Skip to main content

Advertisement

SpringerLink
Log in

Machine learning approaches for sex estimation using cranial measurements

  • Original Article
  • Published:
International Journal of Legal Medicine Aims and scope Submit manuscript

Abstract

The aim of the present study is to apply support vector machines (SVM) and artificial neural network (ANN) as sex classifiers and to generate useful classification models for sex estimation based on cranial measurements. Besides, the performance of the generated sub-symbolic machine learning models is compared with models developed through logistic regression (LR). The study was carried out on computed tomography images of 393 Bulgarian adults (169 males and 224 females). The three-dimensional coordinates of 47 landmarks were acquired and used for calculation of the cranial measurements. A total of 64 measurements (linear distances, angles, triangle areas and heights) and 22 indices were calculated. Two datasets were assembled including the linear measurements only and all measurements and index, respectively. An additional third dataset comprising all possible interlandmark distances between the landmarks was constructed. Two machine learning algorithms—SVM and ANN and a traditional statistical analysis LR—were applied to generate models for sex estimation. In addition, two advanced attribute selection techniques (Weka BestFirst and Weka GeneticSearch) were used. The classification accuracy of the models was evaluated by means of 10 × 10-fold cross-validation procedure. All three methods achieved accuracy results higher than 95%. The best accuracy (96.1 ± 0.5%) was obtained by SVM and it was statistically significantly higher than the best results achieved by ANN and LR. SVM and ANN reached higher accuracy by training on the full datasets than the selection datasets, except for the sample described by the interlandmark distances, where the reduction of attributes by the GeneticSearch algorithm improved the accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Scheuer L (2002) Application of osteology to forensic medicine. Clin Anat 15:297–312

    Article  Google Scholar 

  2. Dedouit F, Savall F, Mokrane F-Z, Rousseau H, Crubézy E, Rougé D, Telmon N (2014) Virtual anthropology and forensic identification using multidetector CT. Br J Radiol 87:20130468

    Article  CAS  Google Scholar 

  3. Iscan MY, Steyn M (2013) The human skeleton in forensic medicine, 3rd edn. Charles C Thomas Publisher, Springfield

    Google Scholar 

  4. Inoue M, Inoue T, Fushimi Y, Okada K (1992) Sex determination by discriminant function analysis of lateral cranial form. Forensic Sci Int 57:109–117. https://doi.org/10.1016/0379-0738(92)90003-f

    Article  CAS  PubMed  Google Scholar 

  5. Hrdlicka A (1939) Practical anthropometry. The Wistar Institute of Anatomy and Biology, Philadelphia

    Google Scholar 

  6. Krogman WM (1962) The human skeleton in forensic medicine. Charles C. Thomas, Springfield

    Google Scholar 

  7. Bass WM (1995) Human osteology: a laboratory and field manual of the human skeleton, 4th edn. Archaeological Society, Missouri

    Google Scholar 

  8. Spradley MK, Jantz RL (2011) Sex estimation in forensic anthropology: skull versus postcranial elements. J Forensic Sci 56:289–296. https://doi.org/10.1111/j.1556-4029.2010.01635.x

    Article  PubMed  Google Scholar 

  9. Jantz RL, Ousley SD (2020) Sexual dimorphism variation in Fordisc samples. In: Klales AR (ed) Sex estimation of the human skeleton: history, methods, and emerging techniques. Elsevier Academic Press, Cambridge, pp 185–200. https://doi.org/10.1016/B978-0-12-815767-1.00012-2

  10. Jantz R, Mahfouz M, Shirley NR, Abdel Fatah E (2013) Improving sex estimation from crania using 3-dimensional CT scans. U.S. Department of Justice, 1–71

  11. Rösing FW, Graw M, Marre B et al (2007) Recommendations for the forensic diagnosis of sex and age from skeletons. HOMO 58:75–89

    Article  Google Scholar 

  12. Santos F, Guyomarc’h P, Bruzek J (2014) Statistical sex determination from craniometrics: comparison of linear discriminant analysis, logistic regression, and support vector machines. Forensic Sci Int 245:204.e1–204.e8. https://doi.org/10.1016/j.forsciint.2014.10.010

