dataesr/scientific-paragraphs-categorization huggingface dataset:
From Table  3  we can confirm the presence of coumarins, tannins, terpenes in the leaves of Blighia unijugata Bak (Sapindaceae) because the values obtained correspond to the values in the database. These molecules have already been identified by the traditional method with the same plants  (Kabran, 2014b). These results thus show the reliability of this identification technique and its simplicity in its implementation. However we found that when the radius of the segmented spot is small, i. e. , when the contour is near the center of the spot, we obtain very satisfactory results. Parameter values for coumarins were not very satirical because the diameters of the segmented areas were not very close to the center of spot.
This paper proposes a method to identify the strain-stress relation of non-linear elastic materials, without any underlying constitutive equation. The approach is based on the concept of Data Driven Computational Mechanics recently introduced by Kirchdoerfer and Ortiz (2016). From a collection of non-homogeneous strain fields, for example measured through Digital Image Correlation, the algorithm builds a database of strain-stress couples that sample the mechanical response of the material for the range of measured strains. The method is first derived for truss structures and then extended to the case of small-strain elasticity. The method accuracy, sensitivity to measurement noise and parameters are discussed using manufactured data.
1. The two states (ϵ e , σ e ) and (ϵ * ie , σ * ie ) associated to a truss element e. The dashed line represents the energetic mismatch between the two states. On the left we see that the mapping ie between elements and material states can assign the same particular material state to two different elements. a database of strain-stress couples (called states) which sample the mechanical response of the material. In this approach, regularization/smoothing/interpolation of experimental data are carried out during the computation of the numerical solution of the boundary value problem. The results presented by the authors are encouraging and open the door to many perspectives from the modeling point of view, since the necessity of an explicit or implicit strain-stress relationship is relaxed.
In the wake of these contributions, Ibañez et al. [3]  investigate the possible use of manifold learning techniques applied to the material database. Let us briefly recall the method of Kirchdoerfer and Ortiz for data-driven simulation in the particular case of truss structures  [1]. It seeks to assign to each truss element e a mechanical state and a material state, a state being a strainstress couple. Considering both mechanical equilibrium (involving stress) and compatibility conditions (involving strain) as non-questionable, the mechanical state of element e consists of a strain-stress pair (ϵ e , σ e ) that exactly satisfies the above equations which can be considered as constraints. The second state associated to e, denoted (ϵ * ie , σ * ie ), is called the material state and is extracted from a collection of admissible material states for the material: (ϵ * i , σ * i ), where i ∈ 1 : N *.
The index ie ∈ 1 : N * specifies the material state of element e. It should be interpreted as a pointer that assigns to each element a specific material state in the material database. Fig. 1  illustrates the main ideas behind the method. The proposed solver seeks, for every element simultaneously, a mechanical and a material state as close to each other as possible and such that the former satisfies mechanical equilibrium and compatibility conditions. This is formally expressed as follows: solution = arg min ϵ e ,σ e ,ie 1 2 ∑ e w e ∥(ϵ e -ϵ * ie , σ e -σ * ie )∥ 2 C , (1) subject to ∑ e w e B ej σ e = f j , (2) and ϵ e = ∑ j B ej u j. (3) In the above equations, ∥(ϵ, σ )∥ C is an energetic norm, the matrix B ej encodes the connectivity and geometry of the truss, and w e denotes the volume of the truss element e.
Furthermore, u j and f j represent, respectively, the displacement and the force applied to truss nodes. For the particular choice ∥(ϵ e , σ e )∥ 2 C = (Cϵ 2 e + 1 C σ 2 e ) , (4) the authors propose an efficient algorithm to solve this problem of combinatorial complexity. The constant parameter (possibly defined element-wise) C is the only parameter of the method and can be interpreted as a modulus associated to the mismatch of mechanical and material states. This mismatch is represented by the dashed lines in Fig. 1. Although there is no need for a constitutive equation, the database of material states is a mandatory pre-requisite of the method before starting the simulation. Building this database computationally, for example through micro-macro approaches such as FE 2  [4, 5] , is expensive and might require efficient model order reduction and high dimensional interpolation techniques.
