on dissimilarity measurements with nonmetric analysis of variance

Classic ANOVA (cA) tests the explanatory power of a partitioning on a set of objects. More fit for clusters proximity analysis, nonparametric ANOVA (npA) extends to a case where instead of the object values themselves, their mutual distances are available. However, extending the cA applicability, the metric conditions in npA are limiting. Based on the central limit theorem (CLT), here we introduce nonmetric ANOVA (nmA) that by relaxing the metric properties between objects, allows an ANOVA-like statistical testing of a network clusters disparity. We present a parametric test statistic which under the null hypothesis of no differences between the competing clusters means, follows an exact F-distribution. We apply our method on three diverse biological examples, discuss its parallel performance, and note the specific use of each method tailored by the inherent data properties. The R code is provided at github.com/AmiryousefiLab/nmANOVA.

Comparison of decision tree and naïve Bayes algorithms in detecting trace residue of gasoline based on gas chromatography-mass spectrometry data

Fire debris analysis aims to detect and identify any ignitable liquid residues in burnt residues collected at a fire scene. Typically, the burnt residues are analysed using gas chromatography-mass spectrometry (GC-MS) and are manually interpreted. The interpretation process can be laborious due to the complexity and high dimensionality of the GC-MS data. Therefore, this study aims to compare the potential of classification and regression tree (CART) and naïve Bayes (NB) algorithms in analysing the pixel-level GC-MS data of fire debris. The data comprise 14 positive (i.e. fire debris with traces of gasoline) and 24 negative (i.e. fire debris without traces of gasoline) samples. The differences between the positive and negative samples were first inspected based on the mean chromatograms and scores plots of the principal component analysis technique. Then, CART and NB algorithms were independently applied to the GC-MS data. Stratified random resampling was applied to prepare three sets of 200 pairs of training and testing samples (i.e. split ratio of 7:3, 8:2, and 9:1) for estimating the prediction accuracies. Although both the positive and negative samples were hardly differentiated based on the mean chromatograms and scores plots of principal component analysis, the respective NB and CART predictive models produced satisfactory performances with the normalized GC-MS data, i.e. majority achieved prediction accuracy >70%. NB consistently outperformed CART based on the prediction accuracies of testing samples and the corresponding risk of overfitting except when evaluated using only 10% of samples. The accuracy of CART was found to be inversely proportional to the number of testing samples; meanwhile, NB demonstrated rather consistent performances across the three split ratios. In conclusion, NB seems to be much better than CART based on the robustness against the number of testing samples and the consistent lower risk of overfitting.

Sex estimation from virtual models: exploring the potential of stereolithic 3D crania models for morphoscopic trait scoring

Modern computed tomography (CT) databases are becoming an accepted resource for the practice and development of identification methods in forensic anthropology. However, the utility of 3D models created using free and open-source visualization software such as 3D Slicer has not yet been thoroughly assessed for morphoscopic biological profiling methods where virtual methods of analysis are becoming more common. This paper presents a study that builds on the initial findings from Robles et al. (2020) to determine the feasibility of estimating sex on stereolithic (STL) 3D cranial models produced from CT scans from a modern, living UK population (n = 80) using equation 2 from the Walker's (2008) morphoscopic method. Kendall's coefficients of concordance (KCC) indicated substantial agreement using cranial features scores in an inter-observer test and a video-inter-observer test. Fleiss' Kappa scores showed moderate agreement (0.50) overall between inter-observer sex estimations, and for observer sex estimations in comparison to recorded sexes (0.56). It was found that novice users could virtually employ morphoscopic sex estimation methods effectively on STL 3D cranial models from modern individuals. This study also highlights the potential that digital databases of modern living populations can offer forensic anthropology.

Key points

First example of Walker's (2008) method applied to a living UK population.Open-source software is a valuable resource for crime reconstruction approaches.Male scoring bias was observed in method application.Forensic anthropologists would benefit from virtual anthropology training to use and interpret 3D models.Digital databases offer more ethical, diverse, modern populations for future research.

