Deep learning-based approach for high spatial resolution fibre shape sensing.pdf
ARTICLE Deep learning-based approach for high spatial resolution ﬁbre shape sensing Samaneh Manavi Roodsari 1✉, Sara Freund1, Martin Angelmahr2, Carlo Seppi1, Georg Rauter1, Wolfgang Schade2 & Philippe C. Cattin 1 Fiber optic shape sensing is an innovative technology that has enabled remarkable advances in various navigation and tracking applications. Although the state-of-the-art ﬁber optic shape sensing mechanisms can provide sub-millimeter spatial resolution for off-axis strain mea- surement and reconstruct the sensor’s shape with high tip accuracy, their overall cost is very high. The major challenge in more cost-effective ﬁber sensor alternatives for providing accurate shape measurement is the limited sensing resolution in detecting shape deforma- tions. Here, we present a data-driven technique to overcome this limitation by removing strain measurement, curvature estimation, and shape reconstruction steps. We designed an end-to-end convolutional neural network that is trained to directly predict the sensor’s shape based on its spectrum. Our ﬁber sensor is based on easy-to-fabricate eccentric ﬁber Bragg gratings and can be interrogated with a simple and cost-effective readout unit in the spectral domain. We demonstrate that our deep-learning model beneﬁts from undesired bending- induced effects (e.g., cladding mode coupling and polarization), which contain high-resolution shape deformation information. These ﬁndings are the preliminary steps toward a low-cost yet accurate ﬁber shape sensing solution for detecting complex multi-bend deformations. https://doi.org/10.1038/s44172-024-00166-8 OPEN 1 Department of Biomedical Engineering, University of Basel, Hegenheimermattweg 167C, Allschwil 4123, Switzerland. 2 Department of Fiber Optical Sensor Systems, Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, HHI, Am Stollen 19H, Goslar 38640, Germany. ✉email: samaneh.manavi@unibas.ch COMMUNICATIONS ENGINEERING |   (2024) 3:19 | https://doi.org/10.1038/s44172-024-00166-8 | www.nature.com/commseng 1 1234567890():,; F iber optic shape sensing has proven to have great potential, especially in medical applications such as catheter naviga- tion, surgical needle tracking, and ﬂexible endoscope navi- gation. Compared to other common navigation technologies (e.g., optical trackers, electromagnetic sensors, or medical imaging), ﬁber shape sensing has many advantages, such as immunity to electromagnetic ﬁelds, bio-compatibility, and high ﬂexibility. Fiber shape sensors are small in diameter, easily integrable into ﬂexible instruments, and require no line-of-sight. Distributed sensors based on multicore ﬁbers can also provide high- resolution shape measurements1,2. Fiber shape sensors measure off-axis strain, which is then used to compute the directional curvature and reconstruct the sensor’s shape3. Various ﬁber sensor conﬁgurations have been investigated for off-axis strain measurement, including multicore ﬁbers with4–6 or without7–9 ﬁber Bragg gratings (FBG) in their cores, ﬁbers with cladding waveguide FBGs10, and ﬁber bundles made from multiple single-mode ﬁbers that contain FBG arrays11–15. Accurate shape reconstruction necessitates high spatial resolution in off-axis strain measurement. With a distributed ﬁber shape sensor, sub-millimeter spatial resolution can be achieved1. However, these sensors require the use of specialized and costly optical reﬂectometers to analyze the back-scattered light and retrieve strain variations16–19. Moreover, the signal-to-noise ratio of the back-scattering trace in such sensors depends on the spatial resolution and the level of applied strain. Quasi-distributed sen- sors, on the other hand, have more cost-effective readout unit systems (e.g., FBG interrogators). However, their spatial resolu- tions are limited by the low sensing plane density4,20, making them inapplicable for tracking complex shape deformations. Therefore, there is a need for a cost-effective, high-resolution, and accurate ﬁber shape sensing technique. Among cost-effective ﬁber shape sensors interrogated in the spectral domain, eccentric FBG (eFBG) sensors show great capacity for tracking applications, thanks to their unique sensing mechanism21–23. Each sensing plane in eFBG shape sensors consists of three highly localized FBGs, written off-axis in the ﬁber’s core (also known as edge-FBG triplet), as shown in Fig. 1a21. Shape deformations are commonly computed from the displacement of the fundamental mode-ﬁeld inside the optical ﬁber, estimated through spectral intensity modiﬁcations (see Fig. 1b, c)21,22. This approach is known as the mode-ﬁeld dis- placement