Vision-based depth estimation is an important research direction of computer vision, which is of great significance to three-dimensional (3D) reconstruction, semantic segmentation, navigation, etc. The monocular depth estimation scheme has the advantages of low cost and easy installation, which cannot be realized by binocular stereo vision and lidar, and it has received more and more attention in recent years. There is a strong correlation between the out-of-focus image degradation and the location of the object being photographed, which can be used as a source of information for monocular depth estimation. Traditional depth estimation algorithms based on depth from defocus (DFD) use mechanical zoom, which results in misaligned images. In addition, mechanical zoom has certain disadvantages in terms of response speed, accuracy, and service life. To avoid these problems, Ye et al. used the liquid crystal lens as the zoom device to implement the DFD algorithm. Liquid crystal lens imaging requires the use of polarizers to filter ordinary light (o-light), so as to reduce the incoming light by half. Ye et al. proposed a liquid crystal lens imaging technology without polarizers. They collected two images: one with voltage applied to the liquid crystal lens, and the other without voltage. They used the image without voltage to obtain the o-light component and subtracted the o-light component from the image taken under voltage to obtain an extraordinary light (e-light) image. The non-polarizer liquid crystal lens imaging scheme requires the collection of at least two images for a single focus setting. If this scheme is employed for DFD, at least four images need to be collected. However, the use of image enhancement techniques such as image filtering to suppress noise can result in the loss of valuable image information. In this work, we propose a polarizer-free scheme that is well-suited for DFD. This scheme eliminates the need for collecting additional images and requires only the capture of two out-of-focus images by using a polarizer-free liquid crystal lens. We demonstrate that the scheme could further improve the accuracy of depth estimation while simplifying system components.

We first established a blur degradation model for liquid crystal lens imaging without polarizers. To simulate the blur degradation under o-light and e-light, we utilized a Gaussian model. Considering that o-light and e-light accounted for nearly 50% of natural light, we simply summed half of the blur degradation models of o-light and e-light to obtain the blur degradation model of natural light. We improved the defocus equalization algorithm by incorporating a weighted deviation function that accounted for depth inconsistency within the local window. In order to obtain the confidence of depth estimation in the spatial domain, we introduced a brightness correction factor to remove the brightness inconsistency. In addition, we introduced semantic segmentation as a guide template and employed the Laplacian matting algorithm to carry out the depth completion. Moreover, we conducted a theoretical analysis of the error associated with the depth estimation algorithm using polarizer-free imaging. Our analysis showed that the effective depth of field of this algorithm was larger than that of the scheme using a polarizer.

We compared the effect of initial depth estimation (without error rejection and depth completion) of liquid crystal imaging systems without polarizers and with polarizers on slope and plane scenes, and the depth of the slope ranges from 0.61 to 1.00 m. For the slope scene, the captured images and the depth estimation results are shown in Fig. 8. For the plane scene, the captured images and depth estimation results are shown in Fig. 9. It can be seen that for a plane scene, the accuracy of depth estimation with and without a polarizer is similar. As for the slope scene, it can be seen from the framed area that the effect of depth estimation without a polarizer is better than that with a polarizer. The numerical comparison results are shown in Table 2. The comparison data of the slope and the plane scenes show that for a certain fixed depth, the effect of depth estimation with and without a polarizer is close. For scenes with depth changes (slope scenes), the range of defocus spot radius is relatively large. According to the analysis of the error model in this study, it can be known that the polarizer-free system can tolerate a larger range of changes in spot size, and it can achieve better results under large spots. At the same time, it exhibits stronger stability against noise disturbance. It can be seen from the experimental data that in the scene of depth changes, the polarizer-free system has a better performance [its root mean square error (RMSE) is reduced by 25%]. We also verified the proposed depth estimation scheme for liquid crystal lenses without polarizers in complex scenes by placing different targets at different depths. The depth ranges of different targets are shown in Table 3. We first compared the difference between the input images with and without polarizers, As shown in Fig. 10, adding a polarizer reduces the amount of light entering the image, which requires increasing the exposure time or adjusting the exposure gain to maintain the same brightness as the image without a polarizer. However, this results in an increase in image noise. At the same time, the depth of field of the image taken without a polarizer is greater, and it can ensure that the radius of the equivalent blurred spot is maintained at a smaller value and that the DFD algorithm can achieve better results in a relatively large depth range. The image results are shown in Fig. 11, and the numerical results are shown in Table 4. In addition, by comparing the sixth and seventh rows of Table 4 with the sixth and seventh columns of Fig. 11, it can be seen that after adding instance segmentation, the RMSE decreases by 42%, and AWT₁₂₅ increases by 26%. Therefore, estimation accuracy has been significantly improved.

In this study, we proposed a depth estimation scheme for liquid crystal lenses without polarizers. The theoretical error analysis and experimental results show that the depth estimation scheme of liquid crystal lenses without a polarizer has more advantages than that with a polarizer. Compared with the traditional polarizer-free solution, the depth estimation scheme for the polarizer-free liquid crystal lens proposed does not simply subtract the component of o-light but uses the blur caused by the o-light in the depth estimation to further improve the accuracy of depth estimation. Removing the polarizer reduces the complexity of the optical system. This is of great significance for the use of liquid crystal lens imaging (especially small aperture) in actual scenes. We improved the unbiased defocus-equalization filter (UDE) algorithm, introduced a weighted energy function and light intensity correction factor, and used instance segmentation to complete the image. The results show that our improvement can effectively enhance the accuracy of the algorithm.