Intelligent handwriting assessment algorithm using the Catmull-Rom spline

The article is devoted to the development and application of an algorithm for analyzing graphomotor writing trajectories in digital educational systems using the Catmull-Rom spline. The problem of improving the accuracy and stability of processing user input received from touch devices (stylus or finger) in the context of digital writing learning is considered. The proposed method includes the stages of coordinate data collection, normalization, noise filtering, and trajectory smoothing. The Catmull-Roma spline is used to ensure the continuity of curves and preserve key motion features, which increases the accuracy of comparison with reference patterns.

The paper presents a computational algorithm that implements an automatic assessment of the quality of letter writing based on a number of parameters: curvature, angular deviations, speed stability and the number of strokes. The algorithm is integrated into a digital diagnostic system capable of generating detailed reports, identifying common errors, and offering personalized tasks. The developed solution can be used in intelligent learning platforms, biometric authentication systems, neuropsychological diagnostics and computer forensics.

The proposed approach demonstrates high adaptability to various input scenarios and provides the basis for building more complex machine learning systems focused on recognizing, analyzing, and generating handwritten text.

1. Al Kendi, W., Gechter, F., Heyberger, L., & Guyeux, C. (2024). Advancements and Challenges in Handwritten Text Recognition: A Comprehensive Survey. Journal of Imaging, 10(1), 18. https://doi.ore/10.3390/iimaging10010018

2. Amruth, A., Mohanty, M., Vimal, C., Ramanan, R., & Beena, B. (2024). Advanced Handwriting Recognition System for Handwritten Scripts With AutoCorrect Feature. 1-9. https://doi.org/10.1109/icccnt61001.2024.10724995

3. P.B., Likhitha, L.K., & Rajesh, D.S. (2021). Handwritten Digit Recognition Using Deep Learning. International Journal of Scientific Research in Science and Technology, 7(4), 153-158. https://doi.org/10.32628/CSEIT217439

4. Wehbi, M., Hamann, T., Barth, J., & Eskofier, B. M. (2021). Digitizing Handwriting with a Sensor Pen: A Writer-Independent Recognizer. https://doi.org/10.1109/ICFHR2020.2020.00061

5. Rane, D., Verma, P., & Lahiri, U. (2022). How Good is your Drawing? Quantifying Graphomotor Skill Using a Portable Platform (pp. 409-422). https://doi.org/10.1007/978-3-031-22131-6 31

6. Dinehart, L.H. (2014). Handwriting in early childhood education: Current research and future implications. Journal of Early Childhood Literacy, 15(1), 97-118. https://doi.org/10.1177/1468798414522825

7. Barker, J. (2022). Characteristics and Graphomotor Skills of Young Children’s Writing and Drawing on a Tablet Screen. 23(3), 273-296. https://doi.org/10.22154/jcle.23.3.12

8. Ceccacci, S., Taddei, A., Del Bianco, N., Giaconi, C., Forteza Forteza, D., & Moreno-Tallon, F. (2024). Preventing Dysgraphia: Early Observation Protocols and a Technological Framework for Monitoring and Enhancing Graphomotor Skills. Information, 15(12), 781. https://doi.org/10.3390/info15120781

9. Safarova, K., Mekyska, J., Urbanek, T., Galaz, Z., Mucha, J., Zvoncak, V., & Bednarova, J. (2022). Grafomotoricke dovednosti. https://doi.org/10.5817/cz.muni.m280-0257-2022

10. Kopnova, O.L., Aytymova, A.M., Abildinova, G., Safaraliev, B.S., Koleva, N.S., & Panova, M. (2024). Assessment of the level of formation of graphomotor skills of preschool and primary school students using graphic tablets. Sovremennye Naukoemkie Tehnologii, 1(5), 154-159. https://doi.org/10.17513/snt.40021

11. Devillaine, L., Lambert, R., Boutet, J., Aloui, S., Brault, V., Jolly, C., & Labyt, E. (2021). Analysis of Graphomotor Tests with Machine Learning Algorithms for an Early and Universal Pre-Diagnosis of Dysgraphia. Sensors, 21(21), 7026. https://doi.org/10.3390/S21217026

12. Tayebi Arasteh, S., Kalisz, A. Conversion Between Cubic Bezier Curves and Catmull-Rom Splines. SN COMPUT. SCI. 2, 398 (2021). https://doi.org/10.1007/s42979-021-00770-x

13. Li, J., & Chen, S. (2016). The Cubica-Catmull-Rom Spline. Mathematical and Computational Applications, 21(3), 33. https://doi.org/10.3390/mca21030033

14. Wu, T., Bai, B., & Wang, P. (2013). Parallel Catmull-Rom Spline Interpolation Algorithm for Image Zooming Based on CUDA. Applied Mathematics & Information Sciences, 7, 533-537. https://www.naturalspublishing.com/Article.asp?ArtcID=1048

15. Tony D. DeRose and Brian A. Barsky. 1988. Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines. ACM Trans. Graph. 7, 1 (Jan. 1988), 1-41. https://doi.org/10.1145/42188.42265

16. C. Kong, A. Luo, S. Wang, H. Li, A. Rocha, and A. Kot, “Pixel -inconsistency modeling for image manipulation localization,” IEEE Trans. Pattern Anal. and Mach. Intell., vol. 47, no. 6, pp. 4455-4472, 2025. https://arxiv.org/abs/2310.00234

17. C. Yu, X. Zhang, Y. Duan, S. Yan, Z. Wang, Y. Xiang, S. Ji, and W. Chen, “Diff-id: An explainable identity difference quantification framework for deepfake detection,” IEEE Trans. Dependable Secure Comput., pp. 1-18, 2024. https://arxiv.org/abs/2303.18174

18. Lyu, S., Pan, X. & Zhang, X. Exposing Region Splicing Forgeries with Blind Local Noise Estimation. Int J Comput Vis 110, 202-221 (2014). https://doi.org/10.1007/s11263-013-0688-y

19. Steve Marschner. Cornell CS4620 Fall 2020. CS 4620 Lecture 14. https://www.cs.cornell.edu/courses/cs4620/2020fa/slides/14splines.pdf

20. Li, Q., Gong, R., & Hase, K. (2024). A Comprehensive Objective Evaluation Method for Handwriting Assistive Devices Using a Tablet and Digital Pen for Individuals with Upper Limb Dysfunction. A p p lie d Sciences, 14(23), 11190. https://doi.org/10.3390/app142311190

21. Begum, N., Akash, M.A.H., Rahman, S., Shin, J., Islam, M.R., & Islam, M.E. (2021). User Authentication Based on Handwriting Analysis of Pen-Tablet Sensor Data Using Optimal Feature Selection Model. F u tu re In tern et, 13(9), 231. https://doi.org/10.3390/fi13090231

22. Rahim, M.A., Farid, F.A., Miah, A.S.M., Puza, A.K., Alam, M.N. et al. (2024). An Enhanced Hybrid Model Based on CNN and BiLSTM for Identifying Individuals via Handwriting Analysis. Computer Modeling in Engineering & Sciences, 140(2), 1689-1710. https://doi.org/10.32604/cmes.2024.048714

23. Mekyska, J. et al. (2023). Assessment of Developmental Dysgraphia Utilising a Display Tablet. In: Parziale, A., Diaz, M., Melo, F. (eds) Graphonomics in Human Body Movement. Bridging Research and Practice from Motor Control to Handwriting Analysis and Recognition. IGS 2023. Lecture Notes in Computer Science, vol 14285. Springer, Cham. https://doi.org/10.1007/978-3-031-45461-5 2