Despite the success of these model-based identification methods, they are all a priori constrained by the choice of a constitutive model and are therefore not suited to the DDCM framework. Here we propose a model-free procedure, based on some inversion of the data-driven solver, to extract strain-stress couples that sample the mechanical response of an elastic material. The method uses a collection of displacement and (non homogeneous) strain fields acquired, for example, using Digital Image Correlation techniques. It identifies simultaneously the stress component of the mechanical state for each loading condition and the full material states database, which is common to all loading conditions. The proposed method is first developed for truss structures. The convergence, the influence of measurement noise and parameters are discussed.
Data-Driven Identification (DDI) Consider a large database of measurements made on real truss structures subject to different loading conditions; all truss elements being of the same material. For each loading condition, or data item, indexed by X , the following quantities are available: • nodal displacements u X j , • truss geometry and connectivity, encoded through the matrix B X ej. The mechanical strains are computed as ϵ X e = ∑ j B X ej u X j , • applied forces f X j , • prescribed nodal displacements. Identifying the material response of truss elements reduces to the determination of a finite number N * of material states (ϵ * i , σ * i ) with i ∈ 1 : N * , common to all the data items (thus independent of X ), and such that 1. for each data item X , the mechanical stress σ X e satisfies mechanical equilibrium for X , 2.
The simplest initialization is to assign to each ie X a random integer between 1 and N * , yielding a random clustering of the mechanical states. Since all the mechanical strains ϵ X e are known, a very good initialization of ie X (or equivalently a clustering of the mechanical states) can be computed through some kmeans-like algorithm  [14, 15]  applied to ϵ X e. In this work, we have used the default Matlab R ⃝ implementation of the Statistics and Machine Learning toolbox. • Step 2 is relatively inexpensive from a computational point of view as it simply computes the material strains as a weighted average of the mechanical strains. • Step 3 entails the solution of a large linear system with the following structure: ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ K 1 S 1 K 2 S 1. K N X S N X S T 1 S T 2 • • • S T N X 0 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ • ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ η 1 η 2.
This is relatively expensive as it requires, for each mechanical state, to compute its distance to all material states in the material database. High dimensional generalization of quad-tree algorithms or neighbor lists methods similar to those used in molecular dynamics simulation codes might improve the efficiency of this step. • Similarly to the data driven solver, the DDI method proposed here entails only few parameters: the number N * of material states to be identified and the pseudo-stiffness C. It should be noted that C is not necessarily the same for all truss elements and data items, and can therefore depend on both e and X : C X e. This provides some additional flexibility in the method and is a tool to weight the data according to some a priori confidence level. • Even for non-linear material response, the identification procedure only requires the solution of linear systems and simple database searches.
Numerical results In this section, the DDI method is applied to the identification of the mechanical response of truss elements exhibiting a non linear strain-stress relation. We use a synthetic dataset generated by applying different loading conditions to the 2D truss structure depicted in Fig. 2. This structure is made of 249 nodes and 657 bar elements with a nonlinear strain-stress behavior of the form: σ = K (ϵ + ϵ 3 ), K being set to 5. N X = 50 different loading scenarios involving uniaxial tension and compression, and simple shear have been simulated. Some representative deformed configurations are depicted in Fig. 3. The single parameter C is set to 10 as we do not assume any noise on the mechanical strains ϵ X e and therefore wish to put more weight on the strain part of the energetic norm (see Eq.
(  9 ) becomes ∑ X ∑ e|ie X =i w X e C(ϵ X e + δϵ X e -ϵ * ie X ) = 0 ∀i. As δϵ X e = B X ej δu X j has zero mean, it does not introduce any systematic bias in the value of ϵ * i. Furthermore, the effect of noisy data is mitigated for large databases of experimental measurements. • If the amount of noise if sufficient to perturb the state mapping, it also affects the computed values of material σ * i and mechanical stress σ X e , thereby reducing the quality of results. In order to mitigate the influence of noisy mechanical strains on the state mapping, we see from Eqs. (  4 ) and (  15 ) that a simple possibility is to reduce the value of C. In Fig. 6  some material states computed for C = 10 and C = 0. 1 are shown. As expected large strain values are less perturbed by noise, and reducing the value of C improves results quality.