    Article  Google Scholar 

  13. McQueen RJ, Holmes G, Hunt L (1998) User satisfaction with machine learning as a data analysis method in agricultural research. N Z J Agric Res 41:577–584

    Article  Google Scholar 

  14. Valdes G, Chan MF, Lim SB, Scheuermann R, Deasy JO, Solberg TD (2017) IMRT QA using machine learning: a multi-institutional validation. J Appl Clin Med Phys 18:279–284

    Article  Google Scholar 

  15. Magoulas GD, Prentza A (2001) Machine learning in medical applications. In: Paliouras G, Karkaletsis V, Spyropoulos CD (eds) Machine learning and its applications, ACAI 1999, lecture notes in computer science, 2049. Springer, Berlin, Heidelberg, pp 300–307. https://doi.org/10.1007/3-540-44673-7_19

    Chapter  Google Scholar 

  16. Kording KP, Benjamin A, Farhoodi R, Glaser JI (2018) The roles of machine learning in biomedical science. In: Frontiers of engineering: reports on leading-edge engineering from the 2017 symposium. National Academies Press, Washington, pp 61–72

    Google Scholar 

  17. Toneva D, Nikolova S, Agre G, Zlatareva D, Hadjidekov V, Lazarov N (2020) Data mining for sex estimation based on cranial measurements. Forensic Sci Int 315:110441. https://doi.org/10.1016/j.forsciint.2020.110441

    Article  PubMed  Google Scholar 

  18. Musilová B, Dupej J, Velemínská J, Chaumoitre K, Bruzek J (2016) Exocranial surfaces for sex assessment of the human cranium. Forensic Sci Int 269:70–77

    Article  Google Scholar 

  19. Čechová M, Dupej J, Brůžek J, Bejdová Š, Horák M, Velemínská J (2019) Sex estimation using external morphology of the frontal bone and frontal sinuses in a contemporary Czech population. Int J Legal Med 133:1285–1294. https://doi.org/10.1007/s00414-019-02063-8

    Article  PubMed  Google Scholar 

  20. Yang W, Zhou M, Zhang P, Geng G, Liu X, Zhang H (2020) Skull sex estimation based on wavelet transform and Fourier transform. Biomed Res Int 2020:8608209–8608210. https://doi.org/10.1155/2020/8608209

    Article  PubMed  PubMed Central  Google Scholar 

  21. Arigbabu OA, Liao IY, Abdullah N, Noor MHM (2018) Novel group variable selection for salient skull region selection and sex determination. In: Ren J, Hussain A, Zheng J, Liu C-L, Luo B, Zhao H, Zhao X (eds) Advances in brain inspired cognitive systems: BICS 2018. Springer International Publishing, Cham, pp 248–259. https://doi.org/10.1007/978-3-030-00563-4_24

  22. Du Jardin P, Ponsaillé J, Alunni-Perret V, Quatrehomme G (2009) A comparison between neural network and other metric methods to determine sex from the upper femur in a modern French population. Forensic Sci Int 192:127.e1–127.e6. https://doi.org/10.1016/j.forsciint.2009.07.014

    Article  Google Scholar 

  23. Mahfouz M, Badawi A, Merkl B, Abdel Fatah EE, Pritchard E, Kesler K, Moore M, Jantz R, Jantz L (2007) Patella sex determination by 3D statistical shape models and nonlinear classifiers. Forensic Sci Int 173:161–170. https://doi.org/10.1016/j.forsciint.2007.02.024

    Article  PubMed  Google Scholar 

  24. Navega D, Vicente R, Vieira DN, Ross AH, Cunha E (2014) Sex estimation from the tarsal bones in a Portuguese sample: a machine learning approach. Int J Legal Med 129:651–659. https://doi.org/10.1007/s00414-014-1070-5

    Article  PubMed  Google Scholar 

  25. Yang W, Liu X, Wang K, Hu J, Geng G, Feng J (2019) Sex determination of three-dimensional skull based on improved backpropagation neural network. Comput Math Methods Med 2019:9163547–9163548. https://doi.org/10.1155/2019/9163547

