Analysis of Bayesian Hyperparameter Optimization Results in Deep Neural Networks for Wide-Angle Camera Geometric Characterization
DOI:
https://doi.org/10.1590/jatm.v18.1410Keywords:
Optuna, Deep learning, Computer vision and image-based navigationAbstract
This paper addresses the challenge of geometric camera characterization, a crucial process in various applications such as computer vision, aerial photogrammetry, remote sensing, and robotics. Traditional calibration methods rely on calibration targets or manually defined geometric structures, which limit automation and adaptability, especially in uncontrolled environments. To overcome these limitations, we propose an innovative approach based on deep learning, capable of estimating the camera’s intrinsic parameters directly from a single image. The developed method integrates the Optuna hyperparameter optimizer, which utilizes Bayesian optimization to enhance model accuracy while reducing computational cost and training time. The application of this approach accelerates the search for optimal configurations for neural networks, ensuring an efficient balance between performance and architectural complexity. Experimental results demonstrate a significant improvement in model accuracy, with mean absolute errors and standard deviations in distortion rates at the hundredth-order magnitude level and focal length determination below 6 mm. Compared to the model without the integrated optimizer, there was an over 95% gain in reducing Mean Squared Error (MSE) and an 82% reduction in the standard deviation. This research significantly contributes to the enhancement of autonomous navigation and image-based positioning systems, providing a scalable and automated alternative to conventional modeling techniques (SDE).
References
Akiba T, Sano S, Yanase T, Ohta T, Koyama M (2019) Optuna: A next-generation hyperparameter optimization framework. Paper presented Proceedings of the 25th ACM Sigkdd International Conference on Knowledge Discovery & Data Mining, 2623–2631.
Alemán-Flores M, Alvarez L, Gomez L, Santana-Cedrés D (2014) Automatic lens distortion correction using one-parameter division models. Image Process On Lin 4:327-343. https://doi.org/10.5201/ipol.2014.106
Badrloo S, Varshosaz M, Pirasteh S, Li J (2022) Image-based obstacle detection methods for the safe navigation of unmanned vehicles: A review. Remote Sens 14(15):3824. https://doi.org/10.3390/rs14153824
Balcan MF, Nguyen AT, Sharma D (2025) Sample complexity of data-driven tuning of model hyperparameters in neural networks with structured parameter dependent dual function. arXiv preprint arXiv:2501.13734. https://doi.org/10.48550/arXiv.1704.04861
Barreto JP, Araujo H (2005) Geometric properties of central catadioptric line images and their application in calibration. IEEE Trans Pattern Anal Mach Intell 27(8):1327-1333. https://doi.org/10.1109/TPAMI.2005.163
Bogdan O, Eckstein V, Rameau F, Bazin JC (2018) Deepcalib: A deep learning approach for automatic intrinsic calibration of wide field-of-view cameras. Paper presented Proceedings of the 15th ACM Siggraph European Conference on Visual Media Production, 1-10.
Bukhari F, Dailey MN (2013) Automatic radial distortion estimation from a single image. J Math Imaging Vis 45:31-45. https://doi.org/10.1007/s10851-012-0342-2
Caron G (2023) Models and calibration methods. In: Vasseur P, Morbidi F, editors. Omnidirectional Vision: From Theory to Applications. London: Wiley. http://doi.org/10.1002/9781394256440.ch2
Carroll R, Agrawala M, Agarwala A (2009) Optimizing content-preserving projections for wide-angle images. ACM Transactions on Graphics 28(3):43. https://doi.org/10.1145/1576246.1531349
Chang A, Dai A, Funkhouser T, Halber M, Niebner M, Savva M, Song S, Zeng A, Zhang Y (2017) Matterport3D: Learning from RGB-D Data in Indoor Environments. Paper presented 2017 International Conference on 3D Vision (3DV), Qingdao, China, 667-676. https://doi.org/10.1109/3DV.2017.00081
Chao CH, Hsu PL, Lee HY, Wang YCF (2020) Self-supervised deep learning for fisheye image rectification. Paper presented ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2248-2252. https://doi.org/10.1109/ICASSP40776.2020.9054191
Chicco D, Warrens MJ, Jurman G (2021) The coefficient of determination r-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation. PeerJ Comput Sci 7:623. https://doi.org/10.7717/peerj-cs.623
Cramariuc A, Petrov A, Suri R, Mittal M, Siegwart R, Cadena C (2020) Learning camera miscalibration detection. Paper presented 2020 IEEE International Conference on Robotics and Automation (ICRA), 4997-5003.
