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A novel method based on Pulse Coupled Neural Network(PCNN) algorithm for the highly accurate and robust compass information calculation from the polarized skylight imaging is proposed,which showed good accuracy and reliability especially under cloudy weather,surrounding shielding and moon light. The degree of polarization (DOP) combined with the angle of polarization (AOP), calculated from the full sky polarization image, were used for the compass information caculation. Due to the high sensitivity to the environments, DOP was used to judge the destruction of polarized information using the PCNN algorithm. Only areas with high accuracy of AOP were kept after the DOP PCNN filtering, thereby greatly increasing the compass accuracy and robustness. From the experimental results, it was shown that the compass accuracy was 0.1805° under clear weather. This method was also proven to be applicable under conditions of shielding by clouds, trees and buildings, with a compass accuracy better than 1°. With weak polarization information sources, such as moonlight, this method was shown experimentally to have an accuracy of 0.878°.
© 2016 Optical Society of America
1. Introduction
Navigation plays an important role in human activities as one of the most important technologies. People are always trying to find a smarter method that can be used for long term navigation, and without any other complicated assistance systems like GPS. Biological research has established that some animals have the ability to orient and navigate with polarized skylight [1–3]. It has been shown that the small brains of insects and other animals are able to accomplish robust and efficient navigation in complex environments [4,5]. The desert ant catalyphis can find their way home without landmarks in the desert [6,7]. Butterflies and dragonflies have also proved to have the ability to use polarized skylight during their navigation activities [8]. Polarized skylight has been shown to be a promising and reliable navigation compass source that can be used independently, or used together with other methods to make a smarter navigation system. Recent research work by Greif’s group has shown that polarized skylight can also be used as a geographical reference by birds to calibrate their cues in their compasses. Meanwhile, greater mouse-eared bats use polarization cues to calibrate their magnetic compass [9].
To understand the compass mechanism, investigators have systematically studied the ommatidia in the compound eye [10]. Different bionic techniques were developed for the application of polarized skylight as a source for navigation information [11]. The point-source based approach was reported in 1990 by Wenher’s group [12,13]. Using four or six channels with polarizer in different directions, the polarization characteristics can be calculated, and can be used to calculate the compass information from the angle between the polarized vector and the meridian line. The sensors that Chu has developed have an accuracy of about 0.2° under clear weather [14–17]. Lu et al. extracted angle based on Hough transform and the measurement accuracy was 0.37° [18].
Because the polarization distributions of the skylight can be affected easily by clouds, pollution and surrounding coverage [19], the reliability could be greatly reduced [20]. Any destruction of the polarization distributions could lead to the wrong compass information. Solving the problems of the calculation of compass information under different harsh conditions has become the key problem for the application of polarized skylight to applications in orientation and navigation [21,22].
In this paper, we propose a robust compass method based on Pulse Coupled Neural Network (PCNN) calculation utilizing polarized skylight [23], that can be applied under different conditions including cloudy weather, surrounding shielding, and weak light from the moon. The basic idea is to combine the two steps of PCNN filters, one filter for the image segmentation of the destructed information region on the DOP images and the other filter for the point noise smoothing. The DOP information was used to eliminate the destroyed polarized information, and was employed as the reference for the selection of the AOP information with good quality, because it is more sensitive to the surrounding conditions. By fitting of the meridian line from the AOP, the realtime compass information will then be calculated. In other words, compared with the traditional calculation method, our method allows to find the compass information only if a small region of the polarization information existed, thereby greatly improving the accuracy and robustness of the measurements. The method was proposed in this paper rely on the atmospheric polarization pattern is the natural attribute of the earth and has characteristics of stability distribution. And it could not be destroyed and interfered in a short period of time, especially suitable for autonomous navigation of the carrier in a weak/no satellite signal. It can provide theoretical basis and key technical support for the research of polarized light positioning technology, so the method has high research value and widely application prospects. Meanwhile because all directions are taken simultaneously, the system was proposed in the paper is well adapted to operate in a changing environment or on a less stable platform, such as ship, unmanned aerial vehicle and automobile [20]. The goal of this approach was proposed in this paper is to develop an understanding of natural systems by building a robot that mimics some aspects of insects sensory and nervous system and their behavior in the future [22].
2. Methods
2.1 Experimental system
A homemade full sky polarimeter system was designed, as shown in Fig. 1. It is composed of three charge-coupled devices (CCDs) and three fish eyes lenses (Sigma EX DC fish-eye). The three polarizers were mounted infront of the CCDs allows for the detection of the polarization mode of the sky light. The fish eye lens were used to provide a 180° view for the full sky imaging. The wireless trigger device can be used to control the instantaneity of the three CCDs during the imaging process. According to the polarization information calculation algorithm, the intersection angles between the polarizer optical axis of the three CCDs and the reference direction are set as 0°, 45° and 90°, as shown in Fig. 1(a). The compass information measurements carried out by utilizing the full sky polarization imaging system. All the data were collected under different environmental conditions in November, 2014. In all the experiments, data was collected with different pre-setted compass informations (0°, 60°, 120°, 180°, 240°, 300°, 360°), defined by the relative angle of the imaging system to the initial position.
