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Underwater Depth Estimation for Spherical Images
Underwater Depth Estimation for Spherical Images
Cui, Jiadi;Jin, Lei;Kuang, Haofei;Xu, Qingwen;Schwertfeger, Sören
Hindawi Journal of Robotics Volume 2021, Article ID 6644986, 12 pages https://doi.org/10.1155/2021/6644986 Research Article Jiadi Cui , Lei Jin, Haofei Kuang, Qingwen Xu, and So ¨ren Schwertfeger Mobile Autonomous Robotic Systems Lab, School of Information Science and Technology, ShanghaiTech University, Shanghai, China Correspondence should be addressed to Jiadi Cui; email@example.com Received 15 December 2020; Accepted 29 May 2021; Published 18 June 2021 Academic Editor: L. Fortuna Copyright © 2021 Jiadi Cui et al. (is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (is paper proposes a method for monocular underwater depth estimation, which is an open problem in robotics and computer vision. To this end, we leverage publicly available in-air RGB-D image pairs for underwater depth estimation in the spherical domain with an unsupervised approach. For this, the in-air images are style-transferred to the underwater style as the ﬁrst step. Given those synthetic underwater images and their ground truth depth, we then train a network to estimate the depth. (is way, our learning model is designed to obtain the depth up to scale, without the need of corresponding ground truth underwater depth data, which is typically not available. We test our approach on style-transferred in-air images as well as on our own real un- derwater dataset, for which we computed sparse ground truth depths data via stereopsis. (is dataset is provided for download. Experiments with this data against a state-of-the-art in-air network as well as diﬀerent artiﬁcial inputs show that the style transfer as well as the depth estimation exhibit promising performance. images to estimate depth. In addition, deep learning was also 1. Introduction applied to estimate the depth of underwater images, for Underwater depth estimation is an open problem for marine example, the study in  used a convolution neural network robotics [1, 2], which is usually used for 3D reconstruction, (CNN) to generate relative depth, which was then one of the navigation, and intermediate steps for underwater color inputs for a color correction network. Learning-based correlation [3, 4]. Due to the properties of underwater methods are very popular these days, and there are many environments, underwater perception is quite diﬀerent from applications about depth estimation, for example also in in-air perception. Images captured underwater usually look some microsystems [10, 11]. bluish because longer wavelengths of the visible sunlight are Apart from normal pin-hole cameras, omnidirectional absorbed earlier than shorter wavelengths. Underwater cameras are becoming popular, due to their large ﬁeld of images may also be more greenish, because of algae in the view (FOV). (ey have been widely used on ground robots water. Besides, the underwater images are more blurred than [12–16]. Some research groups also studied omnidirectional those in-air captured by the same camera, due to turbidity. cameras for underwater use since they provide more in- (ese reasons increase the diﬃculty of depth estimation formation than perspective ones on object detection, lo- from images. (us, many researchers put eﬀort on under- calization, and mapping. (e study in  designed water image processing. For example, using dark channel omnidirectional video equipment and put it on dolphins to priors is proposed to restore underwater images in [5, 6], capture data. (e study in  improved on-land omni- inspired by  on removing haze in air. (e study in  directional cameras for underwater use and proposed the implemented underwater image stitching based on spectral method for camera calibration. methods, which are more robust to turbidity than feature- In addition, the sometimes long visible distances in water based methods. Besides image enhancement, some work increase the region of undeﬁned depth, especially compared focused on depth estimation. (e study in  exploited the to indoor scenes, which makes the depth estimation more relationship between depth and blurriness of underwater diﬃcult. Although there are several papers on active 2 Journal of Robotics methods for underwater 3D imaging , capturing om- constraints to estimate both depth and surface normals. (e nidirectional underwater depth images remains a big study in  investigated the multimodality depth com- pletion task with a self-supervised method by constructing a challenge, which makes ground truth depth unavailable. (is paper proposes to