e-ISSN 2231-8526
ISSN 0128-7680
Nurul Hafiza Rahamathulla and Md Yushalify Misro
Pertanika Journal of Science & Technology, Volume 31, Issue 4, July 2023
DOI: https://doi.org/10.47836/pjst.31.4.10
Keywords: Best-fit curve, continuity Quintic Bézier curve, craniofacial reconstruction, genetic algorithm
Published on: 3 July 2023
A best-fit curve is required to reconstruct craniofacial fracture to ensure the preciseness of the reconstructed contour. A genetic algorithm (GA) is applied to get the best-fit curve in reconstructing the fractured part. This method provides a fast decision in obtaining suitable sets of control points to interpolate both boundary regions to form a reconstructed part without any try-and-error approach that requires altering the control points several times. The optimised sets of control points with different degrees of continuity are used to develop the reconstructed part using the quintic Bézier curve to generate a smooth curve. The best-fit curvature value of the quintic Bézier curve for each degree of continuity is compared, and the curve with the lowest absolute error of curvature is chosen as the inner and outer parts of the craniofacial fracture reconstruction.
Abdel-Aziz, H. S., Zanaty, E. A., Ali, H. A., & Saad, M. K. (2021). Generating Bézier curves for medical image reconstruction. Results in Physics, 23, Article 103996. https://doi.org/10.1016/j.rinp.2021.103996
Adi, D. I. S., Shamsuddin, S. M., & Ali, A. (2009). Particle swarm optimization for NURBS curve fitting. In 2009 Sixth International Conference on Computer Graphics, Imaging and Visualization (pp. 259-263). IEEE Publishing. https://doi.org/10.1109/CGIV.2009.64
Adnan, S. B. Z., Ariffin, A. A. M., & Misro, M. Y. (2020). Curve fitting using quintic trigonometric Bézier curve. In AIP Conference Proceedings (Vol. 2266, No. 1, Article 040009). AIP Publishing LLC. https://doi.org/10.1063/5.0018099
Ali, N. S. S., Ramli, A., & Rahman, N. A. (2020), October. Searching an optimum parameter value for radial basis function by bootstrap error analysis for 2D craniofacial reconstruction. In AIP Conference Proceedings (Vol. 2266, No. 1, Article 050008). AIP Publishing LLC. https://doi.org/10.1063/5.0018115
Ammad, M., & Misro, M. Y. (2020). Construction of local shape adjustable surfaces using quintic trigonometric Bézier curve. Symmetry, 12(8), Article 1205. https://doi.org/10.3390/sym12081205
Ammad, M., Misro, M. Y., & Ramli, A. (2022). A novel generalized trigonometric Bézier curve: Properties, continuity conditions and applications to the curve modeling. Mathematics and Computers in Simulation, 194, 744-763. https://doi.org/10.1016/j.matcom.2021.12.011
Amorim, P. H., Moraes, T. F., Silva, J. V., Pedrini, H., & Ruben, R. B. (2020). Reconstruction of panoramic dental images through Bézier function optimization. Frontiers in Bioengineering and Biotechnology, 8, 794. https://doi.org/10.3389/fbioe.2020.00794
BiBi, S., Misro, M. Y., Abbas, M., Majeed, A., & Nazir, T. (2021). G3 Shape adjustable GHT-Bézier developable surfaces and their applications. Mathematics, 9(19), Article 2350. https://doi.org/10.3390/math9192350
Carr, J. (2014). An introduction to genetic algorithms. Senior Project, 1(40), 1-40.