Fig. 1 The full sky polarimeter system. (a) The full sky polarimeter imaging system for polarization detection; (b) The polarimeter imaging system composed of fish eye lens and CCD.
2.2 Calculation of compass information
The compass information calculation algorithm was demonstrated using the images under cloudy weather, as it is shown in Fig. 2.
Fig. 2 The compass calculation methodology. (a) Compass information in two-dimensional polar coordinates. (b) Compass information of the carrier under geographic coordinate. (c) Original image. (d) The polarization angle image. (e) The polarization degree image. (f) PCNN calculation first step. (g) PCNN calculation second step. (h) Compass information extraction.
The atmospheric polarization pattern is decided by the spatial position of the sun. When the carrier compass information is changing, the detected change of polarization mode is due to the position change of the sun in carrier coordinate. Therefore, the position change of sun's meridian is used to realize the calculation of compass information. The 2d polar coordinates are used to explain the theory of compass information calculation as shown in Figs. 2(a) and 2(b). The straight line defined by the sun and zenith point is divided into two parts where the demarcation point is the zenith point, the straight line closed to the sun side is defined as the solar meridian and the other side is defined as the anti-solar meridian. is defined as the direction angle of the solar meridian under carrier coordinate, is defined as the direction angle of the solar meridian under geographic coordinate, so the compass information of the carrier under geographic coordinate can be obtained:. The can be obtained from polarization angle distribution image, the steps are shown as follows:
- 1) Searching the feature points set with the criterion: 90-|AOP|<αth, where is an arbitrary value which is greater than 0;
- 2) Fitting for the feature points set as y = ax + b, which can be used as the projection of solar meridian on carrier coordinate;
- 3) The direction angle of solar meridian under carrier is , according to polarization degree distribution rules of atmosphere polarization mode, the solar meridian and anti-solar meridian can be further distinguished. Because the polarization degree in solar meridian side is smaller than anti-solar meridian, the sun's quadrant can be confirmed by the polarization degree distribution, and then the direction angle of solar meridian can be obtained by Table 1.
Table 1. The transformation rules of the position of the sun.
The initial polarization image calculations were performed using Stokes vector for polarized imaging [24], which was shown in Figs. 2(c)-2(e). From the initial polarization images, the polarization information maybe too weak for the compass information extraction, such as the cloudy sky. The shading of cloud would destroy the Rayleigh distribution mode, then the pseudo feature points would be obtained in polarization detection which would affect the compass information extraction. By observing the polarization image, it can be clearly seen that the distribution of polarization azimuth which is covered by cloud is high frequency noise without any rules. Therefore, PCNN calculation is introduced for polarization image de-noising.
PCNN has been widely used in various fields of image processing. For the requirement of image processing, simplified PCNN model has been proposed. PCNN can extract useful information from the complex background.When the polarization information is destroyed, PCNN algorithm can extract the active polarization information.Then remove the effects of polarization information noise through its inherent filtering automatically. PCNN not only retains all the basic features of the original model,but also it can extract a more rational image features, and it reduces the complexity of the software simulation time also.When the polarization information was destroyed or too weak for the position calculation, by PCNN image extraction and segmentation can extract a more complete polarization information in complex background.Then remove the noise that effect the positioning accuracy by two of its inherent automatic filter. The PCNN calculation is shown in Figs. 2(f) and 2(g). And the compass information extraction is shown in Fig. 2(h).
3. Results and Discussion
3.1 Experiment under clear weather
The compass information measurement under clear weather was performed at North University of China (37°49′55″E, 112°26′57″N). Figure 3 shows the experimental results under clear weather, where Fig. 3(a) is original image under different compass information. Figures 3(b) and 3(c) are, respectively, the corresponding AOP and DOP images of the full sky. Figure 3(d) is the compass information error, we can see that the error is reduced about 0.3° by using PCNN calculation and the biggest error is 0.594 degree and the average error is 0.1805°. Figure 3(e) is the compass information between theoretical and measured, and it can be seen that the measured compass information is close to the theoretical.
Fig. 3 Polarization experiment results under clear weather. (a) Original image under different compass information. (b) AOP images. (c) DOP images. (d) The compass information error. (d) The compass information error. (e) The compass information between theoretical and measured.
