dataesr/scientific-paragraphs-categorization huggingface dataset:
We use the ICP algorithm implemented in the Python package xDEM (version 0. 0. 5; xdem contributors, 2021), using core functionality from the OpenCV suite (OpenCV contributors, 2021). We run the co-registration in all areas where the dense clouds overlap, plus a buffer of ±15 m (chosen qualitatively through trial and error), to limit the co-registration to reasonable offsets. Once the stereo-panoramas are aligned to each other, a new camera model is calculated with a bundle adjustment and new dense clouds are generated for each subset individually. We filter the dense clouds by excluding points with a "confidence" of less than or equal to 2. This threshold is chosen qualitatively by visually assessing the effect on noise for a few arbitrarily selected dense clouds. The confidence is a statistic provided by the Metashape software, but information on how it is calculated is unavailable.
Temporal standardisation Because both the historical and modern elevation datasets were acquired over several years  (1916-1947 and 2007-2018, respectively) , it is necessary to standardise the periods of observation for the evaluation and interpretation of the results. We adjust each elevation change map to the median years 1931 and 2016 based on an annual dataset of observed mass balance variations that is specified for the major hydrological basins of the Swiss Alps (point 4 in Sect. 2. 3). Regional anomalies in mass balance from the reference period 1961-1990 have been derived by spatially extrapolating all available series acquired using the direct glaciological method (between 8 and 20 glaciers;  Huss et al. , 2015; GLAMOS, 1881 GLAMOS, -2020)). Before 1955, modelled mass balance variations for four glaciers were used  (Huss et al.
e. scaling both elevation and elevation change from 0 to 1 for each glacier in 5th percentiles  (Huss et al. , 2010b). More specifically, we use the approach as implemented in the Python package xDEM. This approach relies on elevation changes estimated at different elevation bins and aims at capturing the glacier-wide hypsometric signal. Consequently, the quality of the interpolation deteriorates with decreasing spatial coverage. For our application, we choose this approach where > 20 % of the glacier area is covered (91. 1 % of all glaciers by area meet this criterion). For glaciers that do not meet this condition, we apply a simple regional hypsometric approach, in which gaps are replaced by the mean regional value within the same elevation band.
We derive the number of effective samples by numerically integrating a sum of variogram models fitted to our empirical variograms within a circular area of the same size as the glacier (Fig. 4 ;  Hugonnet et al. , 2021). This is a generalisation of the approach by  Rolstad et al. (2009). We use the implementation in the Python package xDEM based on spatial statistics of the Python package SciKit-GStat  (Mälicke, 2022).
Glacier outline uncertainty We identify three major sources of uncertainties from the glacier outlines drawn from the LK50 maps: the georeferencing error of the map, the timing uncertainty of the topographic data used (which is unknown but was assumed to largely be the TerrA dataset), and the errors in manual delineation (including the subsequent digitisation from the map) of a glacier front. The temporal concurrency of the LK50 map with the TerrA imagery particularly needs validation as the extent to which data from other times were used is unknown. In the case where the outlines are spatially consistent with the TerrA dataset, the concurrency assumption is verified. We evaluate these three uncertainty sources combined by digitising sparse outlines at 61 sites from orthorectified versions of the photographs generated in the photogrammetric pipeline.
We attribute this difference to (i) poor georeferencing of either dataset; (ii) temporal inconsistencies in the map data, which might not uniformly represent the year 1927; or (iii) a combination of these factors. Also note that for being consistent with  Bauder et al. (2007) , the above values are obtained by excluding the tributary Mittelaletschgletscher. Before 1969, the latter was confluent with Grosser Aletschgletscher  (GLAMOS, 1881 (GLAMOS, -2020;;  this is also reflected in the LK50 outlines). Similar outline inconsistencies at other glaciers might contribute in explaining differences between the two studies as highlighted in Fig. 10a. The above comparison also reveals a potential shortcoming of our interpolation approach near the glacier margins. Indeed, the proximity to glacier margins was not considered, meaning that changes can be overestimated at these specific locations.