method (MFD). However, several other effects, including bending-sensitive mode coupling24–27, polarization- dependent losses28–32, and wavelength-dependent bending losses33–39, also modify the spectral proﬁle of eFBGs. These effects cannot be accurately modeled, and their impact on the sensor’s spectra is indistinguishable from the mode-ﬁeld dis- placements. Further details on the eFBG conﬁguration, sensing mechanism, and bending-induced effects are provided in “Methods”. In this paper, we introduce an end-to-end data-driven mod- eling technique based on deep learning (DL) that effectively identiﬁes meaningful patterns in the eFBG signal, even in the presence of uncontrolled bending-induced effects. By incorpor- ating these additional sources of information, our technique considerably improves the accuracy of shape prediction. More- over, our approach enables high spatial resolution shape esti- mation directly from the eFBG sensor’s signal, eliminating the need for strain measurement, curvature computation, and shape reconstruction steps. Results and discussion Training and testing datasets. The eFBG ﬁber sensor used in this work is 30 cm long and consists of ﬁve sensing planes separated by 5 cm from each other. At each sensing plane, three off-axis FBGs are inscribed at a radial distance of approximately 2 μm from the top, left, and right sides of the ﬁber’s core. The dataset used for developing the DL-based model is collected using a similar setup reported in our previous work40 (see “Methods” for more detail). We used three normalized spectral scans that were consecutively measured as input data to the proposed DL model. Each scan was recorded from 800 to 890 nm, comprising 190 wavelength components. The target data are the relative coordi- nates of 20 discrete points (reﬂective markers of the tracking system) measured over the length of the shape sensor (more detail on data preprocessing is available in41). This dataset con- sists of approximately 58,000 samples collected during 30 min of random movement of the ﬁber sensor. To evaluate the predictive performance of the trained model in an unbiased way, the sam- ples were ﬁrst shufﬂed and then split into Train-Validation-Test subsets, with 80% used for training, 10% for validating, and 10% for testing. In the remainder of this paper, we refer to this testing dataset as Test1. A separate set of data, denoted as Test2, con- sisting of approximately 5800 samples, was recorded to evaluate the performance of the trained model for unseen shapes resulting from continuous movement. Additionally, we collected 320 sam- ples, referred to as Test3, in which speciﬁc sensor regions were bent. Further details are provided in the Methods section. Neural network design. The DL model needs a specially designed network architecture to extract essential features from the sen- sor’s spectra and to accurately predict its corresponding shape. In this study, we employed an optimization algorithm inspired by the Hyperband optimizer42 to ﬁne-tune the network’s hyper- parameters. These hyperparameters, which cannot be directly determined from the training data, play a crucial role in model performance. Figure 2 illustrates the architecture of the best- performing conﬁguration achieved after hyperparameter tuning (see “Methods” for further details). Shape prediction evaluation. We evaluated the performance of the DL approach using the three testing datasets and compared it with the MFD method. It should be noted that the density of sensing planes in our eFBG shape sensor is insufﬁcient for the MFD method to accurately estimate complex deformations. Nevertheless, we conducted this test to highlight the superiority of the proposed data-driven technique (the DL method). Table 1 presents the shape error metrics, including the tip error, that is, the Euclidean distance between the true and the predicted coordinate of the sensor’s tip and the root-mean-square of the Euclidean distance (RMSE) between the true and the predicted coordinates of the discrete points along the sensor’s length. When using the Test1 dataset, the MFD approach yielded a median tip error of 111.3 mm with an interquartile range (IQR) of 121.5 mm. These error values were reduced to 98.5 and 46 mm when using the Test2 dataset. The performance difference can be attributed to the fact that the Test1 dataset contains more diverse shapes as the samples are randomly selected from a larger dataset, whereas Test2 represents continuous sensor movement over a shorter period. As expected, the error values are considerably high across all testing datasets since there is too little information available for the MFD approach to estimate complex shape