3.2 Experiment under clouds
Unlike the clear weather measurements, the covered clouds would destroy the Rayleigh distribution mode of polarization light which was one of the most serious problem of the measurement. This group of experiments were carried out under clouds; the experiment location and method was the same as for the first group of experiments. Figure 4 (a) is a group of original images for which the cloud coverage rate was more than 60%. From Fig. 4 (b)and(C), it can be seen clearly that the DOP is more sensitive to the cloud coverage than the AOP. Under clouds, the DOP has no obvious symmetry distribution feature; but the AOP has an 8-shape feature. There will be many false feature points when using the compass algorithm without any anti-interference. These are the points that satisfy the feature points criterion 90-|AOP|<αth; but still depart meridian area, which would lead to false fitting results. To solve the problems above, median filtering and DOP criteria are introduced. From the polarization image we can see that the AOP obtained under a cover of clouds can be considered as high frequency noise. Thus, the median filtering can be used to eliminate the noise, which make the amplitude of the AOP under clouds not satisfy the feature points criterion. From the polarization image, we can also see that the DOP obtained with a cloud cover is weakened to a large extent. Therefore, the clouds and sky can be separated by DOP. Here, the judgment threshold was set to 0.05; that is, the area can be considered as cloud coverage area when the DOP of the feature points is less than 0.05. The results when using either median filtering or the DOP criterion are shown in Figs. 4(d) and 4(e). We can see that the interference points are suppressed to a large extent, but not radically. The residual interference points will still influence the fitting results; so, it is necessary to fuse the two methods together to eliminate the interference from clouds.
Fig. 4 Results of the polarization experiment under cloud cover. (a) Original image under different compass information. (b) AOP images. (c) DOP images. (d) The compass information error. (e) The compass information between theoretical and measured.
The experimental results under clouds are shown in Figs. 4(a)–4(e). Although the cloud coverage rate was more than 80%, a high accuracy heading angle calculation result could be obtained by using the PCNN calculation algorithm. The largest error was 1.41° and the average error was 0.878°. The error was reduced about 1.5° by using PCNN calculation. For cloud coverage rates of 10%, 40%, 60% and 80%, the error increased from 0.1805°, to 0.2607°, 0.368° and 0.878°, respectively.
3.3 Experiment under clear weather at night (full moon)
Moonlight, like sunlight, is scattered by atmospheric molecules and aerosol particles, giving rise to celestial polarization patterns which contain abundant information of navigation. However experiment at night was influenced by the surrounding lights, and the PCNN calculation can also be used to reduce this influence. This group of experiments was carried out at the North University of China in clear weather, at night, with a full moon. The results are shown in Fig. 5. The polarization patterns can be seen clearly. This shows that the compass calculation method can be used under weak polarization conditions. The compass calculation results show that the largest error was 0.943 degree, and the average error was 0.712 degree.
Fig. 5 Results of the polarization experiment under clear weather at night. (a) Original image under different compass information. (b) AOP images. (c) DOP images. (d) The compass information error. (e) The compass information between theoretical and measured.
3.4 Experiments under clear weather in the presence of trees and buildings
To solve the application about destroyed polarization in the town with trees or buildings around, we tested in the presence of trees and buildings.The experimental result under trees is shown in Fig. 6. This group of experiments was carried out under clear weather, with trees and buildings, at the North University of China. The coverage rate of the trees was more than 80%. However, the influence of the trees on the polarization distribution was not particularly obvious, most likely because the thin trunks of the trees had almost no influence on polarization. The compass calculations show that the largest error was 0.899° and the average error was 0.695°.
Fig. 6 Polarization experiment under clear weather in the presence of trees and buildings. (a) Original image under different compass information. (b) AOP images. (c) DOP images. (d) The compass information error. (e) The compass information between theoretical and measured.
4. Conclusions
A compass information measurement algorithm based on the full sky polarization light distribution image is proposed in this paper. The proposed algorithm has the advantage of a wider range of navigation applications, especially under complex environments. The full sky polarization imaging system is established, and the high quality polarization image is obtained. By using the polarization imaging system, the compass calculation experiments are carried out under four different experimental conditions, namely clear weather without shelter, clear weather with building shelter, clear weather with building and tree shelter, and cloud without shelter. Under clear weather or clear weather with building shelter environments, the average error is less that 0.4 degree. Under clear weather with trees and building shelter and cloud weather, the polarization mode is destroyed to some degree, but the accuracy of the compass calculation is still acceptable. The high stability of the proposed algorithm under complex environments has been verified.
Acknowledgments
We acknowledge the financial support from the Natural Science Foundation of China (51225504, 61171056 and 61127008).