leverage publicly available in-air spherical loss function with photometric constraints, and their images for depth estimation in the underwater domain. method achieved the state of the art (SOTA) on the KITTI Speciﬁcally, our approach follows a two-stage pipeline. (i) depth completion benchmark. (e study in  exploited Given in-air RGB-D spherical pairs from the Stanford 2D- the bilateral cyclic relationship between stereo disparities 3D-S dataset , we train a style-transfer network  to and proposed an adaptive regularization scheme to handle convert in-air images to the underwater domain. (ii) Given covisible and occluded problems in a stereo pair. the generated underwater images and their depth maps, we Diﬀerent from geometric constraints-based methods, train a depth estimation network which is specially designed there are some approaches that try to exploit the constraint for spherical images. During testing, we can generate depth between diﬀerent modalities, called the wrapped-based directly from the input image. Our approach is unsupervised method. (e study in  proposed a wrapped-based method to estimate both depth and pose. (ey designed a in that only underwater images (i.e., no ground truth un- derwater depth) are required for the whole training process. loss based on wrapping nearby views to the target using the Following our preliminary work , the main contri- computed depth and pose. (e study in  proposed butions of our paper are as follows: monodepth2 to combine depth and camera pose with ge- ometry constraints. To improve the robustness of the model, (i) To the best of our knowledge, we are the ﬁrst group they also proposed the minimum reprojection loss and to employ CycleGAN to spherical underwater utilized a multiscale sampling method in their framework. images Currently, monodepth2 achieves SOTA results on the KITTI (ii) (is is also the ﬁrst method to employ deep learning benchmark. Because these methods can predict both depth to estimate depth in spherical underwater images and camera pose, they are wildly used in robotics and self- (iii) We provide a spherical underwater dataset, which driving cars as a visual odometry (VO) system. Zhan et al. investigated the end-to-end unsupervised depth-VO  consists of 3,000 high-quality images from the Great Barrier Reef and also integrated the depth with Perspective-n-Point (PnP) method to achieve high robustness . (iv) We provide a benchmark of the proposed network (is idea was also extended to combine more computer with respect to handcrafted images vision tasks. (e study in  exploited the content con- sistency between the depth and semantic information. (e study in  proposed the GeoNet to utilize the geometric 2. Related Work relationships between depth, optical ﬂow, and camera pose 2.1. Unsupervised Depth Learning. Learning-based methods and use an unsupervised learning framework to predict them. (e study in  proposed a competitive collabo- for depth estimation are popular. However, for adversarial environments, such as underwater or forest scenarios, an- ration framework to predict depth, pose, optical ﬂow, and notated data is diﬃcult to obtain. (erefore, supervised motion segmentation parallel with an unsupervised learning has diﬃculties in achieving a good performance method. with the absence of a large amount of labeled data. Unsu- Currently, unsupervised depth estimation is successful pervised learning and self-supervised learning are two in an indoor or urban scenario. But there are still few ap- methods for utilizing unlabeled data in the learning process. plications in adversarial scenarios. (e study in  pro- One reason for using unlabeled data is that producing a posed a generative model and exploited cycle-consistent dataset with clear labels is expensive, but unlabeled data is constraints to train the model in an unsupervised fashion. being generated all time. (e motivation is to make use of (eir method achieves the SOTA on their dataset, but it is the much larger amount of unlabeled data. (e main idea of also hard to implement in real underwater applications and the amount of available data is also not enough for training. self-supervised learning is to generate the labels from un- labeled data, according to the structure or characteristics of the data itself, and train with this unsupervised data through 2.2. Underwater Depth Estimation and Color Correction. a supervised manner. Self-supervised learning is wildly used in representation learning to make a model learn the latent In contrast to on-land scenarios, underwater depth esti- mation is more challenging due to scattering and absorption features of the data. (ese methods are wildly used