The single observation time period in our study  prevents us from analysing the climatic factors (e. g. temperature, precipitation) that control the temporal variability in glacier mass balance. Such an analysis was already performed by  Huss et al. (2010a) , who used annual mass balance series and found that the multi-decadal mass balance variability is significantly anticorrelated to the Atlantic Multi-decadal Oscillation. By leveraging different datasets, e. g. from repeated aerial surveys or satellite observations, it would be possible to obtain more frequent observations  (Bauder et al. , 2007; Rastner et al. , 2016; Mölg et al. , 2019). This could help constrain the multi-decadal variability in glacier mass changes but is understandably beyond the scope of our study.
Parameter New analysis that is based on terrestrial surveys. Indeed, the time required to acquire such data will always lead to a temporal spread in the time of acquisition. Although this problem is decreasing in importance for modern surveys thanks to a wider image swath, the analysis of historical photographs requires careful consideration of the issue. We suggest that temporal standardisation, in line with (or better than) our study, is a fundamental step in post-processing and interpreting the results derived from historical surveys -especially terrestrial ones. Future improvements in our workflow may help further increase the spatial coverage of the dataset and reduce coregistration errors. While our Swiss-wide total specific mass balance uncertainty is low (0. 09 m w. e. a -1 ), uncertainties at the scale of individual glaciers are on the same order of magnitude as (and sometimes higher than) the magnitude of the change (0.
01-0. 62 m w. e. a -1 , with a median of 0. 17 m w. e. a -1 ). The interpolation necessary over 55 % of the analysed area was the largest contributor of uncertainty in our analysis (0. 00-0. 39 m w. e. a -1 for individual glaciers; Fig. 4c ). Higher coverage or a more accurate interpolation method may reduce this. The TerrA dataset has a theoretical maximum glacier coverage of ca. 86 %, meaning that only about half of the theoretical maximum was realised in our reconstruction. Newer photogrammetric methods, especially those rooted in the machine learning domain (e. g. Mildenhall et al. , 2020; Zheng et al. , 2020; Sarlin et al. , 2020) , can help improve feature description or depth reconstruction. This may increase the coverage of the resulting datasets compared to the methods currently implemented in Agisoft Metashape.
In this respect, we attempted to replace the feature matcher with ASIFT  (Morel and Yu, 2009) , but long processing times and a general lack of robustness to image noise led us to abandon the idea. Concerning the TerrA dataset, it is remarkable that reanalyses such as that presented here are possible at all for a dataset that is almost 100 years old and in some cases even older. This possibility is only provided by the systematic, thorough, and meticulous archiving that was performed at that time and by the preservation efforts that have been invested since then. The Swiss Federal Office of Topography deserves credit for this. In this context, it is in-teresting to note that what have now become known as the "FAIR Guiding Principles for scientific data"  (Wilkinson et al. , 2016)  were respected over the course of almost a century.
Indeed, the FAIR principles require the data to be findable (F), accessible (A), interoperable (I), and reusable (R), and all of these criteria are met for the TerrA archive: the images are easily found and accessed via swisstopo's geodata portal (https://www. swisstopo. admin. ch/en/ geodata/images/terrestrial. html, last access: 1 July 2022), are made interoperable by being distributed in a commonly accepted digital data format, and are reusable thanks to the rich and self-explaining metadata that complement the individual images. Similar databases exist in many other countries including, although not limited to, the United States of America (https://earthexplorer. usgs. gov, last access: 1 July 2022), France (https://remonterletemps. ign. fr, last access: 1 July 2022), and Sweden (https://www.
