Lightweight Distance Estimation from Single Images without Camera Intrinsics

PDF (1067KB), PP.346-362

Views: 0 Downloads: 0

Author(s)

Jaroslaw Bernacki 1

1. Department of Computer Science and Systems Engineering, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, Wrocław, 50-370, Poland

* Corresponding author.

DOI: https://doi.org/10.5815/ijwmt.2026.04.20

Received: 28 May 2026 / Revised: 18 Jun. 2026 / Accepted: 8 Jul. 2026 / Published: 8 Aug. 2026

Index Terms

Digital forensics, camera pinhole model, image processing, privacy

Abstract

In this paper, we address the problem of estimating the distance between a camera and a photographed object using minimal prior information. Specifically, the goal is to obtain distance estimates without access to intrinsic camera parameters such as focal length, sensor size, or lens distortion coefficients. We propose three simple heuristic methods, which can be viewed as lightweight variants of the classical camera pinhole model (CPH), but do not require calibration. Instead, they rely only on the approximate real height of a known object in the scene. The methods were validated on a representative dataset of images captured with several modern cameras and smartphones, using known object dimensions as ground truth. Their performance was compared against CPH using error metrics such as mean absolute error (MAE), mean absolute percentage error (MAPE), root mean squared error (RMSE), mean signed error (MSD), coefficient of determination R2), and supported by statistical testing (Shapiro–Wilk, ANOVA, Kruskal–Wallis). The analysis confirmed that, while less precise than fully calibrated approaches, the proposed heuristics achieve consistent and reliable distance estimates under minimal assumptions. These methods are particularly suited for lightweight applications and devices with fixed focal lengths, such as smartphones.

Cite This Paper

Jarosław Bernacki, "Lightweight Distance Estimation from Single Images without Camera Intrinsics", International Journal of Wireless and Microwave Technologies(IJWMT), Vol.16, No.4, pp. 346-362, 2026. DOI:10.5815/ijwmt.2026.04.20