    Article  PubMed  PubMed Central  Google Scholar 

  26. Bewes J, Low A, Morphett A, Pate F, Henneberg M (2019) Artificial intelligence for sex determination of skeletal remains: application of a deep learning artificial neural network to human skulls. J Forensic Legal Med 62:40–43. https://doi.org/10.1016/j.jflm.2019.01.004

    Article  Google Scholar 

  27. Cignoni P, Callieri M, Corsini M, Dellepiane M, Ganovelli F, Ranzuglia G (2008) MeshLab: an open-source mesh processing tool. In: Scarano V, de Chiara R, Erra U (eds) Sixth eurographics Italian chapter conference. Eurographics Association, Salerno, pp 129–136

    Google Scholar 

  28. Hammer Ø, Harper DAT, Ryan PD (2001) PAST: paleontological statistics software package for education and data analysis. Palaeontol Electron 4:9–18

    Google Scholar 

  29. Franklin D, Cardini A, Flavel A, Kuliukas A (2013) Estimation of sex from cranial measurements in a Western Australian population. Forensic Sci Int 229:158e1–158e8. https://doi.org/10.1016/j.forsciint.2013.03.00

    Article  Google Scholar 

  30. Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20:273–297

    Google Scholar 

  31. Demšar J, Curk T, Erjavec A, Gorup Č, Hočevar T, Milutinovič M, Možina M, Polajnar M, Toplak M, Starič A, Stajdohar M, Umek L, Žagar L, Žbontar J, Žitnik M, Zupan B (2013) Orange: data mining toolbox in Python. JMLR. 14:2349–2353

    Google Scholar 

  32. Witten IH, Frank E, Hall MA, Pal CJ (2017) Data mining: practical machine learning tools and techniques (Morgan Kaufmann series in data management systems), 4th edn. Morgan Kaufmann Publishers, San Francisco

  33. Mitchell T (1997) Machine learning. McGraw-Hill Science/Engineering/Math, New York

    Google Scholar 

  34. Witten IH, Frank E, Hall MA (2011) Data mining: practical machine learning tools and techniques. Morgan Kaufmann Publ, Burlington

    Google Scholar 

  35. Hall MA (1998) Correlation-based feature subset selection for machine learning, PhD Thesis, University of Waikato, Hamilton

  36. Molinaro AM, Simon R, Pfeiffer RM (2005) Prediction error estimation: a comparison of resampling methods. Bioinformatics 21:3301–3307. https://doi.org/10.1093/bioinformatics/bti499

    Article  CAS  PubMed  Google Scholar 

  37. Kim J-H (2009) Estimating classification error rate: repeated cross-validation, repeated hold-out and bootstrap. Comput Stat Data Anal 53:3735–3745

    Article  Google Scholar 

  38. Han J, Kamber M, Pei J (2012) Data mining concepts and techniques, 3rd edn. Morgan Kaufmann Publishers, Waltham

    Google Scholar 

  39. Klales AR, Ousley SD, Passalacqua NV (2020) Statistical approaches to sex estimation. In: Klales AR (ed) Sex estimation of the human skeleton: history, methods, and emerging techniques. Elsevier Academic Press, Cambridge, pp 203–217. https://doi.org/10.1016/B978-0-12-815767-1.00013-4

  40. Abdel Fatah EE, Shirley NR, Jantz RL, Mahfouz MR (2014) Improving sex estimation from crania using a novel three-dimensional quantitative method. J Forensic Sci 59:590–600. https://doi.org/10.1111/1556-4029.12379

    Article  PubMed  Google Scholar 

  41. Giles E, Elliot O (1963) Sex determination by discriminant function analysis of crania. Am J Phys Anthropol 21:53–68

    Article  CAS  Google Scholar 

  42. Steyn M, Iscan MY (1998) Sexual dimorphism in the crania and mandibles of south African whites. Forensic Sci Int 98:9–16. https://doi.org/10.1016/s0379-0738(98)00120-0

    Article  CAS  PubMed  Google Scholar 

  43. Dayal MR, Spocter MA, Bidmos MA (2008) An assessment of sex using the skull of black south Africans by discriminant function analysis. HOMO 59:209–221. https://doi.org/10.1016/j.jchb.2007.01.001