Data-Driven Identification Again, we assume the existence of a large database of measurements, obtained by Digital Image Correlation or any related technique. Furthermore we consider a linearized kinematics discretized by a finite element mesh in which each quadrature point e admits an integration weight w e. For each data item X (or snapshot), the following quantities are available: • nodal displacements u X j , • finite element geometry and connectivity, encoded through a matrix B X ej , which compute the mechanical strain ϵ X e = ∑ j B X ej • u X j , • applied nodal forces f X j , • prescribed nodal displacements. The aim of the DDI method is to compute a number N * of material states (ϵ * i , σ * i ) such that • for each snapshot X and quadrature point e, it is possible to compute the mechanical state σ X e that satisfies mechanical equilibrium, • for each snapshot, a material state (ϵ * ie , σ * ie ) is assigned to each quadrature point e which is the closest to the mechanical state according to a given energetic norm ∥ • ∥ 2 C.
In Fig. 8  we present the first eigenvalue of the material stress tensor (σ * I ) as a function of the eigenvalues of the corresponding material strain (ϵ * I , ϵ * I I ). All points fall very close to the surface that can be built from the constitutive equation used to generate the input data: σ * I G = ϵ I + αϵ 3 I + (ϵ I + ϵ I I ) + α(ϵ I + ϵ I I ) 3. ( 30 ) Computed material states therefore provide a discrete description of the "true" material response in the strain range of input data. The observed distribution of material strain in the (ϵ * I , ϵ * I I ) plane provides an importance sampling of the relevant strain states in the dataset. In particular one can observe the lack data for equibiaxial strain (i. e. ϵ * I = ϵ * I I ). The identification of such states might require carefully crafted experiments sampling these states.
Summary and concluding remarks In this paper, we derive a Data Driven Identification (DDI) method that computes admissible strain-stress couples from a set of experimental data, based on the Data-Driven Computational Mechanics (DDCM) framework recently proposed by Kirchdoerfer & Ortiz  [1]. The method only requires kinematics and applied forces, which are both accessible using Digital Image Correlation. The computed strain-stress couples can then be used either as constitutive law surrogate in DDCM, or to fit a classical constitutive model. Stress fields of the experimental data are also obtained as a byproduct of the algorithm. The proposed method is for now applicable to non-linear elastic behaviors only, where stress is uniquely determined by strain. Future developments will focus on more complex material responses such as viscoelasticity, plasticity and damage which involve strain history.
Close-range photogrammetry as a technique to acquire reality-based 3D data has, in recent times, seen a renewed interest due to developments in sensor technologies. Furthermore, the strong democratization of UAVs (Unmanned Aerial Vehicles) or drones means that close-range photogrammetry can now be used as a viable low-cost method for 3D mapping. In terms of software development, this led to the creation of many commercial black-box solutions (PhotoScan, Pix4D, etc. ). This paper aims to demonstrate how the open source toolbox DBAT (Damped Bundle Adjustment Toolbox) can be used to generate detailed photogrammetric network diagnostics to help assess the quality of surveys processed by the commercial software, PhotoScan. In addition, the Apero module from the MicMac software suite was also used to provide an independent assessment of the results.
The assessment is performed by the careful examination of some of the bundle adjustment metrics generated by both open source solutions. A UAV project was conducted on a historical church in the city center of Strasbourg, France, in order to provide a dataset with a millimetric level of precision. Results showed that DBAT can be used to reprocess PhotoScan projects under similar conditions and derive useful metrics from them, while Apero provides a completely independent verification of the results of commercial solutions. Overall, this paper shows that an objective assessment of photogrammetric results is important. In cases where problems are encountered in the project, this assessment method can be useful to detect errors that may not be explicitly presented by PhotoScan.