Conclusions In this study, we utilise 21 703 terrestrial photographs from the TerrA archive recently made accessible by the Swiss Federal Office of Topography to quantify glacier change over the entire Swiss Alps since 1931. We take advantage of modern photogrammetric techniques and the software Agisoft Metashape to re-process the scanned images in a semi-automated fashion. We use the procedure to reconstruct the ca. 1931 topography for 45 % of the glaciers in the region. We estimate a Swiss-wide glacier mass balance of -0. 52 ± 0. 09 m w. e. a -1 and an area reduction of 6. 2 ± 0. 8 km 2 a -1 between 1931 and 2016. This translates to a halving of glacier volume and a reduction in areal cover by a third. Our results indicate a strong spatial variability in glacier thinning, with glaciers in the north-east losing mass twice as rapidly as in the south-west of Switzerland.
Acknowledgements. We would like to thank swisstopo for acquiring, archiving, scanning, and distributing the TerrA images. This work would not have been possible without over 100 years of efforts. We are particularly grateful to  Philip Joerg  and  Matthias Zesiger  for providing additional details on the images' metadata and acquisition. We are grateful to  Roxana Zehtabchi  for early developments of the data-processing workflow. We would like to thank  Timothée Produit  and  Adrien Gressin  ( HEIG-VD ) for sharing initial TerrA viewsheds and for discussions on the TerrA archive. Financial support. Amaury Dehecq ,  Romain Hugonnet ,  Matthias Huss , and  Daniel Farinotti  received funding from the  Swiss National Science Foundation  (grant no. 184634 ). This project was funded by the  Federal Office of Meteorology and Climatology Me -teoSwiss in the framework of  GCOS Switzerland.
Code and data availability. The source code of the photogrammetric analysis is available at https://doi. org/10. 5905/ethz-1007-552 (Mannerfelt, 2022a). The code for post-processing, uncertainty, and mass balance is available at https://doi. org/10. 5905/ethz-1007-553 (Mannerfelt, 2022b). The Python package xDEM was partly developed for this project and is available at https://doi. org/10. 5281/zenodo. 4809697 (xdem contributors, 2021). All intermediate and output data for this analysis are available at https://doi. org/10. 5281/zenodo. 6675911 (Mannerfelt et al. , 2022).
Small and lightweight unmanned ground or aerial vehicles are perfect devices to reach places otherwise barely accessible and, hence, are often used to venture off road in environments where direct cues about distance, such as object structures, are unknown. Natural landscapes are examples of such environments whose elements (vegetation, ground and relief) do not exhibit normalized structures or patterns. However, datasets suitable to study the task of depth estimation in environments with little structure-we call them "unstructured environments" in the following-were proposed only recently (see Fonder and Van Droogenbroeck  [6] , Wang et al. [7] ). As a result, existing methods for outdoor depth estimation  [8] [9] [10] [11] [12]  are benchmarked against older datasets that only target autonomous driving applications in urban environments.
These methods are all trained to directly infer depth or its inverse, known as disparity. As the motion of a car on a road is strongly constrained and urban areas contain many objects with a specific structure (cars, roads, signs, buildings, etc), the autonomous driving datasets mainly feature constrained trajectories and environments. Since the structure and semantics of elements in a scene likely provide direct cues about depth, it is uncertain if existing methods perform well in environments where such cues are not available. Furthermore, learning to directly infer depth or disparity reduces the capability of networks to generalize in environments where the depth distribution differs from the one used for training. In this paper, we address the challenging task of estimating depth in unstructured environments.
This is taken care of by constructing a dedicated loss function for training and by minimizing the error relative to the distance of the object. During testing, we will use the set of performance metrics defined by Eigen et al. [43]  to better grasp the behavior of our method. Our baseline. Based on the related work, we have selected a representative set of existing methods for which the training code is available, as given in Table  1 ; they constitute the baseline for our performance tests. In this table, we indicate for each method, respectively, the nature of its supervision mode, if it is based on a single or multiple frames, if it is recurrent, how it deals with the camera pose, and if weights for the KITTI are provided by the authors.