in computer vision [23–27], video processing [28, 29], and eﬀects [9, 45], as mentioned above. For that, several methods jointly optimize depth estimation and color correction. In robot control [30–32]. (ere is much previous work related to the self-super- other words, accurate depth helps restore image colors and depth can also be estimated from the information of color vised method for depth estimation. In 2017,  proposed distortion. For example, the authors of [9, 46] presented an the monodepth framework to exploit epipolar geometry constraints and proposed a novel training loss to train their image formulation model to estimate depth from image blurriness. In , a dark channel prior is used for under- model along a self-supervised way. After that, there are some methods related to using geometry constraints to achieve water depth estimation and image restoration to dismiss the attenuation, backscattering eﬀects. (e study in  self-supervision. (e study in  utilized epipolar geometry Journal of Robotics 3 presented adaptive image dehazing based on the depth 3. Methodology information. Figure 1 demonstrates our two-stage pipeline. (i) Given in- As introduced in Section 2.1 (Unsupervised Depth air RGB-D spherical pairs from the Stanford2D-3D-S Learning), there are many successful learning methods to dataset , we train CycleGAN  to convert in-air estimate depth for in-air images. (us, a naive way to es- images to the underwater domain. (ii) Given the generated timate underwater depth is to restore underwater images to underwater images and their depth maps, we train a depth in-air style so that this depth learning strategy can be ap- estimation network to learn depth. In the following, we plied. In , such a strategy proves to be eﬃcient in un- introduce the two parts separately. derwater depth estimation. Both deep learning and mathematical methods are very popular for image resto- ration. In , they use the Jaﬀe-McGlamery model [50, 51], 3.1. Style Transfer. Generative adversarial nets (GANs) are a mathematical method, to handle the problems, which designed for data augmentation and are now widely used in decreases the absorption and scattering eﬀects based on style-transfer tasks. GANs are two-player mini-max games irradiance and depth. In , a learning-based method was between a generative model G and a discriminative model D proposed to solve depth estimation and color correction in . (e value function about this adversarial process is spherical domains at the same time by solving left-right min max V(D, G) � E [logD(x)] consistency under a multicamera setting. However, deep x∼p (x) data G D (1) learning usually requires a large amount of data, which is not + E [log(1 − D(G(z)))], available for the underwater ﬁeld. To overcome this problem, z∼p (z) the study in  proposed a generative adversarial network to where p denotes the features in the data and p holds data z generate synthetic underwater images from in-air datasets. random values at ﬁrst. (is value function is also the loss Our work is inspired by WaterGAN , but also diﬀerent function for the deep neural network. from it. WaterGAN requires depth as input to simulate the (e underwater style-transfer algorithm CycleGAN  attenuation and scattering eﬀect, while our underwater GAN consists of two networks, a network G for forward mapping only needs underwater and in-air images as input. Our pre- and a network F for inverse mapping. Given input images, liminary work is reported in , where we proposed the two- network G converts to the target domain and network F stage pipeline to solve underwater omnidirectional depth es- converts back to the original domain. A cycle consistency is timation. In the ﬁrst perspective image pipeline, the Water- enforced as F(G(X)) ≈ X and vice versa, to ensure the GAN  was used to transfer RGB-D images to underwater mappings will be constrained well. (us, the loss function of RGB-D images. (en, a fully convolutional residual network the forward mapping function G: X ⟶ Y is (FCRN)  depth estimation network was trained with the underwater image as input. In the second omnidirectional L G, D , X, Y � E logD (y) GAN Y y∼p (y) Y data stage, we synthesized images from in-air equirectangular + E log 1 − D (G(x)). x∼p (x) Y images to underwater equirectangular images by decreasing data the values in the red channel (due to its short wavelength (2) nature in the underwater environment) and blurring the image We use X as input to domain D and Y as input to based on its distance to the camera origin. Finally, inspired by domain D . Examples of our input images from the two , a distortion-aware convolution module replaced the Y domains are