dataesr/scientific-paragraphs-categorization huggingface dataset:
Positioning of satellites and space probes GENESIS will provide a breakthrough in space geodesy and by this will contribute to improving the accuracy of many satellite orbits, and consequently, the accuracy of the parameters that these satellites observe. POD is an integral part of analyzing the data of numerous Earth science missions and of inter-planetary space probes. Prominent examples of past, present and future missions devoted to Earth observation are radar altimetry missions such as TOPEX/Poseidon, Jason-1, -2, -3, Sentinel-3, and Sentinel-6A, laser altimetry missions such as ICESat-1 and -2, gravity missions such as CHAMP, GRACE, GOCE, and GRACE-FO, and many other missions such as the SAR/InSAR missions TerraSAR-X, TanDEM-X, and Sentinel-1, the magnetic field mission Swarm or further satellites of the Copernicus Earth observation program of the European Union.
Acknowledgements The GENESIS mission is supported by many scientists, industrial partners, and space agencies, namely:  Elisa Felicitas Arias (Paris Observatory-PSL, France), François Barlier (Côte d' Azur Observatory, France), Bruno Bertrand (Royal Observatory of Belgium, Belgium) ,  Claude Boucher  ( Bureau des Longitudes, France ),  Sara Bruni  ( PosiTim UG  at  ESA/ESOC, Germany), Carine Bruyninx (Royal Observatory of Belgium, Belgium) ,  Hugues Capdeville  (CLS,.
Funding JB and AN are grateful to the  Austrian Science Fund (FWF)  for supporting this work with project  P33925. Work by SD has been supported by  INFN  and by  ASI (Italian Space Agency)  under the  ASI-INFN Joint Lab Agreement n. 2019-15-HH. 0. The contribution of JM was supported by the  Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via Collaborative Research Center CRC   1464  " TerraQ ", project- ID 434617780, and Germany's Excellence Strategy EXC 2123  " QuantumFrontiers ", project-ID 390837967. Work by SG has been supported by the  German Research Foundation (DFG)  under Grant Number  SCHU 1103/8-1  ( GGOS-SIM, Simulation of the Global Geodetic Observing System ) and  SCHU 1103/8-2  ( GGOS-SIM-2 ). The research of VD and HS leading to some of these results has received funding from the  European Research Council  under  ERC  advanced grant  670874  ( RotaNut-Rotation  and Nutation of a wobbly Earth), as well as  ERC synergy Grant   855677  (GRACE-FUL-Gravimetry, magnetism and core flow).
Depth estimation from monocular images has become a prominent focus in photogrammetry and computer vision research. Monocular Depth Estimation (MDE), which involves determining depth from a single RGB image, offers numerous advantages, including applications in simultaneous localization and mapping (SLAM), scene comprehension, 3D modeling, robotics, and autonomous driving. Depth information retrieval becomes especially crucial in situations where other sources like stereo images, optical flow, or point clouds are not available. In contrast to traditional stereo or multi-view methods, MDE techniques require fewer computational resources and smaller datasets. This research work presents a comprehensive analysis and evaluation of some state-of-the-art MDE methods, considering their ability to infer depth information in terrestrial images.
INTRODUCTION Estimating depth from a single image, known as Monocular Depth Estimation (MDE, Figure  1 ), is a fundamental task in the field of computer vision and it is getting also useful in various photogrammetric task. MDE processes hold numerous advantages, being supportive and complementary for simultaneous localization and mapping (SLAM), scene understanding, 3D modelling, robotics, and autonomous driving. The retrieval of depth information becomes especially crucial in scenarios where alternative sources like stereo images, optical flow, or point clouds are unavailable  (Bhoi et al, 2019). Traditional depth estimation methods using stereo images or video sequences  (Kong and Black, 2015; Cheng and Huang, 2015; Ha et al. , 2016; Wei et al. , 2022; Hossain and Lin, 2023; Stathopoulou and Remondino, 2023) , require extensive computational resources and larger datasets than monocular depth estimation techniques, thus leading to the rise of MDE based on deep learning methods that rely on convolutional neural networks rather than hand-crafted features.
