Due to Rayleigh scattering, the distribution pattern of polarized light in the sky varies regularly with the change in the position of the sun. Taking advantage of this distribution, polarized skylight navigation technology can achieve anti-interference and fully autonomous orientation and navigation with no cumulative error, making it widely applied in the areas of aerospace, military operations, and underwater navigation. However, under cloudy weather or complex scenes with obstructions such as trees and buildings, the polarization images of the obstructions do not obey the Rayleigh scattering principle. Therefore, directly using sky polarization images of complex scenes for navigation orientation will reduce navigation accuracy. To solve this issue, various imaging segmentation methods have been proposed for separating sky and occlusion information, but they still have some limitations. For example, the method of using neural networks for obstruction segmentation requires a large amount of data and time for training, making it hard for model application, diagnosis, and repair. Using polarization degree gradient as a threshold to extract effective polarization information often needs to set gradient thresholds manually and requires a large number of experiments, which lacks universality. Therefore, we propose an image segmentation algorithm (SO-Otsu) based on the snake optimization (SO) algorithm and the Otsu method to achieve fast, stable, and self-adaptive polarization navigation of mobile carriers such as drones, cars, and ships under cloudy weather or complex scenes with different obstructions.

Before applying the SO-Otsu algorithm to segment obstructions and sky in the polarization images for navigation accuracy improvement, the bilinear interpolation algorithm is first used to extract four images with different angles from images captured by a polarization camera. Then Stokes vectors are used to obtain the sky polarization degree image and polarization azimuth image. By using the Otsu algorithm, the maximum inter-class variance of polarization degree images and the optimal segmentation threshold for sky and obstructions identification can be found automatically. At the same time, to speed up the optimal threshold finding procedure, the SO algorithm is applied. A binary mask is designed using the optimal threshold to process the sky polarization azimuth image, remove the polarization information of occlusion, and retain the polarization information of the sky in this image. Finally, utilizing the principles of solar vector, the Rayleigh scattering model, and the polarization information obtained from the SO-Otsu method, the relative azimuth of the sun can be calculated for heading angle calculation. To verify the effectiveness of the SO-Otsu method on polarization image segmentation, two sets of polarization images are captured and analyzed: artificial obstruction with an occlusion rate between 25% and 85% and real environments with an occlusion rate between 17% and 83%. Under each specific occlusion rate, the precision turntable is rotated from 0° to 360° with 10° increments, and the images are taken at each angle. A total of 37 images and data are collected and analyzed. In addition, to evaluate the effect of the SO-Otsu method, the polarization image processing parameters including peak signal-to-noise ratio, optimal threshold, iteration times, and run time using SO-Otsu and Otsu methods are compared.

As shown in Table 1, when segmenting the same image, the SO-Otsu algorithm has better iteration times and algorithm performance than traditional Otsu algorithms, effectively reducing the exhaustive search time by about 40%. The calculated heading angle errors under artificial occlusion are shown in Fig. 8 and Table 2. It can be seen that, when the occlusion rate ranges from 25% to 85%, the maximum error of the heading angle is less than 2.6°. The overall accuracy of the calculated heading angle after segmentation is better than that of without segmentation. Although as the occlusion rate increases, the effective number of pixels used for calculation after segmentation decreases, and the root mean square error gradually increases, it remains within 0.95°. The calculated heading angle errors under occlusion including trees and buildings are shown in Fig. 9 and Table 3. It can be seen that, when the occlusion rate ranges from 17% to 83%, due to the interference of abnormal pixels, the maximum heading angle error calculated without segmentation exceeds 180° while the maximum heading angle error calculated by the SO-Otsu method does not exceed 1.59°. Meanwhile, the accuracy of the calculated heading angle after segmentation is significantly improved, with a root mean square error of less than 0.75°.

We first use a bilinear interpolation algorithm to obtain polarization images from four angles for further polarization information analysis and calculation. By combining SO with the Otsu algorithm, the polarization degree image of sky polarization is directly segmented, and then the abnormal pixel information points in the image are removed. The retained effective pixel information points are combined with the Rayleigh scattering model to calculate the heading angle. The experiment results reveal the time using the SO-Otsu algorithm to segment a polarization degree image is less than 0.005 s, effectively reducing the heading angle calculation time by about 40%. By analyzing the experimental results of multiple sets of different occlusion rates and occlusion conditions, we find that when the occlusion is a baffle with an occlusion rate between 25% and 85%, the root mean square error of the calculated heading angle is less than 0.95°. When the occlusion rate of buildings and trees ranges from 17% to 79%, the root mean square error of the calculated heading angle is less than 0.75°. Compared with directly using images with abnormal pixel information to calculate the heading angle, our method can effectively improve the accuracy of the heading angle. The SO-Otsu image segmentation algorithm provides a new approach for fast and self-adaptive polarization navigation of mobile carriers such as drones, cars, and ships under complex scenes. In the future, to further improve the segmentation effect of polarized images, various algorithms need to be considered and combined to eliminate the influence of high polarization reflected light generated by occluded surfaces, thereby achieving more accurate and stable polarization navigation orientation.