Do T, Miksik O, Degol J, Park HS, Sinha SN (2022) Learning to detect scene landmarks for camera localization. Paper presented Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 11132-11142. https://doi.org/10.1109/CVPR52688.2022.01085
Duane CB (1971) Close-range camera calibration. Photogramm Eng 37(8):855-866.
Fan B, Dai Y, He M (2021) SUNet: symmetric undistortion network for rolling shutter correction. Paper presented Proceedings of the IEEE/CVF International Conference on Computer Vision, 2021, 4541-4550.
Faugeras OD, Luong QT, Maybank SJ (1992) Camera self-calibration: Theory and experiments. In: Computer Vision—ECCV’92: Second European Conference on Computer Vision. Santa Margherita Ligure, Italy, 321-334. https://doi.org/10.1007/3-540-55426-2_37
Feng H, Wang W, Deng J, Zhou W, Li L, Li H (2023) SimFIR: A simple framework for fisheye image rectification with selfsupervised representation learning. Paper presented Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 12418-12427. https://doi.org/10.1109/ICCV51070.2023.01141
Fischer P, Dosovitskiy A, Brox T (2015) Image orientation estimation with convolutional networks. Paper presented German Conference on Pattern Recognition, 368-378. https://doi.org/10.1007/978-3-319-24947-6_30
Franceschi L, Donini M, Perrone V, Klein A, Archambeau C, Seeger M, Pontil M, Frasconi P (2024) Hyperparameter optimization in machine learning. arXiv preprint arXiv:2410.22854. https://doi.org/10.48550/arXiv.2410.22854
Fraser CS (1997) Digital camera self-calibration. ISPRS J Photogramm Remote Sens 52(4):149-159. https://doi.org/10.1016/S0924-2716(97)00005-1
Gasparini S, Sturm P, Barreto J (2009) Plane-based calibration of central catadioptric cameras. Paper presented 2009 IEEE 12th International Conference on Computer Vision, 1195-1202. https://doi.org/10.1109/ICCV.2009.5459336
Habib A, Lari Z, Kwak E, Al-Durgham K (2013) Automated detection, localization, and identification of signalized targets and their impact on digital camera calibration. Rev Bras Cartogr 65(4):785-803. https://doi.org/10.14393/rbcv65n4-43860
Hartley RI (1994) Self-calibration from multiple views with a rotating camera. Paper presented Computer Vision—ECCV’94: Third European Conference on Computer Vision. Stockholm, Sweden, 471-478.
He K, Zhang X, Ren S, Sun J (2016) Deep Residual Learning for Image Recognition. arXiv preprint arXiv:1512.03385 https://doi.org/10.48550/arXiv.1512.03385
Hold-Geoffroy Y, Sunkavalli K, Eisenmann J, Fisher M, Gambaretto E, Hadap S, Lalonde JF (2018) A perceptual measure for deep single image câmera calibration. Paper presented Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2354-2363. https://doi.org/10.1109/tpami.2023.3269641
Howard AG, Zhu M, Chen B, Kalenichenko D, Wang W, Weyand T, Andreetto M, Adam H (2017) MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications. arXiv preprint arXiv:1704.04861. https://doi.org/10.48550/arXiv.1704.04861
Huai J, Shao Y, Jozkow G, Wang B, Chen D, He Y, Yilmaz A (2024) Geometric wide-angle camera calibration: A review and comparative study. Sensors 24(20):6595. https://doi.org/10.3390/s24206595
Jau YY, Zhu R, Su H, Chandraker M (2020) Deep keypoint-based camera pose estimation with geometric constraints. Paper presented Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 4950-4957. https://doi.org/10.1109/IROS45743.2020.9341229
Kendall A, Grimes M, Cipolla R (2015) Posenet: A convolutional network for real-time 6-DOF camera relocalization. Paper presented Proceedings of the IEEE International Conference on Computer Vision, 2938-2946. https://doi.org/10.1109/ICCV.2015.336
Lai Y (2024) Application and effectiveness evaluation of Bayesian optimization algorithm in hyperparameter tuning of machine learning models. Paper presented 2024 International Conference on Power, Electrical Engineering, Electronics and Control (PEEEC), 351-355. https://doi.org/10.1109/PEEEC63877.2024.00070
Li Z, Chen J, Baltsavias E (2008) Advances in photogrammetry, remote sensing and spatial information sciences: 2008 ISPRS Congress Book. London: CRC Press.