Paper motivations and aims As MDE has become a key topic of research in the photogrammetric and computer vision communities, a holistic understanding and quantitative evaluation of state-of-the-art methods is necessary. MDE could be a complementary approach to photogrammetric multi-view stereo (MVS) methods or it could support navigation tasks or scene understanding. Therefore, this research work aims to: • Analyze and test some state-of-the-art methods able to infer depth information from single terrestrial images; • Perform quantitative evaluations (cloud-to-cloud distances, MAE, RMSE, MTF, etc. ) with available ground truth data. Despite the numerous state-of-the-art depth estimation algorithms, it is important to evaluate their performance across various datasets and environments. Each algorithm is designed with specific assumptions and optimizations, making it challenging to claim that a single algorithm can effectively address all possible applications and scenarios.
MDE methods This paper is dedicated to exploring monocular depth estimation (MDE) and thoroughly evaluating specific algorithms that play a crucial role in this area. From various available algorithms like VPD  (Zhao et al. , 2023) , NVDS  (Wang et al. , 2023) , DINOv2  (Oquab et al. , 2023) , DepthFormer  (Li et al. , 2023) , etc, we have chosen DPT, ZoeDepth, MiDaS, and DenseDepth. The scientific literature and other reputable sources like Paper with Codes have highlighted these algorithms as top performers, driving our selection. By concentrating on these algorithms, our study seeks to uncover their unique characteristics and contributions, shedding light on their significant roles in the complex realm of monocular depth estimation. It is important to note that in the dynamic landscape of MDE, there is no single algorithm that universally outperforms others across all datasets and scenes.
This resultant vector is then channeled through a sequence of successive up-sampling layers  (Lehtinen et al. 2018) , facilitating the creation of the final depth map at half the initial resolution. The configuration of these up-sampling layers, coupled with their corresponding skip-connections, constitutes the decoder component. The training of DenseDepth models involved 1 million iterations on the NYU Depth V2 dataset and 300,000 iterations on the KITTI dataset.
MiDaS v3. 1 -A Model Zoo for Robust Monocular Relative Depth Estimation  (Ranftl et al. , 2020) : the MiDaS family of models has its roots in a critical study within the realm of relative depth estimation where it is reported the value of dataset integration to attain superior zero-shot performance across diverse datasets. Depth prediction is executed within the realm of disparity space, encompassing inverse depth with considerations for scale and shift. Training employs losses that are invariant to scale and shift to address uncertainties in true depth labels. Existing datasets for depth estimation are amalgamated and enriched with frames and disparity labels extracted from 3D films, thereby creating an extensive meta-dataset. As the evolution of MiDaS releases has unfolded through various iterations, a progressively increasing number of datasets have been integrated over time.
Input Encoder Decoder Output Figure  3 : The MiDaS architecture. ZoeDepth -Zero-shot Transfer by Combining Relative and Metric Depth  (Bhat et al. , 2023) : it combines both monocular depth estimation (MDE) and relative depth estimation (RDE) approaches in a two-stage framework (Figure  44 ). In the first stage, an encoder-decoder structure is trained to estimate relative depths from the input image. This model is trained on a large variety of datasets, which improves its generalization to different scenes and environments. It builds upon the MiDaS  (Ranftl et al. , 2020)  training strategy for relative depth prediction which uses a loss that is invariant to scale and shift. In the second stage, components responsible for estimating metric depth are added as an additional head. This stage helps to refine the depth estimates by incorporating metric depth information, which is the absolute distance between objects in the scene.
The ZoeD-M12-NK architecture, employs relative pretraining across 12 distinct datasets, coupled with metric fine-tuning on both indoor and outdoor datasets-namely, NYU Depth v2  (Silberman et al. , 2012)  and KITTI  (Geiger et al. , 2013)  jointly. Figure  44 : The ZoeDepth architecture  (Bhat et al. , 2023). (Ranftl et al. , 2021) : it is an architecture for dense prediction tasks (Figure  5 ). DPT utilizes an encoder-decoder design, where the encoder incorporates a transformer as the fundamental computational component. The method adopts the Vision Transformer (ViT)  (Dosovitskiy et al. , 2020).