Reference

[1]Mo Chen, Jessica Fridrich, Miroslav Goljan, and Jan Lukas. Determining image origin and integrity using sensor noise. IEEE Transactions on information forensics and security, 3(1):74–90, 2008. DOI: 10.1109/TIFS.2007.916285
[2]Miroslav Goljan. Digital camera identification from images–estimating false acceptance probability. In International workshop on digital watermarking, pages 454–468. Springer, 2008. DOI: 10.1007/978-3-642-04438-0_38
[3]Chiara Galdi, Michele Nappi, and Jean-Luc Dugelay. Multimodal authentication on smartphones: Combining iris and sensor recognition for a double check of user identity. Pattern Recognition Letters, 82:144–153, 2016. An insight on eye biometrics. DOI: 10.1016/j.patrec.2015.09.009
[4]Chiara Galdi, Michele Nappi, and Jean-Luc Dugelay. Combining hardwaremetry and biometry for human authentication via smartphones. In Vittorio Murino and Enrico Puppo, editors, Image Analysis and Processing — ICIAP 2015, pages 406–416, Cham, 2015. Springer International Publishing. DOI: 10.1007/978-3-319-23234-8_38
[5]Ugur Baysal and Gokhan Sengul. Single camera photogrammetry system for eeg electrode identification and localization. Annals of biomedical engineering, 38:1539–1547, 2010. DOI: 10.1007/s10439-010-9950-4
[6]Jan Lukas, Jessica Fridrich, and Miroslav Goljan. Digital camera identification from sensor pattern noise. IEEE Transactions on Information Forensics and Security, 1(2):205–214, 2006. DOI: 10.1109/TIFS.2006.873602
[7]Nitin Khanna, Aravind K Mikkilineni, George TC Chiu, Jan P Allebach, and Edward J Delp. Scanner identification using sensor pattern noise. In Security, steganography, and watermarking of multimedia contents IX, volume 6505, pages 563–573. SPIE, 2007. DOI: 10.1117/12.705837
[8]Arafat Al-Dhaqm, Richard Adeyemi Ikuesan, Victor R Kebande, Shukor Abd Razak, George Grispos, Kim- Kwang Raymond Choo, Bander Ali Saleh Al-Rimy, and Abdulrahman A Alsewari. Digital forensics subdomains: the state of the art and future directions. IEEE Access, 9:152476–152502, 2021. DOI: 10.1109/ACCESS.2021.3124262
[9]Fran Casino, Thomas K Dasaklis, Georgios P Spathoulas, Marios Anagnostopoulos, Amrita Ghosal, Istvan Borocz, Agusti Solanas, Mauro Conti, and Constantinos Patsakis. Research trends, challenges, and emerging topics in digital forensics: A review of reviews. IEEE Access, 10:25464–25493, 2022. DOI: 10.1109/ACCESS.2022.3154059
[10]Jean-Paul A Yaacoub, Hassan N Noura, Ola Salman, and Ali Chehab. Advanced digital forensics and anti-digital forensics for iot systems: Techniques, limitations and recommendations. Internet of Things, 19:100544, 2022. DOI: 10.1016/j.iot.2022.100544
[11]Christian Brauer-Burchardt, Matthias Heinze, Christoph Munkelt, Peter Kuhmstedt, Gunther Notni, and IOF Fraunhofer. Distance dependent lens distortion variation in 3d measuring systems using fringe projection. In BMVC, page 327, 2006. DOI: 10.5244/C.20.34
[12]C Brown Duane. Close-range camera calibration. Photogramm. Eng, 37(8):855–866, 1971.
[13]Arthur A Magill. Variation in distortion with magnification. Journal of the Optical Society of America, 45(3):148–152, 1955. DOI: 10.1364/JOSA.45.000148
[14]John G Fryer and Duane C Brown. Lens distortion for close-range photogrammetry. Photogrammetric engineering and remote sensing, International Archives of Photogrammetry and Remote Sensing Volume: 26(5):30-37, 1986.
[15]Richard Hartley and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003. DOI: 10.1017/CBO9780511811685
[16]David A Forsyth and Jean Ponce. Computer vision: a modern approach. Pearson Education, Prentice Hall professional technical reference, ISBN-10: ‎ 0273764144, 2012.
[17]Juho Kannala and Sami S Brandt. A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses. IEEE transactions on pattern analysis and machine intelligence, 28(8):1335–1340, 2006. DOI: 10.1109/TPAMI.2006.153
[18]Zhengyou Zhang. A flexible new technique for camera calibration. IEEE Transactions on pattern analysis and machine intelligence, 22(11):1330–1334, 2000. DOI: 10.1109/34.888718
[19]Peter Sturm. Pinhole camera model. In Computer Vision: A Reference Guide, pages 983–986. Springer, 2021. DOI: 10.1007/978-3-030-63416-2_472
[20]Nicholas J Wade and Stanley Finger. The eye as an optical instrument: from camera obscura to helmholtz’s perspective. Perception, 30(10):1157–1177, 2001. DOI: 10.1068/p3210
[21]Krzysztof Murawski. Method of measuring the distance to an object based on one shot obtained from a motionless camera with a fixed-focus lens. Acta Physica Polonica A, 127(6):1591–1595, 2015. DOI: 10.12693/APhysPolA.127.1591
[22]Carles Matabosch, David Fofi, Joaquim Salvi, and Josep Forest. Registration of moving surfaces by means of oneshot laser projection. In Pattern Recognition and Image Analysis: Second Iberian Conference, IbPRIA 2005, Estoril, Portugal, June 7-9, 2005, Proceedings, Part I 2, pages 145–152. Springer, 2005. DOI: 10.1007/11492429_18
[23]Daniil A Loktev and Alexey A Loktev. Estimation of measurement of distance to the object by analyzing the blur of its image series. In 2016 International Siberian Conference on Control and Communications (SIBCON), pages 1–6. IEEE, 2016. DOI: 10.1109/SIBCON.2016.7491683
[24]Masahiro Kawakita, Keigo Iizuka, Tahito Aida, Hiroshi Kikuchi, Hideo Fujikake, Jun Yonai, and Kuniharu Takizawa. Axi-vision camera (real-time distance-mapping camera). Applied Optics, 39(22):3931–3939, 2000. DOI: 10.1364/AO.39.003931