deformations accurately. The DL method, on the other hand, considerably improved the accuracy of shape prediction for Test1 samples, resulting in a median tip error of 2.1 mm with an IQR of 2.6 mm. These values increased to 17.1 mm and 12.6 mm on the less diverse Test2 samples. This is because the DL model can only learn to extract the most general and relevant features from the input signal when ARTICLE COMMUNICATIONS ENGINEERING | https://doi.org/10.1038/s44172-024-00166-8 2 COMMUNICATIONS ENGINEERING |    (2024) 3:19 | https://doi.org/10.1038/s44172-024-00166-8 | www.nature.com/commseng convolutional layers (Conv1D), the number of fully connected layers (FC), the layer settings, the choice of batch normalization (BN) and downsampling, training settings, and loss function parameters. The search criteria are outlined in Table 2. In the designed network (Fig. 2), input samples with a batch size of 256 are ﬁrst batch normalized and then fed into a Conv1D layer with 16 channels, followed by a max pooling layer with a kernel size of 3 and a stride of 2. The second Conv1D layer also has 16 channels, followed by a max pooling layer with a kernel size of 2. The third Conv1D layer has 32 channels, followed by a max pooling layer with a kernel size of 3 and a stride of 2. The fourth Conv1D layer also has 32 channels with a stride of 2, followed by a max pooling layer with a kernel size of 3. The last Conv1D layer has 256 channels, followed by batch normalization and a max pooling layer with a kernel size of 2 and a stride of 2. The extracted features are ﬂattened to a 2048-long vector, fed into 5 FC layers, each with 2000 units. The ﬁrst FC layer is followed by batch normalization, a dropout layer with a probability of 0.37, and two more FC layers. A batch normalization, an FC layer, a dropout layer with a probability of 0.16, and a ﬁfth FC layer are the remaining layers before the ﬁnal layer. The last layer is an FC layer that maps the output of the ﬁfth FC layer into the target values, the relative coordinates. In all layers of this network architecture, the rectiﬁed linear unit (ReLU) serves as the activation function, and the kernel size for the Conv1D layers is 3. In this model, the Adam optimizer with a learning rate of 0.0001 minimizes the SmoothL1 loss function with a threshold of 4.04. Decoding the model’s decisions. Inspired by the concept of Gradient-weighted Class Activation Mapping (Grad-CAM), we Table 2 The search criteria for hyperparameter optimization. Hyperparameter Search space Selected values Number of Conv1D layer min: 1, max: 20, step: 1 5 Number of FC layer min: 1, max: 20, step: 1 5 BN after each layer true, false – Dropout after FC layer true, false – Dropout rate min: 0.1, max: 0.8 – Stride min: 1, max: 2, step: 1 – Kernel size (max pooling layer) min: 2, max: 3, step: 1 – Distribution of initial weights standard, Xavier_uniform, Xavier_normal, Kaiming_uniform, Kaiming_normal Xavier_normal Learning rate 0.01, 0.001, 0.0001, 0.00001 0.0001 Sorting Conv1D layers true, false true L2 regularization 0.1, 0.01, 0.001, 0.0001, 0.00001, 0 0 Threshold in SmoothL1 any values between 0.0 and 5.0 4.04 Conv1D 1D convolutional layer, FC fully connected layer, BN batch normalization. 1 2 5 4 3 6 1 2 3 4 5 6 Tracking Camera Interrogator Fiber Sensor Reflective Marker Curvature Template Protecting Tube Fig. 5 Experimental setup for data acquisition. The motion capture system consisted of ﬁve tracking cameras (Oqus 7+, Qualisys AB, Sweden). For protection purposes, the ﬁber sensor was inserted in a Hytrel furcation tubing with an inner diameter of 425 μm and an outer diameter of 900 μm. Two v-clamps were used to hold the protection tubing securely and to ﬁx the optical ﬁber in place before the insertion. Reﬂective markers with a diameter of 6.4 mm and an opening of 1 mm (X12Co., Ltd., Bulgaria) were afﬁxed to the sensor. Additionally, a thermocouple was positioned near the sensor’s base to monitor the temperature throughout the data acquisition process, ensuring that any sudden thermal ﬂuctuations did not impact the sensor’s signal. ARTICLE COMMUNICATIONS ENGINEERING | https://doi.org/10.1038/s44172-024-00166-8 8 COMMUNICATIONS ENGINEERING |    (2024) 3:19 | https://doi.org/10.1038/s44172-024-00166-8 | www.nature.com/commseng decoded the decisions made by our CNN (convolutional neural network)-based model. By decoding our model’s decisions, we gained insights into which parts of the input spectra contribute to coordinate predictions. Grad-CAM is a widely used technique in image classiﬁcation tasks that generates visual explanations from any CNN-based model without requiring re-training or archi- tectural modiﬁcations. The gradient