A Comparative of Two-Dimensional Statistical Moment Invariants Features in Formulating an Automated Probabilistic Machine Learning Identification Algorithm for Forensic Application


  • Zun Liang Chuan Centre for Mathematical Science, Universiti Malaysia Pahang, Lebuh Persiaran Tun Khalil Yaakob, 26300 Kuantan, Pahang, Malaysia
  • David Chong Teak Wei Ever AI Holdings Sdn Bhd, 12, Jalan Anggerik Aranda 31/170c, Kota Kemuning, 40460 Shah Alam, Selangor DE, Malaysia
  • Connie Lee Wai Yan Centre for Mathematical Science, Universiti Malaysia Pahang, Lebuh Persiaran Tun Khalil Yaakob, 26300 Kuantan, Pahang, Malaysia
  • Muhammad Fuad Ahmad Nasser Centre for Mathematical Science, Universiti Malaysia Pahang, Lebuh Persiaran Tun Khalil Yaakob, 26300 Kuantan, Pahang, Malaysia
  • Nor Azura Md Ghani cFaculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor DE, Malaysia
  • Abdul Aziz Jemain Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia
  • Choong-Yeun Liong Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia




Ballistics identification, automated, machine learning identification algorithm, statistical moment invariants


IBIS, ALIS, EVOFINDER, and CONDOR are the massive ballistics computerised technological machines that have typically been utilised in forensic laboratories to automatically locate similarities between images of cartridge cases and bullets. However, it imposed a long execution time and requires physical interpretation to consolidate the analysis results when employing these market-available technologies to accomplish ballistics matching tasks. Therefore, the principal objective of this study is to propose an improvised automated probabilistic machine learning identification algorithm by extracting the two-dimensional (2D) statistical moment invariants from the segmented region of interest (ROI) corresponding to the cartridge case and bullets images. To pursue this principal objective, several 2D statistical moment invariants have been compared and tested to determine the most suitable feature set applied in the proposed identification algorithm. The 2D statistical moment invariants employed include Orthogonal Legendre moments (OLM), Hu moments (HM), Tsirikolias-Mertzois moments (TMM), Pan-Keane moments (PKM), and Central Geometric moments (CGM). Moreover, the proposed identification algorithm is also tested in different scenarios, including based on the classification of strength association measurements between the extracted feature sets. The empirical results in this article revealed that the proposed identification algorithm applied with the CGM comprising the weak association classification yielded the best identification accuracy rates, which are >96.5% across all the sample sizes of the training set. These empirical results also conveyed that the superior proposed identification algorithm in this research could be developed as a mobile application for ballistics identification that can significantly reduce the time taken and conveniently perform the ballistics identification tasks.


Xin, L. -P., Zhou J., G. Rong. (2000). A cartridge identification system for firearms authentication. Proceedings of the 5th International Conference on Signal Processing, IEEE Press, Beijing, China, 1405-1408. https://doi.org/10.1109/icosp.2000.891807.

N. A. M. Ghani, C. -Y. Liong, A. A. Jemain. (2009). Extraction and selection of basic statistical features for forensic ballistic specimen identification. Sains Malaysiana, 38(2) 249-260.

N. A. M. Ghani, C. -Y. Liong, A. A. Jemain. (2009). Extraction and selection of geometric moment features for forensic ballistic specimen identification. Matematika, 25, 15-30. https://doi.org/10.11113/matematika.v25.n.256.

N. A. M. Ghani, C. -Y. Liong, A. A. Jemain. (2010). Analysis of geometric moments as features for firearm identification. Forensic Science International, 198(1-3), 143-149. https://doi.org/10.1016/j.forsciint.2010.02.011.

Z. L. Chuan, A. A. Jemain, C. -Y. Liong, N. A. M. Ghani, Effectiveness of cross-entropy and Tsallis entropy thresholding for automatic forensic ballistics identification system. Journal of Quality Measurement and Analysis, 9(1), (2013) 33-46.