Sexual Dimorphism of Cranial Morphological Traits in an Italian Sample: A Population-Specific Logistic Regression Model for Predicting Sex

Simple Summary

Despite the fact that sex estimation methods from crania are very popular in forensic anthropology, few validation studies have verified their accuracy and reliability in different populations. Different from craniometrics, for which validation studies have remarkably increased lately, the methods based on cranial morphology still need to be thoroughly investigated, even if a large consensus exists on the effects of population variability on sexual cranial dimorphism. When dealing with forensic contexts, appropriately-validated methods should be applied for building accurate biological profiles. Since the possible sexual dimorphism variation of cranial morphological traits needs to be evaluated properly in various populations, in this study, we analyzed the accuracy of existing regression models for predicting sex from cranial morphological traits in an Italian contemporary/modern population. In addition, we propose new logistic regression models that are more accurate and specific for our sample. The results also update the reference standards for populations of this geographical area and provide an additional important warning on sexual dimorphism to anthropologists working in forensic contexts.

Abstract

Although not without subjectivity, the cranial trait scoring method is an easy visual method routinely used by forensic anthropologists in sex estimation. The revision presented by Walker in 2008 has introduced predictive models with good accuracies in the original populations. However, such models may lead to unsatisfactory performances when applied to populations that are different from the original. Therefore, this study aimed to test the sex predictive equations reported by Walker on a contemporary Italian population (177 individuals) in order to evaluate the reliability of the method and to identify potential sexual dimorphic differences between American and Italian individuals. In order to provide new reference data to be used by forensic experts dealing with human remains of modern/contemporary individuals from this geographical area, we designed logistic regression models specific to our population, whose accuracy was evaluated on a validation sample from the same population. In particular, we fitted logistic regression models for all possible combinations of the five cranial morphological traits (i.e., nuchal crest, mastoid process, orbital margin, glabella, and mental eminence). This approach provided a comprehensive set of population-specific equations that can be used in forensic contexts where crania might be retrieved with severe taphonomic damages, thus limiting the application of the method only to a few morphological features. The results proved once again that the effects of secular changes and biogeographic ancestry on sexual dimorphism of cranial morphological traits are remarkable, as highlighted by the low accuracy (from 56% to 78%) of the six Walker’s equations when applied to our female sample. Among our fitted models, the one including the glabella and mastoid process was the most accurate since these features are more sexually dimorphic in our population. Finally, our models proved to have high predictive performances in both training and validation samples, with accuracy percentages up to 91.7% for Italian females, which represents a significant success in minimizing the potential misclassifications in real forensic scenarios.

Artifact3-D: New software for accurate, objective and efficient 3D analysis and documentation of archaeological artifacts

The study of artifacts is fundamental to archaeological research. The features of individual artifacts are recorded, analyzed, and compared within and between contextual assemblages. Here we present and make available for academic-use Artifact3-D, a new software package comprised of a suite of analysis and documentation procedures for archaeological artifacts. We introduce it here, alongside real archaeological case studies to demonstrate its utility. Artifact3-D equips its users with a range of computational functions for accurate measurements, including orthogonal distances, surface area, volume, CoM, edge angles, asymmetry, and scar attributes. Metrics and figures for each of these measurements are easily exported for the purposes of further analysis and illustration. We test these functions on a range of real archaeological case studies pertaining to tool functionality, technological organization, manufacturing traditions, knapping techniques, and knapper skill. Here we focus on lithic artifacts, but the Artifact3-D software can be used on any artifact type to address the needs of modern archaeology. Computational methods are increasingly becoming entwined in the excavation, documentation, analysis, database creation, and publication of archaeological research. Artifact3-D offers functions to address every stage of this workflow. It equips the user with the requisite toolkit for archaeological research that is accurate, objective, repeatable and efficient. This program will help archaeological research deal with the abundant material found during excavations and will open new horizons in research trajectories.

The computational age-at-death estimation from 3D surface models of the adult pubic symphysis using data mining methods