J.T. and N.Z. contributed equally to this work. J.T., N.Z. and J.L. performed the measurements, built-up the algorithm, analyzed the data, and wrote the main manuscript text. D.L. and F.W. performed the measurements. C.W. analyzed the images by the MATLAB software. J.R. and C.S analyzed the data, and contributed to the manuscript writing. C.X.and B.Z. offered helpful discussion in the study. All authors reviewed the manuscript.
References and links
1. G. Horváth and D. Varjú, Polarized Light in Animal Vision—Polarization Patterns in Nature (Springer Berlin, 2003).
2. R. Wehner, “Polarization vision--a uniform sensory capacity?” J. Exp. Biol. 204(Pt 14), 2589–2596 (2001). [PubMed]
3. F. Arago, Astronomie Populaire (Gide et J. Baudry,1855).
4. T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003). [CrossRef] [PubMed]
5. M. Dacke, E. Baird, M. Byrne, C. H. Scholtz, and E. J. Warrant, “Dung beetles use the Milky Way for orientation,” Curr. Biol. 23(4), 298–300 (2013). [CrossRef] [PubMed]
6. K. Fent and R. Wehner, “Oceili: a celestial compass in the desert ant cataglyphis,” Science 228(4696), 192–194 (1985). [CrossRef] [PubMed]
7. R. Wehner, “Desert ant navigation: how miniature brains solve complex tasks,” J. Comp. Physiol. A Neuroethol. Sens. Neural Behav. Physiol. 189(8), 579–588 (2003). [CrossRef] [PubMed]
8. S. Rossel, “Polarization sensitivity in compound eyes,” in Facets of Vision (Springer Berlin Heidelberg, 1989).
9. S. Greif, I. Borissov, Y. Yovel, and R. A. Holland, “A functional role of the sky’s polarization pattern for orientation in the greater mouse-eared bat,” Nat. Commun. 5, 4488 (2014). [CrossRef] [PubMed]
10. B. Vulfovich and V. Fogilev, “New ideas for celestial navigation in the third millennium,” J. Navig. 63(02), 373–378 (2010). [CrossRef]
11. S. Rossel and R. Wehner, “How bees analyse the polarization patterns in the sky,” J. Comp. Physiol. A Neuroethol. Sens. Neural Behav. Physiol. 154(5), 607–615 (1984). [CrossRef]
12. I. Pomozi, G. Horváth, and R. Wehner, “How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation,” J. Exp. Biol. 204(Pt 17), 2933–2942 (2001). [PubMed]
13. E. Wehner, The Polarization-Vision Project: Championing Organismic Biology (Fortschr. Zool., 1994).
14. J. Chu, K. Zhao, Q. Zhang, and T. C. Wang, “Construction and performance test of a novel polarization sensor for navigation,” Sensor Actuat. A-Phys. 148(1), 75–82 (2008).
15. Y. Wang, J. Chu, R. Zhang, L. Wang, and Z. Wang, “A novel autonomous real-time position method based on polarized light and geomagnetic field,” Sci. Rep. 5, 9725 (2015). [CrossRef] [PubMed]
16. K. P. Able and M. A. Able, “Daytime calibration of magnetic orientation in a migratory bird requires a view of skylight polarization,” Nature 364, 523–525 (1993).
17. K. P. Able and M. A. Able, “Daytime calibration of magnetic orientation in a migratory bird requires a view of skylight polarization,” Nature 364(6437), 523–525 (1993). [CrossRef]
18. H. Lu, K. Zhao, Z. You, and K. Huang, “Angle algorithm based on Hough transform for imaging polarization navigation sensor,” Opt. Express 23(6), 7248–7262 (2015). [CrossRef] [PubMed]
19. I. Pomozi, G. Horváth, and R. Wehner, “How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation,” J. Exp. Biol. 204(Pt 17), 2933–2942 (2001). [PubMed]
20. K. J. Voss and Y. Liu, “Polarized radiance distribution measurements of skylight. I. System description and characterization,” Appl. Opt. 36(24), 6083–6094 (1997). [CrossRef] [PubMed]
21. G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Åkesson, B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 366(1565), 772–782 (2011). [CrossRef] [PubMed]
22. D. Lambrinos, R. Möller, T. Labhart, R. Pfeifer, and R. Wehner, “A mobile robot employing insect strategies for navigation,” Robot. Auton. Syst. 30(1-2), 39–64 (2000). [CrossRef]
23. D. Zhang, S. Mabu, and K. Hirasawa, “Image denoising using pulse coupled neural network with an adaptive Pareto genetic algorithm,” IEEJ T. Electr. Electr. 6(5), 474–482 (2011). [CrossRef]
24. D. Miyazaki, M. Ammar, R. Kawakami, and I. Katsushi, “Estimating sunlight polarization using a fish-eye lens,” IPSJ Trans. Computer Vis. Appl. 1, 288–300 (2009).