demonstrated in Figures 2 and 3. Since both our normal convolution in the FCRN based on the spherical input and output operate under the spherical domain, we longitude-latitude mapping. In this work, we replace the directly adopt the network with no modiﬁcation to the simple operations in the red channel with a learning method to convolution operators. generate synthetic underwater omnidirectional images. In Moreover, CycleGAN applies a new idea about cycle addition, we improve the method to estimate underwater consistency, which is y ⟶ F(y) ⟶ G(F(y)) ≈ y. And depth. Finally, we are more thoroughly evaluating the results of the loss function on this step is our algorithm, by estimating ground truth depths for dis- tinctive feature points. In , the FCRN  was identiﬁed as L (G, F) � E ‖F(G(x)) − x‖ cyc x∼p (x) 1 data the state-of-the-art (SOTA) network for omnidirectional (3) + E ‖G(F(y)) − y‖ . CNNs, and we thus adopt it and compare to it in this paper. y∼p (y) 1 data We want to emphasize that, in general, depth estimation Finally, the full objective for CycleGAN is from a single RGB image is a very challenging problem. As our experiments later will show, our approach does not give L G, F, D , D � L G, D , X, Y X Y GAN Y very accurate estimates, neither do the other depth esti- + L F, D , Y, X GAN X mation approaches mentioned in this section. Also, as with (4) any monocular vision problem, our results are up to an + λL (G, F), cyc unknown scale factor. Nevertheless, we believe this work to ∗ ∗ G , F � arg min max L G, F, D , D . X Y be worthwhile because it paves a path towards potentially G,F D ,D x Y more successful approaches (see the future work) and, even not being very accurate, has potential use cases, for example Because the method is pixel-to-pixel, the dataset is preprocessed by resizing the images into a reasonable size. in navigation or color correction. 4 Journal of Robotics Training: Fully convolutional residual network Corresponding In-air image RGB in-air depth + new loss function Depth prediction CycleGAN Underwater RGB Synthetic underwater images Testing: FCRN Test image Depth prediction Figure 1: Full pipeline of our approach. We propose to leverage publicly available RGB-D datasets for style transfer and depth estimation in an unsupervised approach. underwater image. We can then train our network with the converted X and D pairs. Following the recent success of depth estimation in the spherical domain , we adopt FCRN, one of the state-of- the-art single models on NYUv2 . (e network consists of a feature extraction model and then several upconvolu- tions layers to increase the resolution. Here, an UNet  is used as the backbone in all our experiments. Finally, the L1 diﬀerence will be calculated between the output depth and ground truth depth maps: � � � � � � Figure 2: A typical underwater omnidirectional image. � � L � D − D , depth � pred gt� (6) d∈x,y Compared with WaterGAN, the CycleGAN only needs where D denotes the prediction of the network, D pred gt underwater and in-air images as input, whereas WaterGAN denotes the ground truth depth map, and x, y enumerate all requires depth as input to simulate the attenuation and the pixels in the input image. scattering eﬀects. Smoothness regularization has been used frequently for depth estimation in planar images in previous research 3.2. Depth Estimation. With the recent success of con- [33, 38] to encourage the estimated depths to be locally volutional neural networks, diﬀerent CNN-based ap- similar. For depth estimation in perspective images, the term proaches are proposed to solve the supervised depth is deﬁned as follows: � � estimation task [53, 56]. However, most of the above ap- � � � � L � �∇ D p � , sm d t t proaches require large amounts of accurate image and (7) p d∈x,y ground truth depth pairs, currently unavailable in the spherical underwater domain. Instead, we propose to le- where L is a smoothness term that penalizes the L1 norm sm verage an available in-air spherical dataset, the Stanford 2D- of ﬁrst-order depth gradients along both the x and y di- 3D-S benchmark , and convert it to underwater style rections in 2D space. with StyleGAN. Speciﬁcally, given X , D pairs from the raw i i (e equirectangular projection of a 360 image, however, Stanford 2D-3D-S benchmark, we ﬁrst convert X to the is with distortion, and directly leveraging depth smoothness underwater domain X : i terms means we must impose larger weights for the point pairs with larger latitudes. Simply combining the above loss X � CycleGAN X , (5) i i designed for perspective images into the training process where X denotes the original in-air image from the dataset, might