Chen, B., Gao, Q., Song, H., & Xu, M. (2017) Retrospective study of experience of craniofacial reconstruction. International Wound Journal, 14(2), 399-407. https://doi.org/10.1111/iwj.12613
Eliou, N., & Kaliabetsos, G. (2014). A new, simple and accurate transition curve type, for use in road and railway alignment design. European Transport Research Review, 6, 171-179. https://doi.org/10.1007/s12544-013-0119-8
Ibrahim, M. F., Misro, M. Y., Ramli, A., & Ali, J. M. (2017). Maximum safe speed estimation using planar quintic Bézier curve with C2 continuity. In AIP Conference Proceedings (Vol. 1870, No. 1, Article 050006). AIP Publishing LLC. https://doi.org/10.1063/1.4995916
Lee, W. J., & Shin, D. H. (2020). Craniofacial reconstruction in mummy studies. In D. H. Shin & R. Bianucci (Eds.), The Handbook of Mummy Studies (pp. 1-14). Springer. https://doi.org/10.1007/978-981-15-1614-6_5-1
Loucera, C., Gálvez, A., & Iglesias, A. (2014). Simulated annealing algorithm for Bézier curve approximation. In 2014 International Conference on Cyberworlds (pp. 182-189). IEEE Publishing. https://doi.org/10.1109/CW.2014.33
Ma, Y., Pollick, F., & Hewitt, W. T. (2004). Using b-spline curves for hand recognition. In 17th International Conference on Pattern Recognition, 2004 (ICPR) (Vol. 3, pp. 274-277). IEEE Publishing. https://doi.org/10.1109/ICPR.2004.1334520
Majeed, A., Abbas, M., & Miura, K. T. (2022). A comparative study of different schemes based on Bézier-like functions with an application of craniofacial fractures reconstruction. Mathematics, 10(8), Article 1269. https://doi.org/10.3390/math10081269
Majeed, A., Abbas, M., Miura, K. T., Kamran, M., & Nazir, T. (2020). Surface modeling from 2D contours with an application to craniofacial fracture construction. Mathematics, 8(8), Article 1246. https://doi.org/10.3390/math8081246
Majeed, A., Piah, A. R. M., Gobithaasan, R. U., & Yahya, Z. R. (2015). Craniofacial reconstruction using rational cubic ball curves. PLOS One, 10(4), Article e0122854. https://doi.org/10.1371/journal.pone.0122854
Mansour, R. F., (2020). Evolutionary computing enriched ridge regression model for craniofacial reconstruction. Multimedia Tools and Applications, 79, 22065-22082. https://doi.org/10.1007/s11042-017-5015-0
Misro, M. Y., Ramli, A., & Ali, J. M. (2017). S-shaped and c-shaped transition curve using cubic trigonometric Bézier. In AIP Conference Proceedings (Vol. 1870, No. 1, Article 050005). AIP Publishing LLC. https://doi.org/10.1063/1.4995915
Misro, M. Y., Ramli, A., & Ali, J. M. (2018). Quintic trigonometric Bézier curve and its maximum speed estimation on highway designs. In AIP Conference Proceedings (Vol. 1974, No. 1, Article 020089). AIP Publishing LLC. https://doi.org/10.1063/1.5041620
Moiduddin, K., Mian, S. H., Elseufy, S. M., Abdo, B. M. A., Aboudaif, M. K., & Alkhalefah, H. (2022). Craniofacial reconstruction with personalized lightweight scaffold fabricated using electron-beam additive manufacturing. Metals, 12(4), Article 552. https://doi.org/10.3390/met12040552
Suputra, P. H., Sensusiati, A. D., Yuniarno, E. M., Purnomo, M. H., & Purnama, I. K. E. (2020). 3D Laplacian surface deformation for template fitting on craniofacial reconstruction. In Proceedings of the 8th International Conference on Computer and Communications Management (pp. 27-32). ACM Digital Library. https://doi.org/10.1145/3411174.3411175
Ueda, E. K., Tsuzuki, M. S. G., & Barari, A. (2018). Piecewise Bézier curve fitting of a point cloud boundary by simulated annealing. In 2018 13th IEEE International Conference on Industry Applications (INDUSCON) (pp. 1335-1340). IEEE Publishing. https://doi.org/10.1109/INDUSCON.2018.8627161
Zain, S. A. A. A. S. M., Misro, M. Y. & Miura, K. T. (2021). Generalized fractional Bézier curve with shape parameters. Mathematics, 9(17), Article 2141. https://doi.org/10.3390/math9172141
ISSN 0128-7680
e-ISSN 2231-8526