Liao K, Lin C, Zhao Y (2021) A deep ordinal distortion estimation approach for distortion rectification. IEEE Trans Image Process 30:3362-3375. https://doi.org/10.1109/tip.2021.3061283
Liao K, Lin C, Zhao Y, Gabbouj M (2019b) DR-GAN: Automatic radial distortion rectification using conditional gan in realtime. IEEE Trans Circ Syst Video Technol 30(3):725-733. https://doi.org/10.1109/TCSVT.2019.2897984
Liao K, Lin C, Zhao Y, Xu M (2020) Model-free distortion rectification framework bridged by distortion distribution map. IEEE Trans Image Process 29:3707-3718. https://doi.org/10.1109/TIP.2020.2964523
Mahmood AS, Al-Nuaimi BT, Abdul-Wahab A (2024) Multi-cameras calibration system based deep learning approach and beyond: A survey. Bilad Alrafidain J Eng Sci Technol 3(2):93-126. https://doi.org/10.56990/bajest/2024.030209
Marcato Junior J, Tommaselli AMG (2013) Exterior orientation of CBERS-2B imagery using multi-feature control and orbital data. ISPRS J Photogramm Remote Sens 79:219-225. https://doi.org/10.1016/j.isprsjprs.2013.02.018
Marcu DC, Grava C (2021) The impact of activation functions on training and performance of a deep neural network. Paper presented 2021 16th International Conference on Engineering of Modern Electric Systems (EMES), 1-4. https://doi.org/10.1109/EMES52337.2021.9484108
Mathworks (2023) Camera Calibration Tutorial. https://www.mathworks.com/help/vision/camera calibration.html
Maybank SJ, Faugeras OD (1992) A theory of self-calibration of a moving camera. Int J Comput Vision 8(2):123-151. https://doi.org/10.1007/BF00127171
Mei C, Rives P (2007) Single view point omnidirectional camera calibration from planar grids. Paper presented Proceedings 2007 IEEE International Conference on Robotics and Automation, 3945-3950. https://doi.org/10.1109/ROBOT.2007.364084
Nogueira FC, Freitas MJS, Castro RM, Shiguemori EH (2025) Evaluation of deep neural networks for camera geometric characterization in image-based navigation. Rev Foco 18(4):e8197. https://doi.org/10.54751/revistafoco.v18n4-036
OpenCV (2023) Camera Calibration Tutorial. https://docs.opencv.org/4.x/dc/dbb/tutorial_py_calibration.html
Pak A, Reichel S, Burke J (2022) Machine-learning-inspired workflow for camera calibration. Sensors 22(18):6804. https://doi.org/10.3390/s22186804
Samii A, Měch R, Lin Z (2015) Data-driven automatic cropping using semantic composition search. Comput Graph Forum 34:141-151. https://doi.org/10.1111/cgf.12465
Shah S, Aggarwal J (1994) A simple calibration procedure for fish-eye (high distortion) lens camera. Paper presented Proceedings of the 1994 IEEE International Conference on Robotics and Automation, 3422-3427.
Shekhar S, Bansode A, Salim A (2021) A comparative study of hyper-parameter optimization tools. Paper presented 2021 IEEE Asia-Pacific Conference on Computer Science and Data Engineering (CSDE), 1-6.