    Article  CAS  PubMed  Google Scholar 

  44. Ogawa Y, Imaizumi K, Miyasaka S, Yoshino M (2013) Discriminant functions for sex estimation of modern Japanese skulls. J Forensic Legal Med 20:234–238. https://doi.org/10.1016/j.jflm.2012.09.023

    Article  Google Scholar 

  45. Ekizoglu O, Hocaoglu E, Inci E, Can IO, Solmaz D, Aksoy S, Buran CF, Sayin I (2016) Assessment of sex in a modern Turkish population using cranial anthropometric parameters. Legal Med 21:45–52. https://doi.org/10.1016/j.legalmed.2016.06.001

    Article  PubMed  Google Scholar 

  46. Zaafrane M, Ben KM, Naccache I, Ezzedine E, Savall F, Telmon N, Mnif N, Hamdoun M (2017) Sex determination of a Tunisian population by CT scan analysis of the skull. Int J Legal Med 132:853–862. https://doi.org/10.1007/s00414-017-1688-1

    Article  PubMed  Google Scholar 

  47. Franklin D, Cardini A, Flavel A, Kuliukas A (2012) The application of traditional and geometric morphometric analyses for forensic quantification of sexual dimorphism: preliminary investigations in a Western Australian population. Int J Legal Med 26:549–558

    Article  Google Scholar 

  48. Dillon A (2014) Cranial sexual dimorphism and the population specificity of anthropological standards. Master Thesis, University of Western Australia

  49. Marinescu M, Panaitescu V, Rosu M, Maru N, Punga (2014) A sexual dimorphism of crania in a Romanian population: discriminant function analysis approach for sex estimation. Rom J Leg Med 22:21–26. https://doi.org/10.4323/rjlm.2014.21

    Article  Google Scholar 

  50. Ibrahim A, Alias A, Nor FM, Swarhib M, Bakar AN, Das S (2017) Study of sexual dimorphism of Malaysian crania: an important step in identification of the skeletal remains. Anat Cell Biol 50:86–92. https://doi.org/10.5115/acb.2017.50.2.86

    Article  PubMed  PubMed Central  Google Scholar 

  51. Toneva D, Nikolova S, Zlatareva D, Hadjidekov V, Lazarov N (2019) Sex estimation by mastoid triangle using 3D models. HOMO 70:63–73. https://doi.org/10.1127/homo/2019/1010

    Article  PubMed  Google Scholar 

  52. Gao H, Geng G, Yang W (2018) Sex determination of 3D skull based on a novel unsupervised learning method. Comput Math Methods Med 2018:4567267. https://doi.org/10.1155/2018/456726

    Article  PubMed  PubMed Central  Google Scholar 

  53. Yang W, Reziwanguli X, Xu J, Wang P, Hu J, Liu X (2018) Sex determination of skull based on fuzzy decision tree. In: Proceedings of the 4th Workshop on Advanced Research and Technology in Industry (WARTIA 2018), Advances in Engineering Research, vol 173, pp 14–20. https://doi.org/10.2991/wartia-18.2018.4

  54. Nikolova S, Toneva D, Agre G, Lazarov N (2020) Data mining for peculiarities in the configuration of neurocranium when the metopic suture persists. Anthropol Anz 77:89–107. https://doi.org/10.1127/anthranz/2019/1051

    Article  PubMed  Google Scholar 

  55. Kranioti EF, İşcan MY, Michalodimitrakis M (2008) Craniometric analysis of the modern Cretan population. Forensic Sci Int 180:110.e1–110.e5. https://doi.org/10.1016/j.forsciint.2008.06.018

    Article  Google Scholar 

  56. Kimmerle EH, Ross A, Slice DE (2008) Sexual dimorphism in America: geometric morphometric analysis of the craniofacial region. J Forensic Sci 53:54–57

    Article  Google Scholar 

  57. Green H, Curnoe D (2009) Sexual dimorphism in southeast Asian crania: a geometric morphometric approach. HOMO 60:517–534. https://doi.org/10.1016/j.jchb.2009.09.001