Experiments In this section, we present three experiments to analyze the performance of our method. For each of them, we detail the chosen dataset, the training (if appropriate), and discuss the results. Our first and second series of experiments aim to assess the performance in unstructured environments, as driven by our problem statement, and on a standard benchmark, respectively. The experiments present comparisons with baseline methods that might significantly differ, in terms of training procedure, number of parameters, etc. In order to disentangle the intrinsics of the training phase, we have devoted our third series of experiments to generalization tests. We use the metrics from Eigen et al. [43]  for depth maps capped at 80 m to compare the performance of each method. Additionally, we replicate the experiments performed on M4Depth with PWC-Net  [44]  to evaluate the benefits of our proposal over its parent.
As PWC-Net is an optical flow network, we use Equation (  1 ) to obtain the frame-toframe optical flow from depth and motion for training the network. During testing, we compute depth by assuming that the length of the optical flow vectors corresponds to the visual parallax. Please note that we provide all the codes of M4Depth and tested methods on GitHub (https://github. com/michael-fonder/M4Depth), both for training and testing modes.
Unstructured Environments For our first experiment, we compare the performance of our method with those of the state-of-the-art on a dataset featuring unstructured environments. Mid-Air dataset. For this experiment, we used Mid-Air  [6]. This synthetic dataset consists of a set of drone trajectories recorded in large, unstructured, and static environments under varied weather and lighting conditions. All trajectories were recorded in different places of the environments, which means that there was little overlap between the visual content of two individual trajectories. This allows one to build a test set whose content is not present in the training set while belonging to the same data distribution. In addition, Mid-Air meets all the assumptions of our problem statement (see Section 3), which makes it a perfect choice.
The first performance reported on Mid-Air for depth estimation was provided recently by  Miclea and Nedevschi [54]. The authors of this paper do not, however, provide the details required to reproduce their train and test splits and their results. As a result, we have to define our own splits. The dataset features 192 trajectories. We selected one in three to create our test set, which was more varied than the small test set suggested in the original paper  [6]. The frame rate was subsampled by a factor of four (from 25 to 6. 25 fps) to increase the apparent motion between two frames. For all our experiments, images and depth maps were resized to a size of 384 × 384 pixels. We used bilinear interpolation to resize color images and the nearest-neighbor method for depth maps. Training. We used the He initialization  [55]  for our variables and the Adam optimizer  [56]  for the training itself.
We used the default moment parameters for the latter (β 1 = 0. 9, β 2 = 0. 999). The learning rate was set to 10 -4. We trained our network with six levels. All our trainings were performed on sequences of four time steps and with a batch size of three sequences. The network was trained on a GPU with 16 GB of VRAM for 220 k iterations. After each epoch, we computed the performance of the network on the validation set of the KITTI dataset to avoid any overfitting, and keep a copy of the best set of weights to be used for the tests after the training. A series of data augmentation steps were performed on each sequence during the training to boost the robustness of our trained network to visual novelties. More precisely, we applied the same random brightness, contrast, hue, and saturation change to all the RGB images of a sequence and the colors of a sequence were inverted with a 50% probability.
Finally, we randomly rotated the data of the sequence by a multiple of 90 degrees around the z-axis of the camera when training on Mid-Air. With these settings, a training takes approximately 30 h. Because of the lack of reproducible performances reported on Mid-Air, we had to train a selection of state-of-the-art methods drawn in Table  1  to build a baseline. The training details for the chosen methods are given in the Appendix A. We could not guarantee obtaining the best performance out of DeepV2D  [42]  because of the importance of its hyper-parameters and the excessive duration of its training time. We, therefore, decided to discard it for this experiment. Results. The results are reported in Table  2. In this table and following tables, the best score for a metric is highlighted in bold and the second best is underlined.