Shi Y, Tong X, Wen J, Zhao H, Ying X, Zha H (2020) Position-aware and symmetry enhanced gan for radial distortion correction. Paper presented 2020 25th International Conference on Pattern Recognition (ICPR), 1701-1708.
Song Z, Peng L, Hu J, Yao D, Zhang Y (2024) A re-calibration method for object detection with multi-modal alignment bias in autonomous driving. arXiv preprint arXiv:2405.16848. https://arxiv.org/html/2405.16848v1
Szegedy C, Vanhoucke V, Ioffe S, Shlens J, Wojna Z (2015) Rethinking the Inception Architecture for Computer Vision. arXiv preprint arXiv:1512.00567. https://doi.org/10.48550/arXiv.1512.00567
Tan Z, Zhang X, Teng S, Wang L, Gao F (2024) A review of deep learning-based LiDAR and camera extrinsic calibration. Sensors 24(12):3878. https://doi.org/10.3390/s24123878
Vujović ŽD (2021) Classification model evaluation metrics. Int J Adv Comput Sci Appl 12(6):599-606. https://doi.org/10.14569/IJACSA.2021.0120670
Wang R, Nabney I, Golbabaee M (2024) Efficient hyperparameter importance assessment for CNNs. arXiv preprint arXiv:2410.08920. https://doi.org/10.48550/arXiv.2410.08920
Watanabe S (2023) Tree-structured parzen estimator: Understanding its algorithm components and their roles for better empirical performance. arXiv preprint arXiv:2304.11127, 2023. https://doi.org/10.48550/arXiv.2304.11127
Weng J, Cohen P, Herniou M, et al. (1992) Camera calibration with distortion models and accuracy evaluation. IEEE Trans Pattern Anal Mach Intell 14(10):965-980. https://doi.org/10.1109/34.159901
Workman S, Greenwell C, Zhai M, Baltenberger R, Jacobs N (2015) Deepfocal: A method for direct focal length estimation. Paper presented 2015 IEEE International Conference on Image Processing (ICIP), 1369-1373.
Xian W, Li Z, Fisher M, Eisenmann J, Shechtman E, Snavely N (2019) UprightNet: Geometry-aware camera orientation estimation from single images. Paper presented Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 9974-9983.
Yang J, An W, Yan C, Zhao P, Huang J (2021) Context-aware domain adaptation in semantic segmentation. Paper presented Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, 514-524.
Yang L, Shami, A (2020) On hyperparameter optimization of machine learning algorithms: Theory and practice. Neurocomputing 415:295-316. https://doi.org/10.1016/j.neucom.2020.07.061
Yang S, Lin C, Liao K, Zhang C, Zhao Y (2021) Progressively complementary network for fisheye image rectification using appearance flow. Paper presented Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 6348-6357.
Zhang C, Rameau F, Kim J, Argaw DM, Bazin JC, Kweon IS (2020) DeepPTZ: Deep self-calibration for PTZ cameras. Paper presented Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), 1041-1049.
Zhang Z (1999) Flexible camera calibration by viewing a plane from unknown orientations. Paper presented Proceedings of the 7th IEEE International Conference on Computer Vision 1:666-673. https://doi.org/10.1109/ICCV.1999.791289
Zhang Z (2000) A flexible new technique for camera calibration. IEEE Trans Pattern Anal Mach Intell 22(11):1330-1334. https://doi.org/10.1109/34.888718
Zhao K, Lin C, Liao K, Yang S, Zhao Y (2021) Revisiting radial distortion rectification in polar-coordinates: A new and efficient learning perspective. IEEE Trans Circ Syst Video Tech 32(6):3552-3560. https://doi.org/10.1109/TCSVT.2021.3119293
Zhuang B, Tran QH, Ji P, Cheong LF, Chandraker M (2019) Learning structure-and-motion-aware rolling shutter correction. Paper presented Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 4551-4560.
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Copyright (c) 2026 Fabiano da Cruz Nogueira, Luan Orion de Oliveira Baráuna Ferreira, Ruy Morgado de Castro, Elcio Hideiti Shiguemori
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