One of the approaches for determining MTF is utilizing edges. The edge spread function (ESF) characterizes how the system responds to a high-contrast edge. The Fourier Transform of the LSF's (Line Spread Function) normalized magnitude yields a one-dimensional cross-section within the two-dimensional MTF structure. Alternative techniques exist to directly compute the system's MTF from the ESF, thereby obviating the necessity for differentiation  (Tatian, 1965). A prerequisite for determining MTF from edges is the presence of an accurate ESF representation. The slanted edge algorithm capitalizes on the edge's phase shift across the sampling grid to generate an enhanced ESF, termed "super-resolved". In-house scripts are used to compute MTF, ESF and LSF on specific edges in the inferred depth maps and compare them to the GT (Section 4).
DATASETS The considered datasets focus mainly on terrestrial architectural outdoor and indoor scenarios, with large depth changes in the scene. Two publicly available datasets were considered and used for evaluating the MDE methods presented in Section 2: 1) ENRICH 1  (Marelli et al. , 2023)   Moreover, images collected with our in-house stereo-vision SLAM-based system GuPho  (Torresani et al. , 2021; Menna et al. , 2022)  were also used to apply MDE methods and perform metric evaluations of derived point clouds.
ENRICH-Statue images ENRICH-Statue comprises four sub-sets of images. For our evaluation, we selected the dataset labeled "camera 1" consisting of 50 images captured in partly cloudy weather conditions. Figure  6  present samples of estimated depth maps obtained using ZoeDepth, MiDaS, and DPT algorithms. From a visual standpoint, it is evident that DPT demonstrates superior performance in estimating the depth of nearby objects compared to ZoeDepth while it exhibits a higher likelihood of producing inaccurate depth estimates for far away objects. Table  1  and 2  report the evaluation of the MDE methods using various metrics (Section 2. 2), including inference time, on all images of the ENRICH-Statue dataset. Following  Marelli et al. (2023) , we provide evaluation results using a depth threshold suitable as well as non-capped predictions.
Such depth cap is used to exclude far away areas belonging, e. g. , to the sky. Our assessment shows that ZoeDepth demonstrates the fastest inference on the ENRICH-Statue dataset, surpassing the second fastest algorithm (MiDaS) by approximately twice the speed. In terms of metrics, the DPT algorithms (DPT-Large and DPT-Hybrid) outperform both ZoeDepth and MiDaS in most of the metrics, although ZoeDepth exhibits superior performance in terms of SSIM. The predicted depth maps are also converted into point clouds using the Open3D library  (Zhou et al. , 2018). Figure  7  shows the resulting shaded point clouds from the viewpoints close to the original camera perspective. Two distinctive cases are presented: the former image, partially containing the sky (upper row) and the latter one, representing the same object from another viewpoint, without any distant object in the frame (bottom row).
Finally, an edge sharpness analysis was also used to assess the achieved details of estimated depths by ZoeDepth, DPT, and MiDaS. The aim is to assess the edge quality within the estimated depth and determine whether it effectively conveys the intricate details of objects in the scene. A specific area from the ground truth of an image within the ENRICH-Statue dataset and from the corresponding inferred depth maps was chosen (Figure  8a ) to compute the ESF, LSF and MTF curves for ZoeDepth, DPT, and MiDaS methods (Figure  8b-d ). As an indicative metric, the length of a 10% -90% edge transition interval, i. e. , edge width in pixels, was computed from ESF plots. Results for the ground truth depth image are also included for reference as almost perfect target scores. All graphs indicate clearly that the worst sharpness was achieved by ZoeDepth output.
ArchDepth images Within the repository, the Piazza subset includes 9,000 pairs of RGB images and depth maps, organized based on cardinal directions and rendering cameras. The Piazza subset comprises four smaller datasets, named CityE, CityN, CityS, and CityW. We specifically utilized the CityW dataset (Folder cam6 -640x480 px, pinhole camera, 36mm sensor size, 20mm focal length), which contains 800 pairs of RGB images and depth maps. ZoeDepth, DPT, MiDaS, and DenseDepth algorithms are evaluated and Figure  9  and Table  3  display visuals and metrics. Once again, it is notable ZoeDepth's remarkable inference speed. Despite the DPT algorithm's superior performance in MAE, MRE, RMSE, and PSNR, it lags behind in terms of depth estimation speed per image, taking approximately 3x more time. In the terms of SSIM, DenseDepth outperforms the other three algorithms, while in terms of MAE, PSNR, and MRE, it exhibits superior performance compared to MiDaS and ZoeDepth.