The development of computer vision-derived algorithms has largely facilitated the photogrammetric workflow, enabling the automation of much of the previously manual work. This includes the development of image feature matching  [11]  that enables the automatic extraction and matching of tie points. Similarly, improvements in dense matching algorithms  [12, 13]  have rendered the photogrammetric process very powerful, enabling it to produce dense point clouds up to one point per pixel  [14]. In photogrammetry, UAVs (Unmanned Aerial Vehicles) have provided the means to capture images at close ranges, but from aerial points of view. This has enabled the 3D mapping of difficult or inaccessible parts  [15]. The developments in the field of photogrammetry, aided by the popularization of UAVs, have sparked the creation of various software packages that offer photogrammetric and/or Structure-from-Motion (SfM) processing.
An important aspect of photogrammetric quality is exterior orientation. This step influences the quality of the rest of the workflow, such as the dense image matching. Exterior orientation is often resolved using a bundle adjustment, with initial values calculated from other methods such as the Direct Linear Transformation (DLT), consecutive relative orientation, spatial resection, etc. [20]. The main aim of this paper was to demonstrate how two open source bundle adjustment solutions can be used to provide valuable diagnostics for the output of a commercial software. The commercial software evaluated was Agisoft PhotoScan, which is a popular software for 3D mapping  [18]. The open source solutions used to evaluate the PhotoScan results were DBAT (Damped Bundle Adjustment Toolbox)  [21]  and Apero  [16].
While Apero is a full photogrammetric module representing the whole photogrammetric process (usually coupled with MicMac for its dense matching step), DBAT has the capability to take PhotoScan projects as the input. This effectively means that DBAT can be used to reprocess PhotoScan's results, while providing more flexibility and detailed metrics than PhotoScan (e. g. , posterior standard deviations, sigma naught, correlations between parameters, etc. )  [22]. These statistics can be used, for example, to determine the quality of images, the presence of outlier observations in the bundle adjustment process or the quality of the computed external and internal parameters. Comparisons of bundle adjustment computation between PhotoScan and other open source solutions have been the object of study of several other papers.
Open source solutions are often used to perform the comparison, as they provide a more open algorithm, which the users may parametrize to match their needs. Apero in particular has been used for such comparisons in previous research  [23] [24] [25]. Other papers focus on optimizing PhotoScan processing  [26]  and assessing the results of PhotoScan projects in terms of computed covariances of both internal and external parameters  [27] , similar to DBAT's functionality. The method applied in this paper follows the work already described in a previous publication  [22]. However, the experiments in this paper were performed on a new dataset with a higher number of high-precision control points, which allows a more robust comparison. Furthermore, another independent comparison with Apero was also performed in order to give an objective assessment of the PhotoScan project.
Software Solutions In parallel with improvements in imaging sensors, a significant development in image processing algorithms has led to various photogrammetric software programs. In general, modern SfM/photogrammetry-based solutions are available in both a commercial and an open source nature. In terms of commercial software, Agisoft PhotoScan is one of the most commonly used  [18, 33, 43]. Other popular solutions include Pix4D, Photomodeler, RealityCapture and 3DF Zephyr  [39, 44]. The openMVG page (https://github. com/openMVG accessed on 20 December 2017) provides a comprehensive list of the available open source 3D reconstruction libraries. Some notable examples of open source programs offering a complete photogrammetric workflow include IGN (the French national mapping agency)'s Apero-MicMac package  [42] , the ISPRS Scientific Initiative project GRAPHOS  [17]  or VisualSFM  [45].