Z. L. Chuan, A. A. Jemain, C. -Y. Liong, N. A. M. Ghani, L. K. Tan. (2017). A robust firearm identification algorithm of forensic ballistics specimens. Journal of Physics: Conference Series, 890, 012126. https://doi.org/10.1088/1742-6596/890/1/012126.

C. L. Smith, D. Li. (2008). Intelligent imaging of forensic ballistics specimens for ID. Proceedings of the 2008 Congress on Image and Signal Processing, IEEE Press, Sanya, China, 37-41. https://doi.org/10.1109/CISP.2008.760.

D. G. Li. (2003). Image processing for the positive identification of ballistics specimens. Proceedings of the 6th International Conference on Information Fusion, IEEE Press, Queensland, Australia, 1494-1498. https://doi.org/10.1109/ICIF.2003.177417.

J. Zhou, L. -P. Xin, D. -S. Gao, C. -S. Zhang, D. Zhang. (2001). Automated identification for firearms authentication. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, IEEE Press, Kauai, USA, 749-754. https://doi.org/10.1109/CVPR.2001.990551.

J. Leng, Z. Huang. (2012). On analysis of circle moments and texture features for cartridge images recognition. Expert Systems with Applications, 39(2), 2092-2101. https://doi.org/10.1016/j.eswa.2011.08.003.

S. B. A. Kamaruddin, N. A. M. Ghani, C. -Y. Liong, A. A. Jemain. (2012). Firearm classification using neural networks on ring of firing pin impression images. ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal, 1(3), 27-34. https://doi.org/10.14201/ADCAIJ20121312734.

Z. L. Chuan, N. A. M. Ghani, C. -Y. Liong, A. A. Jemain. (2013). Automatic anchor point detection approach for firearms firing pin impression. Sains Malaysiana, 42(9), 1339-1344.

Z. L. Chuan, C. -Y. Liong, A. A. Jemain, N. A. M. Ghani. (2014). An efficient automatic firearm identification system. AIP Conference Proceedings, 1602(1), 1185-1189. http://dx.doi.org/10.1063/1.4882634.

N. A. Razak, C. -Y. Liong, A. A. Jemain, N. A. M. Ghani, S. Zakaria, H. Sulaiman. (2017). Firing pin impression segmentation using Canny edge detection operator and Hough Transform. Journal of Telecommunication, Electronic and Computer Engineering (JTEC), 9(1) 23-26.

N. A. M. Ghani, C. -Y. Liong, A. A. Jemain. (2018). Neurocomputing approach for firearm identification. Pertanika Journal of Science & Technology, 26(1), 341-352.

R. C. Gonzalez, R. E. Woods. (1993). Digital image processing, 3rd edn. Pearson Prentice Hall.

K. Tsirikolias, B. G. Mertzios. (2017). Statistical pattern recognition using efficient two-dimensional moments with applications to character recognition. Pattern Recognition, 26(6), 877-882. https://doi.org/10.1016/0031-3203(93)90053-Y.

L. Moura, R. Kitney. (1991). A direct method for least-squares circle fitting. Computer Physics Communications, 64(1), 57-63. https://doi.org/10.1016/0010-4655(91)90049-Q.

J. Flusser, T. Suk, B. Zitová. (2009). Moments and moment invariants in pattern recognition. John Wiley and Sons.

C. -Y. Liong, N. A. M., Ghani, S. B. A. Kamaruddin, A. A. Jemain. (2012). Firearm classification based on numerical features of the firing pin impression. Procedia Computer Science, 13, 144-151. https://doi.org/10.1016/j.procs.2012.09.123.

R. A. Fisher. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2) 179-188. https://doi.org/10.1111/j.1469-1809.1936.tb02137.x.

Z. L. Chuan. (2014). Statistical firearm identification for forensic ballistics. Universiti Kebangsaan Malaysia. Unpublished Doctoral Thesis.