lead to suboptimal results. (e reason is that the D its corresponding depth, and X is the converted equirectangular projection of spherical images oversamples i i Journal of Robotics 5 Figure 3: Generated images with our CycleGAN. (a) On the left are examples from Domain I (in-air). (b) On the right are our generated images. We are able to produce the lightening color eﬀects from the original underwater dataset. the image in the polar regions. Taking inspiration from the exact ground truth to quantitatively evaluate the algorithm. recent work of learning in the spherical domain , we Here, we also compare to the SOTA algorithm for in-air propose that the weight of the distance of two points is based spherical images: FCRN , in two setups. We test FCRN on their spherical distance, after which we arrive at the with the synthetic (GAN) images, as well as with the original following spherical depth smoothness regularizer: RGB images as input. All algorithms are trained using the synthetic underwater images. (e second experiment uses Θ,Φ � � sph � � real omnidirectional underwater images and sparse ground � � L � ω ∇ D p , � � (8) sm θ,ϕ d t t truth points estimated via bundle adjustment to test the θ�0,ϕ�0 algorithm with in situ data. where ω are the weights for each point and ω ∝Ω(θ, ϕ). In the following, we ﬁrst introduce the datasets, θ,ϕ i,j Ω(θ, ϕ) is the solid angle corresponding to the sampled area hyperparameters, and evaluation metrics used in the sph on the depth map located at (θ, ϕ). L is a spatial experiments. sm smoothness term that penalizes the L1 norm of second-order depth gradients along both the θ and ϕ directions in 2D 4.1. Datasets. Stanford 2D-3D-S  is one of the standard space. benchmarks for in-air datasets. (e dataset provides om- Our ﬁnal loss is a weighted combination of the above nidirectional RGB images and corresponding depth infor- factors with λ as the weighting factor: mation, which is necessary data for depth estimation sph (9) training. Furthermore, it also provides semantics in 2D and L � L + λ L . depth 1 sm 3D, 3D mesh, and surface normals. In addition, we use a dataset that we collected by scuba diving in the Great Barrier Reef. We use this for training our 4. Experimental Details CycleGAN with original, spherical underwater images as We evaluate our approach with two experiments. Firstly, we well as for testing our approach. (is omnidirectional use the synthetic underwater Stanford 2D-3D-S dataset with dataset for style transfer and testing was collected with an 6 Journal of Robotics Insta360 ONE X (https://www.insta360.com/product/ insta360-onex) camera at depths between 1 m and 25 m. To evaluate the ﬁnal results from our two-stage pipeline, the ground truth depth of the underwater scenario is gen- erated based on epipolar geometry. (e generation steps are as follows: ﬁrstly, a pair of stereo images with a known baseline are used to estimate sparse map points by feature matching, ﬁve-point algorithm , and triangulation . (en, two pairs of stereo images, taken at diﬀerent times, with big enough spatial disparity, including the one for map points, are used to ﬁne-tune the position of the map points Figure 4: An example of ground truth points. (e picture is with bundle adjustment. Finally, the depth of these map captured by Insta360 ONE X camera at real ocean scenarios. Green points is normalized to 0 to 255 and used as up-to-scale points represent the interest points, whose depths are calculated by ground truth. stereopsis. Figure 4 shows an example of points (green dots) that are used as ground truth. It can be seen that most of these points be denoted by (i, j), we ﬁnd the corresponding depth in the are on the reef instead of water because the open water and ground truth and estimated depth. (e result of our esti- the surface do not have feature points. (ough only sparse mation is up to an unknown scale factor. We thus minimize points are generated, we believe that they are suﬃcient for the error by calculating the best ﬁtting scale factor for the the evaluation of our depth results. On the underwater ground truth. To do so, we calculate the scale parameter dataset used for evaluation, we generate about 100 points for between each pair of ground truth and result and then get each image. the median factor. To be more speciﬁc, in one pair of ground truth and result, there is the ratio of the ground truth value 4.2. Hyperparameters. (e hyperparameters for the style P (i, j) to the result value P(i, j) for each point pairs. (en, gt transfer include the resolution of input images, which is set using these ratios for one image, we can calculate their to 512 × 256 pixel. We then