[25]Rajesh Kannan Megalingam, Vignesh Shriram, Bommu Likhith, Gangireddy Rajesh, and Sriharsha Ghanta. Monocular distance estimation using pinhole camera approximation to avoid vehicle crash and back-over accidents. In 2016 10th international conference on intelligent systems and control (ISCO), pages 1–5. IEEE, 2016. DOI: 10.1109/ISCO.2016.7727017
[26]Scott Leorna, Todd Brinkman, and Timothy Fullman. Estimating animal size or distance in camera trap images: Photogrammetry using the pinhole camera model. Methods in Ecology and Evolution, 13(8):1707–1718, 2022. DOI: 10.1111/2041-210X.13880Digital Object Identifier (DOI)
[27]Dany Eka Saputra, Aloysius Shendy Mulyana Senjaya, Joshua Ivander, and Alex William Chandra. Experiment on distance measurement using single camera. In 2021 4th International Conference on Information and Communications Technology (ICOIACT), pages 80–85. IEEE, 2021. DOI: 10.1109/ICOIACT53268.2021.9564010
[28]Ka Seng Chou, Teng Lai Wong, Kei Long Wong, Lu Shen, Davide Aguiari, Rita Tse, Su-Kit Tang, and Giovanni Pau. A lightweight robust distance estimation method for navigation aiding in unsupervised environment using monocular camera. Applied Sciences, 13(19):11038, 2023. DOI: 10.3390/app131911038
[29]Fatih Gokce, Gokturk Ucoluk, Erol Sahin, and Sinan Kalkan. Vision-based detection and distance estimation of micro unmanned aerial vehicles. Sensors, 15(9):23805–23846, 2015. DOI: 10.3390/s150923805
[30]Gafencu Natanael, Cristian Zet, and Cristian Fosalau. Estimating the distance to an object based on image processing. In 2018 International Conference and Exposition on Electrical and Power Engineering (EPE), pages 0211–0216. IEEE, 2018. DOI: 10.1109/ICEPE.2018.8559642
[31]Clement Godard, Oisin Mac Aodha, Michael Firman, and Gabriel Brostow. Digging into self-supervised monocular depth estimation, 2019. DOI: 10.48550/arXiv.1806.01260
[32]Rene Ranftl, Katrin Lasinger, David Hafner, Konrad Schindler, and Vladlen Koltun. Towards robust monocular depth estimation: Mixing datasets for zero-shot cross-dataset transfer, 2020. DOI: 10.48550/arXiv.1907.01341
[33]Hong Liang, Zizhen Ma, and Qian Zhang. Self-supervised object distance estimation using a monocular camera. Sensors, 22(8), 2022. DOI: 10.3390/s22082936
[34]Armin Masoumian, David G.F. Marei, Saddam Abdulwahab, Julian Cristiano, Domenec Puig, and Hatem A. Rashwan. Absolute Distance Prediction Based on Deep Learning Object Detection and Monocular Depth Estimation Models. IOS Press, October 2021. DOI: 10.3233/FAIA210151
[35]Rene Ranftl, Alexey Bochkovskiy, and Vladlen Koltun. Vision transformers for dense prediction, 2021. DOI: 10.1109/ICCV48922.2021.01196
[36]Rafael Hidalgo, Aparna S. Varde, Jesse Parron, and Weitian Wang. Incorporating commonsense knowledge to enhance robot perception. IEEE Transactions on Automation Science and Engineering, 22:15488–15501, 2025. DOI: 10.1109/TASE.2025.3565191
[37]Jan Pauls, Max Zimmer, Una M. Kelly, Martin Schwartz, Sassan Saatchi, Philippe Ciais, Sebastian Pokutta, Martin Brandt, and Fabian Gieseke. Estimating canopy height at scale, 2024. Proceedings of the 41st International Conference on Machine Learning, PMLR 235:39972-39988, 2024. DOI: 10.48550/arXiv.2406.01076
[38]Aparna Varde, Elke Rundensteiner, Giti Javidi, Ehsan Sheybani, and Jianyu Liang. Learning the relative importance of features in image data. In 2007 IEEE 23rd International Conference on Data Engineering Workshop, pages 237–244, 2007. DOI: 10.1109/ICDEW.2007.4400998
[39]Hongxiang Jiang, Jihao Yin, Qixiong Wang, Jiaqi Feng, and Guo Chen. Eaglevision: Object-level attribute multimodal llm for remote sensing, 2025. DOI: 10.48550/arXiv.2503.23330
[40]Blessing Austin-Gabriel, Cristian Noriega Monsalve, and Aparna S. Varde. Power plant detection for energy estimation using gis with remote sensing, cnn & vision transformers, 2024. DOI: 10.48550/arXiv.2412.04986
[41]Tim Havers, Lukas Masur, Eduard Isenmann, Stephan Geisler, Christoph Zinner, Billy Sperlich, and Peter Duking. Reproducibility and quality of hypertrophy-related training plans generated by gpt-4 and google gemini as evaluated by coaching experts. Biology of Sport, 42(2):289–329, 2025. DOI: 10.5114/biolsport.2025.145911
[42]Zeying Gong, Rong Li, Tianshuai Hu, Ronghe Qiu, Lingdong Kong, Lingfeng Zhang, Yiyi Ding, Leying Zhang, and Junwei Liang. Stairway to success: Zero-shot floor-aware object-goal navigation via llm-driven coarse-to-fine exploration, 2025. DOI: 10.48550/arXiv.2505.23019
[43]Jarosław Bernacki and Rafał Scherer. Imagine dataset: Digital camera identification image benchmarking dataset. In Proceedings of the 20th International Conference on Security and Cryptography – SECRYPT, pages 799–804. INSTICC, SciTePress, 2023. DOI: 10.5220/0012130300003555
[44]Samuel Sanford Shapiro and Martin B Wilk. An analysis of variance test for normality (complete samples). Biometrika, 52(3/4):591–611, 1965. DOI: 10.1093/biomet/52.3-4.591
[45]WH Kruskal and WA Wallis. Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, pages 583–621, 1952. DOI: 10.2307/2280779
[46]William H. Kruskal. A Nonparametric test for the Several Sample Problem. The Annals of Mathematical Statistics, 23(4):525 – 540, 1952. DOI: 10.1214/aoms/1177729332