    Article  PubMed  Google Scholar 

  58. Bigoni L, Velemínská J, Brůžek J (2010) Three-dimensional geometric morphometric analysis of cranio-facial sexual dimorphism in a Central European sample of known sex. HOMO 61:16–32. https://doi.org/10.1016/j.jchb.2009.09.004

    Article  CAS  PubMed  Google Scholar 

  59. Bejdová Š, Dupej J, Krajíček V, Velemínská J, Velemínský P (2018) Stability of upper face sexual dimorphism in central European populations (Czech Republic) during the modern age. Int J Legal Med 132:321–330. https://doi.org/10.1007/s00414-017-1625-3

    Article  PubMed  Google Scholar 

  60. Chovalopoulou ME, Bertsatos A (2018) Exploring the shape variation of the human cranium. A geometric morphometrics study on a modern Greek population sample. In: Rissech C, Lloveras L, Nadal J, Fullola JM (eds) Geometric morphometrics. Trends in biology, paleobiology and archaeology. SERP-UB, Barcelona, pp 25–39

  61. Gonzalez PN, Bernal V, Perez SI (2009) Analysis of sexual dimorphism of craniofacial traits using geometric morphometric techniques. Int J Osteoarchaeol 21:82–91. https://doi.org/10.1002/oa.1109

    Article  Google Scholar 

  62. Franklin D, Freedman L, Milne N (2005) Sexual dimorphism and discriminant function sexing in indigenous South African crania. HOMO 55:213–228. https://doi.org/10.1016/j.jchb.2004.08.001

    Article  CAS  PubMed  Google Scholar 

  63. Saini V, Srivastava R, Rai RK, Shamal SN, Singh TB, Tripathi SK (2011) An osteometric study of northern Indian populations for sexual dimorphism in craniofacial region. J Forensic Sci 56:700–705. https://doi.org/10.1111/j.1556-4029.2011.01707.x

    Article  PubMed  Google Scholar 

  64. Chovalopoulou ME, Bertsatos A, Manolis SK (2017) Landmark based sex discrimination on the crania of archaeological Greek populations. A comparative study based on the cranial sexual dimorphism of a modern Greek population. Mediter Archaeol Archaeom 17:37–46

    Google Scholar 

  65. Verhoff MA, Ramsthaler F, Krähahn J, Deml U, Gille RJ, Grabherr S, Thali M, Kreutz K (2008) Digital forensic osteology—possibilities in cooperation with the Virtopsy® project. Forensic Sci Int 174:152–156. https://doi.org/10.1016/j.forsciint.2007.03.017

    Article  PubMed  Google Scholar 

  66. Franklin D, Cardini A, Flavel A, Kuliukas A, Marks MK, Hart R, O’Higgins P (2013) Concordance of traditional osteometric and volume-rendered MSCT interlandmark cranial measurements. Int J Legal Med 27:505–520. https://doi.org/10.1007/s00414-012-0772-9

    Article  Google Scholar 

  67. Stull KE, Tise ML, Ali Z, Fowler DR (2014) Accuracy and reliability of measurements obtained from computed tomography 3D volume rendered images. Forensic Sci Int 238:133–140. https://doi.org/10.1016/j.forsciint.2014.03.005

    Article  PubMed  Google Scholar 

  68. Toneva D, Nikolova S, Georgiev I (2017) Accuracy of linear measurements on polygonal models of dry mandibles generated from industrial CT data. Acta Morphol Anthropol 24:55–62

    Google Scholar 

  69. Park HK, Chung JW, Kho HS (2006) Use of hand-held laser scanning in the assessment of craniometry. Forensic Sci Int 160:200–206

    Article  Google Scholar 

  70. Richard AH, Parks CL, Monson KL (2014) Accuracy of standard craniometric measurements using multiple data formats. Forensic Sci Int 242:177–185

    Article  Google Scholar 

  71. Toneva D, Nikolova S, Georgiev I (2016) Reliability and accuracy of angular measurements on laser scanning created 3D models of dry skulls. J Anthropol 2016:6218659