train the CycleGAN  with median s to simulate the optimization procedure, like the these hyperparameters: learning rate (2e-4) and number of least-square method, and set the median s as the scale pa- epochs (8). rameter between the ground truth and result. Finally, we We implement the FCRN for depth estimation with the rescale the result and compute the error E about each point. PyTorch framework and train our network with the fol- (e error E about each image is calculated by lowing hyperparameters settings during pretraining: mini- P (i, j) − s · P(i, j) gt batch size (8), learning rate (1e-2), momentum (0.9), weight ⎛ ⎝ ⎞ ⎠ E � Q , if P (i, j)≠ 0. (10) 1/2 gt decay (0.0005), and number of epochs (50). We gradually P (i, j) gt reduce the learning rate by 0.1 every 10 epochs. Finally, we tune the whole network with learning rate (1e-4) for another Here, the operation Q is to calculate the median of all 1/2 20 epochs. λ is set to 1e-4 in all our experiments. cases for the ground truth points and the result points. 5. Results 4.3. Metrics. For our depth estimation network, we adopt FCRN  and compare the model with the initial loss In this section, we will demonstrate the results on the function and our new loss function. Apart from these two converted Stanford 2D-3D-S dataset and real underwater networks, we also use FCRN based on the original in-air images collected in the Great Barrier Reef. images, which are not processed by CycleGAN. For eval- uation, we use the following common metrics for the 5.1. Evaluation of Synthetic Images. Since there are few comparisons on the datasets mentioned above: root mean ���������������� underwater datasets with ground truth depth, we synthesize square error (RMS) (1/T) (g − z ) , mean relative p p p underwater style images from the Stanford 2D-3D-S dataset. error (Rel) (1/T) (‖g − z ‖/g ), mean log 10 error CycleGAN  is used to generate synthetic underwater p p p p (log 10 ) (1/T) ‖log g − log z ‖, and pixel accuracy as images in this work. Figure 4 shows several examples of the p 10 p 10 p gt gt synthetic images. It can be seen the generated images suc- the percentage of pixels with max((z /z ), (z /z ))< δ for i i i i 2 3 cessfully transfer the in-air images to underwater style, es- δ ∈ [1.25, 1.25 , 1.25 ]. T denotes the numbers of pixels and pecially with respect to color. g and z represent the ground truths and the depth map p p One interesting phenomenon during the transfer is that predictions, respectively. if we attempt to train for many epochs in the style-transfer network, a lot of unnecessary and unreasonable features are 4.4. Metric for Real Experiment. To evaluate the ﬁnal results also learned. However, in most cases, we just need to transfer of our two-stage approach, we rely on the sparse ground some speciﬁc features, like color. (e testing on our own truth points captured with the approach described in Section underwater dataset revealed that the estimation results for 4.1. (Datasets). For all nonzero points, whose positions will some water-only parts are not accurate enough. (is may Journal of Robotics 7 Figure 5: Generated depth from style-transferred underwater Stanford 2D-3D-S dataset. (a) On the left are the input images. (b) On the right are the corresponding predicted depth maps. also be due to the fact that indoor scenarios are too diﬀerent of our knowledge, we are the ﬁrst to propose an algorithm from the underwater domain. for depth estimation on spherical underwater images. Fig- ure 6 demonstrates the estimated depth on our underwater Figure 5 presents the results of the estimated depth from the synthetic underwater Stanford 2D-3D-S dataset, where dataset. Similarly, it can be seen that the brighter parts on the right correspond to areas more far away on the right of brighter pixels represent a larger depth and darker pixels are closer. It can be seen that the estimated depths on the right of Figure 6, which implies that the network at least estimates Figure 5 corresponding to the left image are acceptable, es- the depth correctly in some regions. pecially the further area. Additionally, Table 1 gives a more Because our network is based on the Stanford 2D-3D-S rigorous evaluation of the results. Comparing to the classic dataset, in which the original images are all lacking the upper FCRN network, our improved loss function gives slightly and lower parts (15.6% of the image height for each part), better results as indicated by the smaller RMS, Rel, and log10. these parts are ﬁlled with pure black pixels. (erefore, the It can also be seen from the FCRN RGB experiment that upper and lower parts in the ﬁnal results about underwater using RGB images for