Age-at-death estimation of adult skeletal remains is a key part of biological profile estimation, yet it remains problematic for several reasons. One of them may be the subjective nature of the evaluation of age-related changes, or the fact that the human eye is unable to detect all the relevant surface changes. We have several aims: (1) to validate already existing computer models for age estimation; (2) to propose our own expert system based on computational approaches to eliminate the factor of subjectivity and to use the full potential of surface changes on an articulation area; and (3) to determine what age range the pubic symphysis is useful for age estimation. A sample of 483 3D representations of the pubic symphyseal surfaces from the ossa coxae of adult individuals coming from four European (two from Portugal, one from Switzerland and Greece) and one Asian (Thailand) identified skeletal collections was used. A validation of published algorithms showed very high error in our dataset-the Mean Absolute Error (MAE) ranged from 16.2 and 25.1 years. Two completely new approaches were proposed in this paper: SASS (Simple Automated Symphyseal Surface-based) and AANNESS (Advanced Automated Neural Network-grounded Extended Symphyseal Surface-based), whose MAE values are 11.7 and 10.6 years, respectively. Lastly, it was demonstrated that our models could estimate the age-at-death using the pubic symphysis over the entire adult age range. The proposed models offer objective age estimates with low estimation error (compared to traditional visual methods) and are able to estimate age using the pubic symphysis across the entire adult age range.

Forensic Tools for Species Identification of Skeletal Remains: Metrics, Statistics, and OsteoID

Although nonhuman remains constitute a significant portion of forensic anthropological casework, the potential use of bone metrics to assess the human origin and to classify species of skeletal remains has not been thoroughly investigated. This study aimed to assess the utility of quantitative methods in distinguishing human from nonhuman remains and present additional resources for species identification. Over 50,000 measurements were compiled from humans and 27 nonhuman (mostly North American) species. Decision trees developed from the long bone data can differentiate human from nonhuman remains with over 90% accuracy (>98% accuracy for the human sample), even if all long bones are pooled. Stepwise discriminant function results were slightly lower (>87.4% overall accuracy). The quantitative models can be used to support visual identifications or preliminarily assess forensic significance at scenes. For species classification, bone-specific discriminant functions returned accuracies between 77.7% and 89.1%, but classification results varied highly across species. From the study data, we developed a web tool, OsteoID, for users who can input measurements and be shown photographs of potential bones/species to aid in visual identification. OsteoID also includes supplementary images (e.g., 3D scans), creating an additional resource for forensic anthropologists and others involved in skeletal species identification and comparative osteology.

Development of the decision tree model for distinguishing individuals of Chinese four surnames from Zhanjiang Han population based on Y-STR haplotypes

Co-separation studies between surnames and Y chromosome genetic markers are beneficial to revealing population migrations, surname origins, population formation histories and forensic familial searching. Genetic distributions of 27 Y-STRs in Chinese four surnames (Li, Lin, Chen and Huang) from Zhanjiang Han population were investigated. Meanwhile, we tried to develop a decision tree model for surname predictions based on Y-STR haplotypes. Allelic frequencies of 27 Y-STRs showed that unique alleles were only observed in a certain surname; besides, some alleles displayed higher frequencies in a certain surname than those in other surnames, implying these alleles might be employed as the useful indicators for surname predictions. Haplotype match probability values of 27 Y-STRs in these surnames revealed that the system could be used as a valuable tool for forensic male identification. The developed decision tree model performed well for the training set with the accuracy of 0.9860 and obtained the relatively high accuracy (>0.70) for surname predictions of the testing set. To sum up, we explored the power of the machine learning to the surname predictions based on obtained Y-STR haplotypes, which showed promising application values in forensic familial searching.

Three-dimensional geometric morphometric studies of modern human occipital variation

Objectives

To investigate three-dimensional morphological variation of the occipital bone between sexes and among populations, to determine how ancestry, sex and size account for occipital shape variation and to describe the exact forms by which the differences are expressed.

Methods

CT data for 214 modern crania of Asian, African and European ancestry were compared using 3D geometric morphometrics and multivariate statistics, including principal component analysis, Hotelling’s T² test, multivariate regression, ANOVA, and MANCOVA.

Results

Sex differences in average occipital morphology are only observed in Europeans, with males exhibiting a pronounced inion. Significant ancestral differences are observed among all samples and are shared by males and females. Asian and African crania have smaller biasterionic breadths and flatter clivus angles compared to Europeans. Asian and European crania are similar in their nuchal and occipital plane proportions, nuchal and occipital angles, and lower inion positions compared to Africans. Centroid size significantly differs between sexes and among populations. The overall allometry, while significant, explains little of the shape variation. Larger occipital bones were associated with a more curved occipital plane, a pronounced inion, a narrower biasterionic breadth, a more flexed clivus, and a lower and relatively smaller foramen magnum.