Partial algorithms and software programs performing a specific part of the general photogrammetric workflow also exist, for example DBAT  [21] , which calculates the bundle adjustment step, and SURE  [46] , which generates 3D dense point clouds from pre-oriented images. The programs listed above perform the computations locally. Other software programs that perform the computations in the cloud include Autodesk's Recap, KU Leuven's Arc3D  [39]  and the Replicate project  [10]. In this paper, a critical analysis of the bundle adjustment results of the commercial software PhotoScan was performed. This involved the reprocessing of the PhotoScan project using DBAT, in order to derive detailed metrics. These metrics were then used to verify the results given by PhotoScan. In addition, an independent bundle adjustment processing using Apero was also performed.
Agisoft PhotoScan PhotoScan is a stand-alone software developed by the company Agisoft LLC. It performs 3D reconstruction of objects from images and employs the whole photogrammetric workflow. PhotoScan has a user-friendly interface with several simplified functionalities and parameters, which nevertheless manages to deliver a fairly accurate result. Few things are known about the algorithms employed by PhotoScan. The tie point extraction and detection may employ an improved version of SIFT  [33]. Furthermore, the dense matching method used may be a variant of the Semi-Global Matching (SGM) algorithm  [12, 19]. In terms of bundle adjustment, little has been published about the approach used by PhotoScan. As a commercial software, PhotoScan focuses on the results rather than detailed control of the processing parameters.
DBAT The Damped Bundle Adjustment Toolbox (DBAT) is a set of functions developed in the MATLAB language (www. mathworks. com/products/matlab. html accessed on 20 December 2017) for the purpose of calculating bundle adjustment solutions  [40]. DBAT was originally developed to test different damping methods for the bundle adjustment process. This has been applied, for example, to help camera self-calibration using the extended collinearity equations to converge by only using the Exif values of the images  [41, 47]. Furthermore, DBAT has been tested to reprocess real-world datasets, such as a small sample of large-format aerial images  [21]  and close-range photogrammetry projects, both terrestrial and UAV-based  [22, 48]. DBAT provides comprehensive statistics, such as posterior standard deviations of exterior and interior parameters, intersecting angles between images, sigma naught, correlations between the computed parameters, etc.
The reported statistics can be used to validate the results and if necessary to detect errors and redress the project in order to increase its quality  [22]. Originally, DBAT was designed to process export files from Photomodeler, but can today load and process PhotoScan projects as well. In this regard, DBAT can be used to reprocess PhotoScan projects and derive more detailed metrics from them. However, DBAT reproduces PhotoScan projects in a broad manner, while generating some bundle adjustment diagnostics. Some inconsistencies are therefore to be expected. For example, PhotoScan seems to relatively scale the tie point image observations by a factor related to the feature scale, which is not reproduced in DBAT. In this paper, the used DBAT Version was 0. 7. 0. 1, available from GitHub (https://github.
Apero Apero is part of an open source 3D reconstruction module developed by the French national mapping agency (IGN). Apero performs bundle adjustment with the Levenberg-Marquardt damping method  [42]  from the tie points generated and matched by the Pastis module. Pastis is an interface to SIFT++  [16, 33] , which itself is an improved version of the SIFT feature detection algorithm  [11]. Pastis and Apero are usually coupled with the dense matching module MicMac  [49]. Together, the Pastis-Apero-MicMac family of functions enables the user to perform the complete photogrammetric workflow up to the generation of mesh models and orthophotos. The functionality of the Pastis-Apero-Micmac suite can be accessed by performing commands on two levels  [42]. The lower level involves the manipulation of XML-files, and the higher level consists of automated commands that may be invoked in a command window environment.
At the end of the topographical survey, all measurements were calculated in a least-squares block adjustment using the software Covadis (http://www. geo-media. com/solutions/logiciel-covadis accessed on 20 December 2017). This was done in order to determine the standard deviation values for each control point and enable the use of weighting in the bundle adjustment process. The obtained standard deviation values were of the order of 5 mm. On average, the planimetric precision of the control points resulting from this process was 4 mm, while the average altimetric precision was 2 mm. The UAV was flown using a combination of perpendicular and oblique photos in order to cover difficult parts of the building. The flight strips were performed systematically in a vertical fashion; the oblique photos followed the same flight strip design.