training the SOTA network gives far depth estimation are also not evaluated. In the other words, we only use panorama images instead of spherical images worse results compared to ours and also to FCRN trained with GAN images. Because the style-transferred images actually. mainly imitate the color information, the network was (ough our underwater dataset does not have ground adopted to estimate the depth information from these truth depth maps, we can evaluate the results with the sparse images. map points. We randomly choose 20 images to test with the corresponding ground truth calculated by stereopsis. According to the metric presented, the results are shown 5.2. Evaluation of Real Underwater Images. After achieving in the ﬁrst row of Table 2. (ere, each column shows results acceptable results on the synthetic dataset, we also evaluate averaged over all images. In the ﬁrst column, we take the the results on the real underwater images. Note that we median of the errors of all pixels for which we have ground cannot compare to any other methods here, since, to the best truth in that image, in the second column we take the mean 8 Journal of Robotics Table 1: Performance comparison on 1412 images from the Stanford 2D-3D-S dataset. 2 3 Methods RMS (m) ↓ Rel (m) ↓ log10 ↓ δ< 1.25↑ δ< 1.25 ↑ δ< 1.25 ↑ sph Ours: + L 0.683 0.177 0.075 0.744 0.919 0.972 grad FCRN GAN 0.687 0.181 0.078 0.737 0.920 0.972 FCRN RGB 1.281 0.327 0.181 0.387 0.648 0.801 All tests use images transformed with GAN as input. Our approach and FCRN GAN were trained with synthetic images, while FCRN RGB uses, for comparison, RGB images as training data. (e terms are explained below. (e arrows indicate that smaller (↓) or bigger (↑) values are better. Figure 6: Generated depth from our underwater dataset. (a) On the left are the input images. (b) On the right are the corresponding predicted depth maps. We can ﬁnd the upper and lower parts (15.6% of the image width for each part) are not good, and the reasons are shown in Evaluation Section. Table 2: Performance comparison between the ground truth and various results. Results types Average median error Average mean error Average standard deviation Ours 0.22 0.40 0.62 FCRN (trained with RGB) 0.30 3.76 7.16 Black result 1.00 1.00 0.00 White result 0.95 1.10 0.65 Random noise result 0.96 2.83 3.31 Gray-scale result 0.95 1.10 7.12 Black input 0.27 3.75 7.18 White input 0.31 3.70 6.91 Random noise input 0.32 3.77 7.00 Gray-scale input 0.24 0.51 1.26 More details are shown in the Supplementary Material. Journal of Robotics 9 generated for meaningless data. But looking at the average error in each pixel, and the last column shows the standard deviation in each image, each averaged over all images. We mean error and standard deviation, we see that those generated depth maps have a very big error, thus showing can see that the average median error is 22% of the estimated depth, with a mean error of 40% and a standard deviation of that our result is clearly much better. 62%. Of course, those values show that the estimated depth is In the last row, we use the gray-scale version of the color quite inaccurate. Nevertheless, we believe that they are still frame as the input. As could be expected, this has reasonable, somewhat useful for certain applications, for example, nav- second-best results. Nevertheless, it is still worse than the igation, colorization, dehazing, or location ﬁngerprinting. color input, so the color seems to be important. Comparing Furthermore, we hope that, in the future, those values can be the result of our method to all other tests, we see that the improved, for example by better and more training data and average median error, average mean error, and average by providing a few consecutive or stereo frames as input. standard deviation are much better for our approach, clearly showing that our approach does work to a certain extend. In order to better understand the properties of our ap- proach and put the evaluation results for our method into perspective, we use the same test frames to compare with 6. Conclusions three other cases. (e new row in Table 2 shows the results of the original FCRN, trained with the normal RGB images from (is paper presented a supervised depth learning method for Stanford 2D-3D-S. When testing this network with our real underwater spherical images. Firstly, we implemented style underwater data, we see that the average mean error and the transfer based on CycleGAN to synthesize the underwater average standard deviation are very big, compared to our images. (e results show that CycleGAN learned the features proposed approach. (is shows that using the CycleGAN of underwater