GuPho images Further experiments are conducted using indoor images collected with the FBK GuPho system  (Torresani et al. , 2021; Menna et al. , 2022)  and the ZoeDepth method (Figure  11 ). Inferred depth maps are converted into point clouds using the Open3D library  (Zhou et al. , 2018)   11 ): the RMSE (σ) was calculated individually for the floor, ceiling, right wall, and left wall. Additionally, the average (Mean) of RMSE was also determined as the part of the analysis. 4 ) for the recovered depths and point clouds derived from ZoeDepth on the GuPho dataset.
CONCLUSIONS The crucial role of MDE methods and performances on some datasets were presented. MDE is of interest in various fields such as scene comprehension, 3D modeling, robotics, and autonomous driving. MDE is becoming more and more popular due to their reliability and deep learning performances. This study has provided an analysis and evaluation of some MDE methods using different metrics such as inference time, MAE, MRE, RMSE, PSNR, and SSIM. According to our evaluating, defining an algorithm as a winner is impossible. Determining a singular optimal algorithm exhibiting superior performance across all datasets proves to be a challenging task. This challenge arises due to the nuanced influence of application, training and varying scenarios on the algorithm process. When considering the aspect of time, ZoeDepth demonstrated the quickest inference time compared to the other algorithms.
While when we consider different metrics, DPT and MiDaS had better performances. In our view, the majority of existing MDE algorithms suffer from a limitation in training diversity, specifically in terms of various areas and image types. For instance, when the training dataset lacks a sufficient number of images featuring the sky, it can lead to challenges in accurately estimating depth in those particular regions. In future work, our focus will be on the integration of MDE into the GuPho V-SLAM system to achieve real-time depth prediction. By combining the capabilities of V-SLAM with MDE, we aim to enhance the robustness and completeness of 3D reconstruction e. g. , in textureless environments. Additionally, our research will explore alternative methods for MDE, considering various deep learning architectures and traditional computer vision approaches.
ACKNOWLEDGMENTS This study was partially carried out within the  Interconnected Nord-Est Innovation Ecosystem  (iNEST) and received funding from the  European Union Next-GenerationEU  ( Piano Nazionale Di Ripresa e Resilienza (PNRR) -Missione   4, Componente 2, Investimento 1. 5 -D. D. 1058 23/06/2022 ,  ECS00000043 ). The work is also partly supported by the project " AI@TN " funded by the  Autonomous Province of Trento, Italy.
as the foundational architecture, converting its bag-of-words (tokens) representation into imagelike feature representations at different resolutions. These representations are then progressively merged using a convolutional decoder to generate the ultimate dense prediction output. DPT-Base, DPT-Large, and DPT-Hybrid are three DPT architectures which are based on ViT architectures (Vit-Base, ViT-Large, and ViT-Hybrid) in terms of reassembling tokens from different layers. ViT-Base employs the patch-based embedding approach and includes 12 transformer layers, while ViT-Large adopts the same embedding technique but incorporates 24 transformer layers and features a broader feature size D (feature dimension of each token). Additionally, ViT-Hybrid utilizes a ResNet50 for calculating the image embedding, and it is followed by the inclusion of 12 transformer layers and is fine-tuned on the KITTI and NYUv2 datasets.
Numerical examples In previous work  [12, 13] , we have demonstrated the ability of ASPEN to reduce the number of nonlinear iterations and improve the general robustness of the nonlinear solve compared to Newton. For this, we have used the automatic differentiation (AD-OO) simulator framework of MRST  [14]. In  [12] , we also presented a simplified complexity analysis which indicates that under ideal parallelization, the extra cost incurred from the local solves is small compared to the cost of the global correction stage. Use of memory-optimized backends for automatic differentiation and high-performing linear solvers written in complied languages has brought the computational power of MRST to the level of compiled simulators  [16]. Implementations in native MATLAB will nonetheless inevitably have a certain computational overhead that will bias actual runtimes observed when comparing nonlinear solvers.
We could therefore not back up claims regarding ASPEN's computational efficiency with credible observations of reduced runtime. To do this, we will herein instead rely on a highly optimized computational backend (Jutul) written in Julia, a dynamic, open-source programming language for scientific computing that aims to achieve the same performance as Fortran or C++ with a high-level syntax similar to Python or MATLAB. Jutul relies on MRST for preprocessing simulation cases for immiscible, black-oil, and equation-of-state compositional flow. Thanks to a highly efficient prototype implementation with static, hard-coded stencils, the performance of Jutul's automatic differentiation library is a factor 3-5 times faster than in OPM Flow  [17]  and AD-GPRS  [18, 19] , which in turn gives significantly faster assembly.