Conclusions

Although significant shape differences were observed among populations, it is not recommended to use occipital morphology in sex or population estimation as both factors explained little of the observed variance. Other factors, relating to function and the environment, are suggested to be greater contributors to occipital variation. For the same reason, it is also not recommended to use the occiput in phylogenetic studies.

On the use of machine learning algorithms in forensic anthropology

The classification performance of the statistical methods binary logistic regression (BLR), multinomial and penalized multinomial logistic regression (MLR, pMLR), linear discriminant analysis (LDA), and the machine learning algorithms naïve Bayes classification (NBC), decision trees (DT), random forest (RF), artificial neural networks (ANN), support vector machines (linear, polynomial or radial) (SVM), multivariate adaptive regression splines (MARS), and extreme gradient boosting (XGB) is examined in skeletal sex/ancestry estimation. The datasets used to test the performance of these methods were obtained from a documented human skeletal collection, Athens Collection, and the Howells Craniometric data set. For their implementation, an R package has been written to search for the optimum tuning parameters under cross-validation and perform sex/ancestry classification. It was found that the classification performance may vary significantly depending on the problem. From the methods tested, LDA and the machine learning technique of linear SVM exhibit the best performance, with high prediction accuracy and relatively low bias in most of the tests. ANN and pMLR can generally be considered to give satisfactory predictions, whereas NBC when using metric traits and DT are the worst of the classification methods examined. The possibility of making the models developed via the machine learning algorithms applicable to other assemblages without the use of a training sample is also discussed.

Data mining for sex estimation based on cranial measurements

The aim of the present study is to develop effective and understandable classification models for sex estimation and to identify the most dimorphic linear measurements in adult crania by means of data mining techniques. Furthermore, machine learning models and models developed through logistic regression analysis are compared in terms of performance. Computed tomography scans of 393 adult individuals were used in the study. A landmark-based approach was applied to collect the metric data. The three-dimensional coordinates of 47 landmarks were acquired and used for calculation of linear measurements. Two datasets of cranial measurements were assembled, including 37standard measurements and 1081 interlandmark distances, respectively. Three data mining algorithms were applied: the rule induction algorithms JRIP and Ridor, and the decision tree algorithm J48. Two advanced attribute selection methods (Weka BestFirst and Weka GeneticSearch) were also used. The best accuracy result (91.9 %) was achieved by a set of rules learnt by the JRIP algorithm from the dataset constructed by application of the GeneticSearch selection algorithm to the dataset of standard cranial measurements. The set consisted of five rules including seven cranial measurements. Its accuracy was even better than the classification rates achieved by the logistic regression models. Concerning the second dataset of nonstandard measurements, the best accuracy (88.3 %) was obtained by using classification models learnt by two algorithms - JRIP with a dataset preprocessed by the BestFirst selection algorithm and Ridor with preprocessing by the GeneticSearch selection algorithm. Our experiments show that for the two datasets mentioned above the rule-based models contain smaller sets of rules with shorter lists of measurements and achieve better classification accuracy results in comparison with decision tree-based models.

Advanced procedures for skull sex estimation using sexually dimorphic morphometric features

This paper introduces an automated method for estimating sex from cranial sex diagnostic traits by extracting and evaluating specialized morphometric features from the glabella, the supraorbital ridge, the occipital protuberance, and the mastoid process. The proposed method was developed and evaluated using two European population samples, a Czech sample comprising 170 crania reconstructed from anonymized CT scans and a Greek sample of 156 crania from the Athens Collection. It is based on a fully automatic algorithm applied on 3D models for extracting sex diagnostic morphometric features which are further processed by computer vision and machine learning algorithms. Classification accuracy was evaluated in a population specific and a population generic 2-way cross-validation scheme. Population-specific accuracy for individual morphometric features ranged from 78.5 to 96.7%, whereas population generic correct classification ranged from 71.7 to 90.8%. Combining all sex diagnostic traits in multi-feature sex estimation yielded correct classification performance in excess of 91% for the entire sample, whereas the sex of about three fourths of the sample could be determined with 100% accuracy according to posterior probability estimates. The proposed method provides an efficient and reliable way to estimate sex from cranial remains, and it offers significant advantages over existing methods. The proposed method can be readily implemented with the skullanalyzer computer program and the estimate_sex.m GNU Octave function, which are freely available under a suitable license.