is a measure that shows the effect on the output caused by the input, indicating the part of the input with the highest impact on the model’s output. However, the gradient heat map produced by the last Conv1D layer has limited resolution due to the small output dimension in each channel. Therefore, instead of the gradient of the Conv1D layers, we computed the forward ﬁnite difference of the model’s loss with respect to the input spectral elements. The spacing constant was chosen to be 0.1, higher than the spectral intensity noise level. In this method, we modiﬁed the intensity value of one spectral element and observed the resulting changes in the model’s loss value. We repeated this process for all 190 spectral elements. The resulting color maps are illustrated in Figs. 3b and 4b, representing the impact of the changes in each spectral element on the model’s SmoothL1 loss value. To analyze the contribution of each spectral element to the coordinate prediction of individual markers, we computed the Euclidean distance between the predicted coordinates of each marker before and after spectral modiﬁcation. This allowed us to identify the spectral elements contributing to the relative coordinate prediction of each marker. By highlighting these spectral elements, we gained a better understanding of the factors inﬂuencing the model’s predictions. Data availability The datasets generated during and/or analyzed during the current study are available in the Academic Torrents repository. 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Acknowledgements We gratefully acknowledge the funding of this work by Werner Siemens Foundation through the MIRACLE project. The authors express their appreciation to Yi Jiang for performing the eFBG calibration. Author contributions All authors participated in the discussions and contributed to the completion of this paper. S.M.R. designed and built the experimental setup, conducted experiments, implemented the deep learning model, and, in collaboration with P.C.C., analyzed the results. C.S. imple- mented the hyperparameter optimization algorithm. M.A. and W.S. supplied the eFBG ﬁber sensor and validated the analytical MFD approach, serving as the baseline for sensor evaluation. S.F., G.R., and P.C.C. provided supervision throughout the entire research process. S.M.R. and P.C.C. wrote the paper with input from the other co-authors. Competing interests The authors declare no competing interests. Additional information Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s44172-024-00166-8. Correspondence and requests for materials should be addressed to Samaneh Manavi Roodsari. Peer review information Communications Engineering thanks the anonymous reviewers for their contribution to the peer review of this work. Primary Handling Editors: Mengying Su. A peer review ﬁle is available. Reprints and permission information is available at http://www.nature.com/reprints Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional afﬁliations. 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Title: Deep learning-based approach for high spatial resolution fibre shape sensing ​
Authors: Samaneh Manavi Roodsari ​,Sara Freund,Martin Angelmahr,Carlo Seppi,Georg Rauter,Wolfgang Schade,Philippe C. Cattin
Publisher: Springer Nature ​
Date: 15 January 2024 ​
Abstract: Fiber optic shape sensing is an innovative technology that has enabled remarkable advances in various navigation and tracking applications. ​ Although the state-of-the-art fiber optic shape sensing mechanisms can provide sub-millimeter spatial resolution for off-axis strain measurement and reconstruct the sensor’s shape with high tip accuracy, their overall cost is very high. ​ The major challenge in more cost-effective fiber sensor alternatives for providing accurate shape measurement is the limited sensing resolution in detecting shape deformations. ​ Here, we present a data-driven technique to overcome this limitation by removing strain measurement, curvature estimation, and shape reconstruction steps. ​ We designed an end-to-end convolutional neural network that is trained to directly predict the sensor’s shape based on its spectrum. ​ Our fiber sensor is based on easy-to-fabricate eccentric fiber Bragg gratings and can be interrogated with a simple and cost-effective readout unit in the spectral domain. ​ We demonstrate that our deep-learning model benefits from undesired bending-induced effects (e.g., cladding mode coupling and polarization), which contain high-resolution shape deformation information. ​ These findings are the preliminary steps toward a low-cost yet accurate fiber shape sensing solution for detecting complex multi-bend deformations.