Standard Depth Estimation Benchmark The purpose of the second experiment was to assess the performance on a standard depth estimation benchmark. KITTI dataset  [14]. Most real datasets that provide RGB+D and motion data focus on cars driving in partially dynamic urban environments  [14, 57, 58]. In this field, KITTI is the reference benchmark dataset when evaluating the performance of a depth estimation method. KITTI is not fully compliant with our problem statement: it has incomplete depth maps, there are some moving objects, and the camera has only three degrees of freedom, etc. Despite that, it is a good practical choice for performing tests on real data. We used the dataset split proposed by Eigen et al. [43]. The camera pose was estimated by a combined GPS-inertial unit and was therefore subject to measurement imperfections.
Shortcomings created by these imperfections can be mitigated by fine-tuning on both datasets. During the fine-tuning, we also performed random color augmentation on the sequences. With these settings, the fine-tuning takes three hours. Results. The performance of M4Depth with six levels on the KITTI dataset is reported in Table  3. Table  3. Performance of M4Depth (best of 5 trainings) on the KITTI dataset. The scores reported for reference methods are the ones published by their respective authors. The best score for a metric is highlighted in bold and the second best is underlined. The four first metrics need to be minimized (↓) and the three last ones need to be maximized (↑).
Generalization In this last experiment, we wanted to evaluate the generalization capabilities of all the methods. For this, we wanted to use static scenes that were semantically close to either the Mid-Air dataset (natural unstructured environments) or the KITTI dataset (urban environments), and test the performance of the method trained on Mid-Air (respectively KITTI) on the selected unstructured (respectively urban) scenes without any fine-tuning. As we wanted to focus only on the generalization performance for depth estimation, we bypassed the pose estimation network for ManyDepth and DeepV2D, and used the ground-truth motion to generate the depth maps with these methods. Additionally, the depth maps produced by baseline methods were not guaranteed to be at the correct scale. To alleviate this issue in performance tests, we applied a median scaling to the depth maps of baseline methods.
TartanAir dataset  [7]. For this experiment, we used TartanAir. It is a synthetic dataset consisting of trajectories recorded by a free-flying camera in a series of different environment scenes. With each scene being relatively small in size, there is a lot of overlap in the visual content recorded for different trajectories within a same scene. As such, assembling clearly separated train and test sets drawn from the same data distribution is not possible. Despite this drawback, the diversity of the scenes makes TartanAir an interesting choice for testing the generalization capabilities of methods. For the generalization test from the Mid-Air dataset, we selected the "Gascola" and "season forest winter" scenes of TartanAir and used the weights trained for the baseline. For the one from the KITTI dataset, we selected the "Neighborhood" and "Old Town" scenes and used the pre-trained weights released by the authors of the methods.
We resized the images of this dataset to 384 × 576 pixels and subsampled the frame rate by a factor of two. Additionally, some scenes appeared to have large, underexposed areas where there was no color information in the RGB frames. Having large pitch-black areas in an RGB image is unrealistic in practice as cameras dynamically adapt their shutter speed depending on the exposure of the scene. To prevent the errors made by depth estimation methods in these areas from dominating the performance analysis, we discarded all the pixels for which the color in the RGB image had a value equal to zero. Results. The results of our experiments are reported in Tables  4  and 5. Overall M4Depth outperforms the other methods with a significant margin both for structured and unstructured environments. As on Mid-Air, PWC-Net slightly outperforms M4Depth on some relative metrics, but not for both sequences.
Method Test Size Abs Rel ↓  [16]  384   5. Performance for the generalization test on two structured environments from TartanAir, that are neighborhood (N) and old town (OT). Scores were generated by using the same network weights as the ones used to report the performance on KITTI in Table  3. The best score for a metric is highlighted in bold and the second best is underlined. The four first metrics need to be minimized (↓) and the three last ones need to be maximized (↑). The images obtained in generalization on TartanAir are shown in Figures  6  and 7. It can be seen that the visual quality of the outputs in generalization is similar to that of the outputs produced on the dataset used for training. This confirms the strong performance of M4Depth in generalization as established with metrics.