Abstract
Camera calibration is an avoidable process for computational vision applications, such as 3D reverse engineering, industrial robot calibration, optic-pattern recognition, simultaneous localization and mapping, autonomous visual-driving and photogrammetric vision. The camera calibration problem is too complex, nonlinear and multimodal. Traditional camera calibration methods using gradient-based optimization often trap to one of the many local solutions available. Accurate computation ability of traditional camera calibration methods is limited since they use gradient-based optimization methods. Since evolutionary computing algorithms can avoid local solutions of numerical problems, they have the potential to accurately compute the required camera calibration parameters for high-precision computational vision applications. In this paper, the camera calibration parameters are computed by using 11 evolutionary computing algorithms, i.e., WDE, ABC, PSO, COBIDE, DE, CS, GWO, TLBO, MVMO, FOA and LSHADE. In order to make unbiased evaluation of the camera calibration results provided by the related evolutionary computing algorithms, two gradient-based traditional camera calibration methods, i.e., Zhang and Bouguet, have been used in the conducted experiments in this paper. The camera calibration results of the related methods were used to model a 3D physical test scene by using Structure from Motion photogrammetry method. The reference data set of the related 3D physical scene has been captured by using a 3D terrestrial laser scanner. Statistical comparison of the camera calibration results exposed that WDE supplies statistically better results than other comparison algorithms.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Markov BN, Konov SG, Loginov AA (2012) Calibration of cameras of photogrammetric measuring systems with the use of a genetic solution search algorithm. Meas Tech 55(5):551–554
Westoby MJ, Brasington J, Glasser NF et al (2012) Structure-from-motion photogrammetry: a low-cost, effective tool for geoscience applications. Geomorphology 179:300–314
Qi W, Li, F, Zhenzhong L (2010). Review on camera calibration. In: IEEE Chinese conference in control and decision. An 11403827
Wang L, Wu F, Hu Z (2007) Multi-camera calibration with one-dimensional object under general motions. In: IEEE 11th international conference on computer vision, pp 1–7
Fuhr G, Jung CR (2017) Camera self-calibration based on nonlinear optimization and applications in surveillance systems. IEEE Trans Circuits Syst Video Technol 27(5):1132–1142
Weng J, Cohen P, Herniou M (1992) Camera calibration with distortion models and accuracy evaluation. IEEE Trans Pattern Anal 1992(10):965–980
Abdel-Aziz YI (1974) Photogrammetric potential of non metric cameras. Ph.D. thesis, Illinois University, Champaign
Li J, Liu Z (2018) Efficient camera self-calibration method for remote sensing photogrammetry. Opt Express 26(11):14213–14231
Li W, Bertin S, Friedrich H (2018) Combining structure from motion and close-range stereo photogrammetry to obtain scaled gravel bar DEMs. Int J Remote Sens 39(23):9269–9293
Abdel-Aziz Y, Karara H, Hauck M (2015) Direct linear transformation from comparator coordinates into object space coordinates in close-range photogrammetry. Photogramm Eng Remote Sens 81(2):103–107
Zhang Z (2000) A flexible new technique for camera calibration. IEEE Trans Pattern Anal Mach Intell 22(11):1330–1334
Zhang Z (1999) Flexible camera calibration by viewing a plane from unknown orientations. In: Proceedings of the seventh IEEE international conference on computer vision, AN: 6365272
Zhang Z (2014) Camera calibration. In: Szeliski R (ed) Computer vision. Springer, New York, pp 76–77
Zhang Z et al (2018) A single-image linear calibration method for camera. Measurement 130:298–305
Civicioglu P, Besdok E (2006) Implicit camera calibration by using resilient neural networks. LNCS 4233:632–640
Horaud R, Mohr R, Lorecki B (1992). Linear camera calibration. In: Proceedings 1992 IEEE international conference on robotics and automation. AN: 4377425
Ismail K, Sayed T, Saunier N (2013) A methodology for precise camera calibration for data collection applications in urban traffic scenes. Can J Civ Eng 40(1):57–67
Douskos V, Kalisperakis I, Karras G, Petsa E (2008) Fully automatic camera calibration using regular planar patterns. In: International archives of the photogrammetry, remote sensing and spatial information science, vol XXXVII, no. Part B5, pp 21–26
Kang DJ, Ha JE, Jeong MH (2008) Detection of calibration patterns for camera calibration with irregular lighting and complicated backgrounds. Int J Control Autom 6(5):746–754
Maybank SJ, Faugeras OD (1992) A theory of self-calibration of a moving camera. Int J Comput Vis 8(2):123–151
Armstrong M, Zisserman A, Hartley R (1996) Self-calibration from image triplets. LNCS 1064:1–16
Sturm P, Maybank SJ (1999) On plane-based camera calibration: a general algorithm, singularities, applications. In: IEEE computer society conference on computer vision and pattern recognition, pp 432–437
Tsai R (1987) A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses. IEEE Trans Robot 3(4):323–344
Deng L et al (2016) A novel camera calibration technique based on differential evolution particle swarm optimization algorithm. Neurocomputing 174:456–465
Bouguet JY (2019) Camera calibration toolbox for Matlab. http://www.vision.caltech.edu/bouguetj/calib_doc/. Accessed 29 Dec 2019
Zhang WM, Zhong YX (2004) Camera calibration based on improved differential evolution algorithm. Opt Tech 30(6):720–723
Deep K et al (2013) Stereo camera calibration using particle swarm optimization. Appl Artif Intell 27(7):618–634
Liu X, Qi D (2016) Camera calibration based on self-adaptive cuckoo search algorithm. In: 2016 IEEE 8th international conference on intelligent human-machine systems and cybernetics, vol 2, pp 95–98