Development and validation of a risk prediction model to diagnose Barrett's oesophagus (MARK-BE): a case-control machine learning approach

Background

Screening for Barrett's Oesophagus (BE) relies on endoscopy which is invasive and has a low yield. This study aimed to develop and externally validate a simple symptom and risk-factor questionnaire to screen for patients with BE.

Methods

Questionnaires from 1299 patients in the BEST2 case-controlled study were analysed: 880 had BE including 40 with invasive oesophageal adenocarcinoma (OAC) and 419 were controls. This was randomly split into a training cohort of 776 patients and an internal validation cohort of 523 patients. External validation included 398 patients from the BOOST case-controlled study: 198 with BE (23 with OAC) and 200 controls. Identification of independently important diagnostic features was undertaken using machine learning techniques information gain (IG) and correlation based feature selection (CFS). Multiple classification tools were assessed to create a multi-variable risk prediction model. Internal validation was followed by external validation in the independent dataset.

Findings

The BEST2 study included 40 features. Of these, 24 added IG but following CFS, only 8 demonstrated independent diagnostic value including age, gender, smoking, waist circumference, frequency of stomach pain, duration of heartburn and acid taste and taking of acid suppression medicines. Logistic regression offered the highest prediction quality with AUC (area under the receiver operator curve) of 0.87. In the internal validation set, AUC was 0.86. In the BOOST external validation set, AUC was 0.81.

Interpretation

The diagnostic model offers valid predictions of diagnosis of BE in patients with symptomatic gastroesophageal reflux, assisting in identifying who should go forward to invasive testing. Overweight men who have been taking stomach medicines for a long time may merit particular consideration for further testing. The risk prediction tool is quick and simple to administer but will need further calibration and validation in a prospective study in primary care.

Funding

Charles Wolfson Trust and Guts UK.

Virtual reconstruction of the Upper Palaeolithic skull from Zlatý Kůň, Czech Republic: Sex assessment and morphological affinity

The incomplete cranium discovered at the Zlatý kůň site in the Bohemian Karst is a rare piece of skeletal evidence of human presence in Central Europe during the Late Glacial period. The relative position of cranial fragments was restored and missing parts of the cranium were virtually reconstructed using mirroring and the Thin-plate splines algorithm. The reconstruction allowed us to collect principal cranial measurements, revise a previous unfounded sex assignment and explore the specimen's morphological affinity. Visual assessment could not reliably provide a sexual diagnosis, as such methods have been developed on modern populations. Using a population-specific approach developed on cranial measurements collected from the literature on reliably sexed European Upper Palaeolithic specimens, linear discriminant analysis confirmed previous assignment to the female sex. However, caution is necessary with regard to the fact that it was assessed from the skull. The Zlatý kůň specimen clearly falls within the range of Upper Palaeolithic craniometric variation. Despite the shift in cranial variation that accompanied the Last Glacial Maximum (LGM), the Zlatý kůň skull exhibits a morphological affinity with the pre-LGM population. Several interpretations are proposed with regard to the complex population processes that occurred after the LGM in Europe.

Investigating the sex-related geometric variation of the human cranium

Accurate sexing methods are of great importance in forensic anthropology since sex assessment is among the principal tasks when examining human skeletal remains. The present study explores a novel approach in assessing the most accurate metric traits of the human cranium for sex estimation based on 80 ectocranial landmarks from 176 modern individuals of known age and sex from the Athens Collection. The purpose of the study is to identify those distance and angle measurements that can be most effectively used in sex assessment. Three-dimensional landmark coordinates were digitized with a Microscribe 3DX and analyzed in GNU Octave. An iterative linear discriminant analysis of all possible combinations of landmarks was performed for each unique set of the 3160 distances and 246,480 angles. Cross-validated correct classification as well as multivariate DFA on top performing variables reported 13 craniometric distances with over 85% classification accuracy, 7 angles over 78%, as well as certain multivariate combinations yielding over 95%. Linear regression of these variables with the centroid size was used to assess their relation to the size of the cranium. In contrast to the use of generalized procrustes analysis (GPA) and principal component analysis (PCA), which constitute the common analytical work flow for such data, our method, although computational intensive, produced easily applicable discriminant functions of high accuracy, while at the same time explored the maximum of cranial variability.