    Article  Google Scholar 

  72. Toneva D, Nikolova S, Georgiev I, Tchorbadjieff A (2017) Accuracy of linear craniometric measurements obtained from laser scanning created 3D models of dry skulls. In: Georgiev K, Todorov M, Georgiev I (eds) Advanced computing in industrial mathematics, vol 681. Springer, Cham, pp 215–229

  73. Bertsatos A, Chovalopoulou M-E, Brůžek J, Bejdová Š (2020) Advanced procedures for skull sex estimation using sexually dimorphic morphometric features. Int J Legal Med 134:1927–1937. https://doi.org/10.1007/s00414-020-02334-9

    Article  PubMed  Google Scholar 

  74. Keen J (1950) A study of differences between male and female skulls. Am J Phys Anthropol 8:65–80

    Article  CAS  Google Scholar 

  75. Sierp I, Henneberg M (2015) The difficulty of sexing skeletons from unknown populations. J Anthropol 2015:908535–908513. https://doi.org/10.1155/2015/908535

    Article  Google Scholar 

  76. Kotěrová A, Velemínská J, Dupej J, Brzobohatá H, Pilný A, Brůžek (2017) Disregarding population specificity: its influence on the sex assessment methods from the tibia. Int J Legal Med 131:251–261. https://doi.org/10.1007/s00414-016-1413-5

    Article  PubMed  Google Scholar 

  77. Isçan MY, Yoshino M, Kato S (1995) Sexual dimorphism in modem Japanese crania. Am J Hum Biol 7:459–464

    Article  Google Scholar 

  78. Langley NR, Jantz RL (2020) Secular change. In: Klales AR (ed) Sex estimation of the human skeleton: history, methods, and emerging techniques. Elsevier Academic Press, Cambridge, pp 295–306. https://doi.org/10.1016/B978-0-12-815767-1.00018-3

Download references

Acknowledgments

This work was supported by the Bulgarian National Science Fund [Grant numbers DN01/15-20.12.2016 and DN11/9-15.12.2017].

Funding

This study was funded by the Bulgarian National Science Fund (Grant numbers DN01/15-20.12.2016 and DN11/9-15.12.2017).

Author information

Authors and Affiliations

  1. Department of Anthropology and Anatomy, Institute of Experimental Morphology, Pathology and Anthropology with Museum, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 25, 1113, Sofia, Bulgaria

    Diana Toneva & Silviya Nikolova

  2. Department of Linguistic Modelling and Knowledge Processing, Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Gennady Agre

  3. Department of Diagnostic Imaging, Medical University of Sofia, 1431, Sofia, Bulgaria

    Dora Zlatareva & Vassil Hadjidekov

  4. Department of Anatomy and Histology, Medical University of Sofia, 1431, Sofia, Bulgaria

    Nikolai Lazarov

  5. Department of Synaptic Signaling and Communications, Institute of Neurobiology, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Nikolai Lazarov

Authors
  1. Diana Toneva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Silviya Nikolova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gennady Agre
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dora Zlatareva
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Vassil Hadjidekov
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Nikolai Lazarov
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Diana H. Toneva: Conceptualization, methodology, formal analysis, investigation, validation, data curation, visualization, writing—original draft, project administration, and funding acquisition

Silviya Y. Nikolova: Conceptualization, methodology, investigation, validation, writing—review and editing, project administration, and funding acquisition

Gennady P. Agre: Formal analysis, methodology, data curation, writing—review and editing

Dora K. Zlatareva: Resources, writing—review and editing

Vassil G. Hadjidekov: Resources, writing—review and editing

Nikolai E. Lazarov: Writing—review and editing

Corresponding author

Correspondence to Diana Toneva.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethics approval

This study was performed in line with the principles of the Declaration of Helsinki. Approval was granted by the Human Research Ethics Committee at the Institute of Experimental Morphology, Pathology and Anthropology with Museum, Bulgarian Academy of Sciences.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

ESM 1

(DOCX 14 kb)

ESM 2

(DOCX 37 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Toneva, D., Nikolova, S., Agre, G. et al. Machine learning approaches for sex estimation using cranial measurements. Int J Legal Med 135, 951–966 (2021). https://doi.org/10.1007/s00414-020-02460-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00414-020-02460-4

Keywords

Search

Navigation