J. Canny. (1986). A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8, 6, 679-698. https://doi.org/10.1109/TPAMI.1986.4767851.

D. Marr, E. Hildreth. (1980). Theory of edge detection. Proceedings of the Royal Society B, 207(1167), 187-217. https://doi.org/10.1098/rspb.1980.0020.

C. -Y. Liong, N. A. M. Ghani, S. B. A. Kamaruddin, A. A. Jemain. (2020). Conceptual design of firearm identification mobile application (FIMA). AIP Conference Proceedings, 2266, 090014. https://doi.org/10.1063/5.0018445.

F. W. Smith, M. H. Wright. (1971). Automatic ship photo interpretation by the method of moments. IEEE Transactions on Computers, C-20(9), 1089-1095. https://doi.org/10.1109/T-C.1971.223408.

S. A. Dudani, K. J. Breeding, R. B. McGhee. (1977). Aircraft identification by moment invariants. IEEE Transactions on Computers, C-26(1), 39-46. https://doi.org/10.1109/TC.1977.5009272.

Y. C. Chim, A. A. Kassim, Y. Ibrahim. (1999). Character recognition using statistical moments. Image and Vision Computing, 17(3-4), 299-307. https://doi.org/10.1016/S0262-8856(98)00110-3.

C. -Y. Liong, N. A. M. Ghani, A. A. Jemain, C. Thompson. (2012). Momen ortogon Legendre sebagai suatu fitur untuk pengecaman kedudukan penumpang, Jurnal Teknologi, 48(1), 41-58. https://doi.org/10.11113/jt.v48.224.

P. Kaur, H. S. Pannu, A. K. Malhi. (2020). Comprehensive study of continuous orthogonal moments-a systematic review. ACM Computing Surveys, 52(4), 1-30. https://doi.org/10.1145/3331167,

C. Camacho-Bello, J. S. Rivera-Lopez. (2018). Some computational aspects of Tchebichef moments for higher orders. Pattern Recognition Letters, 112, 332-339. https://doi.org/10.1016/j.patrec.2018.08.020.

M. -K. Hu. (1962). Visual pattern recognition by moment invariants. IRE Transactions on Information Theory, 8(2), 179-187. https://doi.org/10.1109/TIT.1962.1057692.

F. Pan, M. Keane. (1994). A new set of moment invariants for handwritten numeral recognition. Proceedings of the 1st International Conference on Image Processing, IEEE Press, Texas, USA, 154-158. https://doi.org/10.1109/ICIP.1994.413294.

N. Otsu. (1979). A threshold selection method from gray-level histograms. IEEE Transactions on Systems, Man and Cybernetics, 9(1), 62-66. https://doi.org/10.1109/TSMC.1979.4310076.

D. Indra, T. Hasanuddin, R. Satra, N. R. Wibowo. (2018). Eggs detection using Otsu thresholding method. Proceedings of the 2nd East Indonesia Conference on Computer and Information Technology (EIConCIT), IEEE Press, Makassar, Indonesia, 10-13. https://doi.org/10.1109/EIConCIT.2018.8878517.

C. V. V. S. Srinivas, M. V. R. V. Prasad, M. Sirisha. (2020). Remote sensing image segmentation using OTSU algorithm. International Journal of Computer Application, 178(12), 46-50.

M. Sholihin, M. Arif, M. H. Alfansury, N. M. Yuzi, Sumijan. (2019). Identification of palm using Otsu method and mathematical morphology to open house doors. Jurnal KomtekInfo, 7(2), 101-109. https://doi.org/10.35134/komtekinfo.v7i2.70.

A. Albano. (1974). Representation of digitized contours in terms of conic arcs and straight-line segments, Computer Graphics and Image Processing, 3(1), 23-33. https://doi.org/10.1016/0146-664X(74)90008-2.