Ji Q, Zhang Y (2001) Camera calibration with genetic algorithms. IEEE Trans Syst Man Cybern A 31(2):120–130
Koch A, Bourgeois-Republique C, Dipanda A (2015) Evolutionary algorithms for a mixed stereovision uncalibrated 3D reconstruction. Multimed Tools Appl 74(19):8703–8721
Yang Z et al (2012) A novel camera calibration method based on genetic algorithm. In: 3rd IEEE conference on industrial electronics and applications, pp 2222–2227
Civicioglu P et al (2018) Weighted differential evolution algorithm for numerical function optimization: a comparative study with cuckoo search, artificial bee colony, adaptive differential evolution, and backtracking search optimization algorithms. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3822-5:1-15
Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214(1):108–132
Clerc M (2012) Beyond standard particle swarm optimisation. Innov Dev Swarm Intell Appl 1(4):1–19
Wang Y et al (2014) Differential evolution based on covariance matrix learning and bimodal distribution parameter setting. Appl Soft Comput 18:232–247
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35
Mirjalili S et al (2016) Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst Appl 47:106–119
Rao RV, Savsani VJ, Vakharia D (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43(3):303–315
Erlich I et al (2014) Evaluating the mean-variance mapping optimization on the IEEE-CEC 2014 test suite. In: IEEE congress on evolutionary computation (CEC), pp 1625–1632
Pan WT (2012) A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowl Based Syst 26:69–74
Awad NH et al (2016) An ensemble sinusoidal parameter adaptation incorporated with L-SHADE for solving CEC2014 benchmark problems. In: IEEE congress on evolutionary computation (CEC), pp 2958–2965
Song X et al (2009) Camera calibration based on particle swarm optimization. In: 2nd international congress on image and signal processing, pp 1–5
de la Fraga LG, Schütze O (2009) Direct calibration by fitting of cuboids to a single image using differential evolution. Int J Comput Vis 81(2):119–127
de la Fraga LG, Silva IV (2008) Direct 3D metric reconstruction from two views using differential evolution. In: IEEE congress on evolutionary computation (IEEE world congress on computational intelligence), pp 3266–3273
Civicioglu P, Besdok E (2019) Bernstain-search differential evolution algorithm for numerical function optimization. Expert Syst Appl 138:112831
Civicioglu P, Besdok E (2018) A plus evolutionary search algorithm and QR decomposition based rotation invariant crossover operator. Expert Syst Appl 103:49–62
Gunen MA, Atasever UH, Taskanat T, Besdok E (2019) Usage of Unmanned Aerial Vehicles (UAVs) in determining drainage networks. Nat Sci 14:1–10
Jiang J, Cheng J, Chen XJN (2009) Registration for 3-D point cloud using angular-invariant feature. Neurocomputing 72(16–18):3839–3844
Aspert N, Santa-Cruz D, Ebrahimi T (2002) Mesh: measuring errors between surfaces using the hausdorff distance. In: 2002 IEEE international conference on multimedia and expo. AN: 7540733
Wang L et al (2016) A convex relaxation optimization algorithm for multi-camera calibration with 1D objects. Neurocomputing 215:82–89
Gunen MA, Atasever UH, Besdok E (2017) A novel edge detection approach based on backtracking search optimization algorithm (BSA) clustering. In: IEEE 8th international conference on information technology (ICIT). AN 17285591
Kriegman D (2007) Homography estimation. Lecture computer vision I, CSE a, p 252
Kang L et al (2014) A highly accurate dense approach for homography estimation using modified differential evolution. Eng Appl Artif Intell 31:68–77
Karolczak M et al (2001) Implementation of a cone-beam reconstruction algorithm for the single-circle source orbit with embedded misalignment correction using homogeneous coordinates. Med Phys 28(10):2050–2069
Guan B, Shang Y, Yu Q (2017) Planar self-calibration for stereo cameras with radial distortion. Appl Opt 56(33):9257–9267
Wu J, Liu G (2012) Noniterative calibration of a camera lens with radial distortion. Meas Sci Technol 23(10):105013
Garg V, Deep K (2016) Performance of Laplacian Biogeography-Based Optimization Algorithm on CEC 2014 continuous optimization benchmarks and camera calibration problem. Swarm Evol Comput 27:132–144
QiShen L, LiCai L, ZeTao J (2009) A camera self-calibration method based on hybrid optimization algorithm. In: Second international symposium on electronic commerce and security, pp 60–64
Espiau B (1994) Effect of camera calibration errors on visual servoing in robotics. In: Yoshikawa Tsuneo, Miyazaki Fumio (eds) Experimental robotics III. Springer, New York, pp 182–192
Matsumoto M, Nishimura T (1998) Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans Model Comput Simal 8(1):3–30
Navidi WC (2008) Statistics for engineers and scientists. McGraw-Hill, New York
Reyes-Acosta AV et al (2019) 3D pipe reconstruction employing video information from mobile robots. Appl Soft Comput 75:562–574
Gunen MA (2017) Comparison of point cloud filtering algorithms. In: Geomatics engineering. 2017, master thesis, Institute of Science, Erciyes University
Nguyen HL et al (2017) A comparative study of automatic plane fitting registration for MLS sparse point clouds with different plane segmentation methods. In: ISPRS annals of photogrammetry, remote sensing and spatial information sciences, vol IV-2/W4, pp 115–122
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Gunen, M.A., Besdok, E., Civicioglu, P. et al. Camera calibration by using weighted differential evolution algorithm: a comparative study with ABC, PSO, COBIDE, DE, CS, GWO, TLBO, MVMO, FOA, LSHADE, ZHANG and BOUGUET. Neural Comput & Applic 32, 17681–17701 (2020). https://doi.org/10.1007/s00521-020-04944-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-020-04944-1