scenarios and synthesizes nice images in the synthetic images during training is very advantageous. Even underwater style. (ose images are then used in a second though this does not prove that the CycleGAN provides a very network, a Fully Convolutional Residual Network (FCRN), realistic underwater transfer, it is a very strong indication to train underwater spherical depth estimation. (e network towards it. is trained in a supervised manner. Our ﬁrst experiment was (e other two cases we show in Table 2 aim to show that using the synthetic images from CycleGAN for evaluation our approach is indeed doing something useful and not just and comparison with FCRN. Furthermore, we tested our giving some random values. Firstly, we make four diﬀerent method on real underwater data from the Great Barrier Reef, fake depth results for comparison. (e “black result” depth for which we estimated sparse ground truth depth points image is all black (0 distance), the “white result” depth image using stereopsis and bundle adjustment. We also compared is all white, and the “random noise result” depth image has our results to artiﬁcial input and output data, to show that random distances. Finally, there is also a depth image called the network is indeed performing depth estimation. (e “gray-scale result,” which is simply the input underwater experiments demonstrated that the style transfer, as well as image in grey scale. Please note that, in the “black result” the depth estimation results, is convincing. Our method case, there are all 0’s in the image, so the scale parameter s achieves better results than training without GAN. It ach- cannot be obtained by the metric presented above. However, ieves slightly better results than FCRN trained with GAN, so any scale that acts on 0 is itself. (us, we just change the our updated loss function is beneﬁcial. (e experiments also metric to a speciﬁc way, that is, setting scale parameter s � 1. showed that the estimated depth on real underwater images (en, the error in that case is always 1; thus, the standard is somewhat reasonable and better than all other methods deviation is 0. We can see that the evaluations of all those and options we compared to. fake results are much worse than our result. Nevertheless, the approach is far from perfect, especially Secondly, we used the same data as above (black, white, regarding the accuracy of the estimated depth. (is is mainly random noise, gray-scale input image) as the input to our due to the fact that estimating the depth from a single image is approach. (is can be regarded as a test to see if the network a very challenging task. Our approach is also not very general. is overﬁtting too much. Generating good results on (e underwater dataset was taken only at one location with meaningless data would be a clear indication of overﬁtting, very good visibility. (ere are many more underwater sce- for example, because the training data is not diverse enough. narios with diﬀering styles. So, more underwater training data We can see that the average median error is in the range of is needed. In the future, we plan to work on a uniﬁed ap- our result. We think this is due to two reasons: (i) provided proach that can work in all kinds of diﬀerent underwater with meaningless data, the network seems to generate depth situations. In addition, for testing in the real underwater images that somewhat resemble typical depth images; thus, it environments, we also plan to mask water-only areas by a might be overﬁtting a bit. (ii) (e rescaling process of our segmentation process. Collecting an in-air dataset with depth evaluation is optimizing the generated depth maps, such that that looks closer to the underwater images might also further they best ﬁt the ground truth (for the underwater image that improve our performance. (ose might be some canyons or is not being used here). (e median error of that ground deserts. Since the underwater data we collected actually also truth may be quite small for those “typical” depth images contains spherical videos from two more cameras, we will 10 Journal of Robotics Pattern Analysis and Machine Intelligence, vol. 33, no. 12, investigate using this stereo data for depth training. Fur- pp. 2341–2353, 2011. thermore, more complicated network structures that take  M. Pﬁngsthorn, A. Birk, S. Schwertfeger, H. Bulow, ¨ and previous frames into account may provide even better results. K. 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Journal of Robotics
Hindawi Publishing Corporation
Underwater Depth Estimation for Spherical Images
Journal of Robotics
, Volume 2021 –
Jun 18, 2021
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