{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T16:31:48Z","timestamp":1780763508886,"version":"3.54.1"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,29]],"date-time":"2025-11-29T00:00:00Z","timestamp":1764374400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper introduces a novel approach to handwritten digit recognition based on directional flood simulation and topological feature extraction. While traditional pixel-based methods often struggle with noise, partial occlusion, and limited data, our method leverages the structural integrity of digits by simulating water flow from image boundaries using a modified breadth-first search (BFS) algorithm. The resulting flooded regions capture stroke directionality, spatial segmentation, and closed-area characteristics, forming a compact and interpretable feature vector. Additional parameters such as inner cavities, perimeter estimation, and normalized stroke density enhance classification robustness. For efficient prediction, we employ the Annoy approximate nearest neighbors algorithm using ensemble-based tree partitioning. The proposed method achieves high accuracy on the MNIST (95.9%) and USPS (93.0%) datasets, demonstrating resilience to rotation, noise, and limited training data. This topology-driven strategy enables accurate digit classification with reduced dimensionality and improved generalization.<\/jats:p>","DOI":"10.3390\/e27121218","type":"journal-article","created":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T09:34:37Z","timestamp":1764581677000},"page":"1218","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Handwritten Digit Recognition with Flood Simulation and Topological Feature Extraction"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7255-6951","authenticated-orcid":false,"given":"Rafa\u0142","family":"Brociek","sequence":"first","affiliation":[{"name":"Department of Artificial Intelligence Modelling, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4971-5360","authenticated-orcid":false,"given":"Mariusz","family":"Pleszczy\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jakub","family":"B\u0142aszczyk","sequence":"additional","affiliation":[{"name":"Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-2512-8380","authenticated-orcid":false,"given":"Maciej","family":"Czaicki","sequence":"additional","affiliation":[{"name":"Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3336-5853","authenticated-orcid":false,"given":"Christian","family":"Napoli","sequence":"additional","affiliation":[{"name":"Department of Computer, Control, and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185 Roma, Italy"},{"name":"Department of Artificial Intelligence, Czestochowa University of Technology, Dabrowskiego 69, 42-201 Czestochowa, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Morooka, E.V., Omae, Y., H\u00e4m\u00e4l\u00e4inen, M., and Takahashi, H. (2025). Benchmarking Point Cloud Feature Extraction with Smooth Overlap of Atomic Positions (SOAP): A Pixel-Wise Approach for MNIST Handwritten Data. AppliedMath, 5.","DOI":"10.20944\/preprints202502.2316.v1"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mukhamediev, R.I. (2024). State-of-the-Art Results with the Fashion-MNIST Dataset. Mathematics, 12.","DOI":"10.3390\/math12203174"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ranga, D., Prajapat, S., Akhtar, Z., Kumar, P., and Vasilakos, A.V. (2024). Hybrid quantum\u2013classical neural networks for efficient MNIST binary image classification. Mathematics, 12.","DOI":"10.3390\/math12233684"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wen, Y., Ke, W., and Sheng, H. (2024). Improved Localization and Recognition of Handwritten Digits on MNIST Dataset with ConvGRU. Appl. Sci., 15.","DOI":"10.3390\/app15010238"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ghimire, D., Kil, D., and Kim, S.h. (2022). A survey on efficient convolutional neural networks and hardware acceleration. Electronics, 11.","DOI":"10.3390\/electronics11060945"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Nemavhola, A., Chibaya, C., and Viriri, S. (2025). A Systematic Review of CNN Architectures, Databases, Performance Metrics, and Applications in Face Recognition. Information, 16.","DOI":"10.3390\/info16020107"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1007\/s42979-022-01359-8","article-title":"A Critical Scrutiny of ConvNets (CNNs) and Its Applications","volume":"3","author":"Shanmuganathan","year":"2022","journal-title":"SN Comput. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s10462-024-10721-6","article-title":"A review of convolutional neural networks in computer vision","volume":"57","author":"Zhao","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Brociek, R., and Pleszczy\u0144ski, M. (2024). Differential Transform Method and Neural Network for Solving Variational Calculus Problems. Mathematics, 12.","DOI":"10.3390\/math12142182"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Brociek, R., and Pleszczy\u0144ski, M. (2024). Differential Transform Method (DTM) and Physics-Informed Neural Networks (PINNs) in Solving Integral\u2013Algebraic Equation Systems. Symmetry, 16.","DOI":"10.3390\/sym16121619"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1109\/5.726791","article-title":"Gradient-Based Learning Applied to Document Recognition","volume":"86","author":"Lecun","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/978-3-030-17798-0_47","article-title":"MNIST dataset classification utilizing k-NN classifier with modified sliding-window metric","volume":"Volume 21","author":"Grover","year":"2020","journal-title":"Advances in Computer Vision: Proceedings of the 2019 Computer Vision Conference (CVC)"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/34.993558","article-title":"Shape matching and object recognition using shape contexts","volume":"24","author":"Belongie","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Makkar, T., Kumar, Y., Dubey, A.K., Rocha, A., and Goyal, A. (2017, January 21\u201323). Analogizing time complexity of KNN and CNN in recognizing handwritten digits. Proceedings of the 2017 Fourth International Conference on Image Information Processing (ICIIP), Shimla, India.","DOI":"10.1109\/ICIIP.2017.8313707"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"220","DOI":"10.15837\/ijccc.2013.2.303","article-title":"Improving offline handwritten digit recognition using concavity-based features","volume":"8","author":"Karic","year":"2013","journal-title":"Int. J. Comput. Commun. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1023\/A:1012454411458","article-title":"Training Invariant Support Vector Machines","volume":"46","author":"Decoste","year":"2003","journal-title":"Mach. Learn."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Baldominos, A., Saez, Y., and Isasi, P. (2019). A Survey of Handwritten Character Recognition with MNIST and EMNIST. Appl. Sci., 9.","DOI":"10.3390\/app9153169"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Chang, Y.J., Lin, Y.L., and Pai, P.F. (2025). Support Vector Machines with Hyperparameter Optimization Frameworks for Classifying Mobile Phone Prices in Multi-Class. Electronics, 14.","DOI":"10.3390\/electronics14112173"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"107221","DOI":"10.1016\/j.knosys.2021.107221","article-title":"Evolving data-adaptive support vector machines for binary classification","volume":"227","author":"Dudzik","year":"2021","journal-title":"Knowl.-Based Syst."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Liu, C., and Jia, G. (2019). Industrial big data and computational sustainability: Multi-method comparison driven by high-dimensional data for improving reliability and sustainability of complex systems. Sustainability, 11.","DOI":"10.3390\/su11174557"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1007\/s10462-017-9611-1","article-title":"Selecting training sets for support vector machines: A review","volume":"52","author":"Nalepa","year":"2019","journal-title":"Artif. Intell. Rev."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"012108","DOI":"10.1088\/1757-899X\/1022\/1\/012108","article-title":"Handwritten Digits Identification Using Mnist Database via Machine Learning Models","volume":"1022","author":"Gope","year":"2021","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_23","unstructured":"Wan, L., Zeiler, M., Zhang, S., Le Cun, Y., and Fergus, R. (2013, January 17\u201319). Regularization of Neural Networks using DropConnect. Proceedings of the 30th International Conference on Machine Learning, Atlanta, GA, USA."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Larasati, R., and KeungLam, H. (2017, January 8\u201310). Handwritten digits recognition using ensemble neural networks and ensemble decision tree. Proceedings of the 2017 International Conference on Smart Cities, Automation and Intelligent Computing Systems (ICON-SONICS), Yogyakarta, Indonesia.","DOI":"10.1109\/ICON-SONICS.2017.8267829"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2753941","DOI":"10.1155\/2023\/2753941","article-title":"A novel technique for handwritten digit recognition using deep learning","volume":"2023","author":"Ahmed","year":"2023","journal-title":"J. Sens."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Im, S.K., and Chan, K.H. (2025). Enhanced Localisation and Handwritten Digit Recognition Using ConvCARU. Appl. Sci., 15.","DOI":"10.3390\/app15126772"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"29","DOI":"10.17509\/ijost.v3i1.10795","article-title":"Handwritten digit recognition using machine learning algorithms","volume":"3","author":"Shamim","year":"2018","journal-title":"Indones. J. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Shi, H., Zhu, Z., Zhang, C., Feng, X., and Wang, Y. (2025). Multimodal Handwritten Exam Text Recognition Based on Deep Learning. Appl. Sci., 15.","DOI":"10.3390\/app15168881"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"9","DOI":"10.35940\/ijitee.L1002.10812S319","article-title":"Comparison and performance evaluation of boundary fill and flood fill algorithm","volume":"8","author":"Kumar","year":"2020","journal-title":"Int. J. Innov. Technol. Explor. Eng"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"503","DOI":"10.7763\/IJCTE.2013.V5.738","article-title":"Quantitative comparison of flood fill and modified flood fill algorithms","volume":"5","author":"Law","year":"2013","journal-title":"Int. J. Comput. Theory Eng."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Nosal, E.M. (2008, January 14\u201317). Flood-fill algorithms used for passive acoustic detection and tracking. Proceedings of the 2008 IEEE New Trends for Environmental Monitoring Using Passive Systems, Hyeres, France.","DOI":"10.1109\/PASSIVE.2008.4786975"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Qian, H., Sun, H., Cai, Z., Gao, F., Ni, T., and Yuan, Y. (2024). RC Bridge Concrete Surface Cracks and Bug-Holes Detection Using Smartphone Images Based on Flood-Filling Noise Reduction Algorithm. Appl. Sci., 14.","DOI":"10.3390\/app142110014"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kramer, O. (2013). K-Nearest Neighbors. Dimensionality Reduction with Unsupervised Nearest Neighbors, Springer.","DOI":"10.1007\/978-3-642-38652-7"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1007\/978-981-97-4393-3_22","article-title":"A Study of PyTorch-Based Algorithms for Handwritten Digit Recognition","volume":"Volume 2146","author":"Li","year":"2024","journal-title":"International Symposium on Intelligence Computation and Applications"},{"key":"ref_35","first-page":"850","article-title":"Semi-supervised classification algorithm based on L1-Norm and KNN superposition graph","volume":"29","author":"Zhang","year":"2016","journal-title":"Pattern Recognit. Artif. Intell. 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