Linear systems are solved with a standard Krylov method together with a constrained-pressure residual (CPR) preconditioner  [20, 21]  that uses AMG and block-ILU(0) for the first and second stages, respectively. All wells are treated as multisegment wells. Jutul is open source software 2  , but our ASPEN implementation is not yet public. In the following, we present a total of five test cases. The first test case is a conceptual example included to illustrate typical convergence of the different nonlinear solvers, whereas the following four test cases compare computational performance of ASPEN and Newton in terms of both iteration counts and actual runtimes observed. We will also discuss a few strategies to hybridize the two methods for optimal performance.
The profiling of multiple molecular layers from the same set of cells has recently become possible. There is thus a growing need for multi-view learning methods able to jointly analyze these data. We here present Multi-Omics Wasserstein inteGrative anaLysIs (Mowgli), a novel method for the integration of paired multi-omics data with any type and number of omics. Of note, Mowgli combines integrative Nonnegative Matrix Factorization (NMF) and Optimal Transport (OT), enhancing at the same time the clustering performance and interpretability of integrative NMF. We apply Mowgli to multiple paired single-cell multi-omics data profiled with 10X Multiome, CITE-seq and TEA-seq. Our in depth benchmark demonstrates that Mowgli's performance is competitive with the state-of-the-art in cell clustering and superior to the state-of-the-art once considering biological interpretability.
Integrative Matrix Factorization (integrative MF) and variational autoencoders perform dimensionality reduction, jointly embedding the highdimensional multi-omics cellular profilings into a shared lower-dimensional latent space by leveraging common cells/observations  13, 26. Integrative MF, due to its linear nature, defines a latent space with a natural biological interpretation, but it is too simple to catch complex biological processes  13, 26. On the other hand, non-linear methods, as variational autoencoders, have shown great potential in clustering cells, but despite recent works on the subject  27, 28  , they inherently lack biological interpretability. Improving integrative MF methods is thus crucial to striking a balance between interpretability and performance. We here propose Multi-Omics Wasserstein inteGrative anaLysIs (Mowgli github.
com/cantinilab/mowgli), a novel integrative MF method for single-cell multiomics data combining integrative Nonnegative Matrix Factorization 29 (integrative NMF) with Optimal Transport 30 (OT). On one hand, Mowgli employs integrative NMF, popular in computational biology due to its intuitive representation by parts and further enhances its interpretability  29. On the other hand, Mowgli enhances the clustering performances of integrative MF by taking advantage of OT, which we have previously shown to better capture similarities between single-cell omics profiles  31. We then extensively benchmark Mowgli with respect to the state-of-the-art in the integration of several paired multi-omics data profiled with CITE-seq  5  , 10X Genomics Multiome and TEA-seq 7 platforms. Of note, while we focus on the integration of the currently available omics data, Mowgli can deal with paired multi-omics datasets with any type and number of omics, without any statistical assumption on the data.
The performed in-depth comparison shows that Mowgli's embedding and clustering quality outperform the state-of-the-art in controlled settings derived from real multi-omics data and are competitive with the state-of-the-art in more complex real multi-omics data. Of note, the latter are affected by the lack of an absolute groundtruth annotation on most real datasets. Finally, Mowgli is shown to improve the state-of-the-art in terms of biological interpretability through an in-depth biological analysis of TEA-seq data.
In addition, as in Rolet et al. 40  , we add to the optimization problem (Eq1) two entropic regularization terms and (see Methods). These terms ensure that the loadings and embeddings are positive distributions and they control their sparsity (see Methods), a crucial feature to further enhance the known NMF's "representation by parts" property  29. and are the coldness parameters of softmax functions (see Methods) and thus offer a natural way to adjust sparsity. For instance, as approaches 0, cells will be assigned to only one factor. As instead increases, cells will be a combination of several factors. For all details on the mathematical formulation of Mowgli see Methods. Of note, Mowgli is implemented as an open-source Python package seamlessly integrated into the classical Python single-cell analysis pipeline (github.