TestGrids: Evaluating and Optimizing Map Projections

[EN] In the study of map projections, it is relatively simple to obtain meaningful estimators of distortion for a small area. The definition and especially the evaluation of global distortion measures (i.e., estimators representing the distortion worldwide or in a continent-like area) are undoubtedly more troublesome. Therefore, it is relatively common to find that recommendations for the parameters to use in a particular map projection, be it devised for a continent or a country, are based on simple rules (like the one-sixth rule of thumb for conic projections), with no possibility of further improvement in terms of resulting distortions and sometimes even with no knowledge at all of the sizes of these distortions. Although the choice of map defining parameters is normally made for reasons other than distortion minimization, such as ease of use (e.g., integer or half-integer numbers may be preferable), preservation of conventional or traditional definitions, and uniformity of parameters between neighboring regions, it is always worthwhile to know the optimal set of parameters in terms of minimal distortion. Then, the cartographer may mindfully deviate from this optimal set, documenting the differences in defining parameters and in the resulting distortions. The present research provides a means to do this by extending a related work presented in a previous contribution, where the evaluation and optimization of distortions were studied for a single map projection and only two areas of interest. To this end, a new tool has been developed and presented in this paper. This tool allows users to evaluate several measures of distortion for the most common conformal and equal-area projections within user-defined geographic boundaries of interest. Also embedded in the tool and transparent to users are global optimization techniques operating on Fibonacci grids, which permit the optimization of parameters for the particular map projection and area of interest under two possible criteria: minimization of typical distortion or minimization of extreme distortions. This tool and the associated techniques are applied to several official projections to analyze their original performance and to propose new parameters that significantly improve the resulting distortions while leaving room for users to easily evaluate and optimize the tool for the lowest distortions of these projections within their regions of interest.Baselga Moreno, S. (2019). TestGrids: Evaluating and Optimizing Map Projections. Journal of Surveying Engineering. 145(3):1-8. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000279S18145

Two Conformal Projections for Constant-Height Surface to Plane Mapping

[EN] Regions at high elevations may require specific mapping solutions other than the conventional ellipsoid-to-grid projections, which produce large discrepancies between ground and projected distances. These particular solutions are known as low-distortion projections (LDPs). They can be realized by using an elevated ellipsoid (EE) or a constant-height surface (ChS) above the ellipsoid as the reference surface, or by means of a scaled projection. No conformal projections have been derived thus far for the ChS-to-plane transformation. This work aims to solve this problem by deriving the formulation of direct and transverse Mercator-type projections for ChS-to-plane conformal mapping.Baselga Moreno, S. (2021). Two Conformal Projections for Constant-Height Surface to Plane Mapping. Journal of Surveying Engineering. 147(2):1-7. https://doi.org/10.1061/(ASCE)SU.1943-5428.000034517147

Automated detection of discontinuities in EUREF permanent GNSS network stations due to earthquake events

[EN] The EUREF Permanent GNSS Network (EPN) provides the users with data and products such as station coordinate time series. These are subject to possible discontinuities and trend changes, being earthquake events one of the possible natural causes for these variations. We present here a fully automated tool for the analysis of the coordinate time series of EPN stations located in the desired neighbourhood of an earthquake epicentre. The tool is made freely available to the public and applied here to two significant earthquake events occurred in Europe in recent years, where several trend changes and jumps are revealed.Baselga Moreno, S.; Najder, J. (2022). Automated detection of discontinuities in EUREF permanent GNSS network stations due to earthquake events. Survey Review. 54(386):420-428. https://doi.org/10.1080/00396265.2021.19642304204285438

Intersection and point-to-line solutions for geodesics on the ellipsoid

[EN] The paper presents two algorithms for the computation of intersection of geodesics and minimum distance from a point to a geodesic on the ellipsoid, respectively. They are based on the iterative use of direct and inverse problems of geodesy by means of their implementations with machine-precision accuracy in GeographicLib. The algorithms yield the same results as those obtained by Karney¿s approach based on the use of auxiliary ellipsoidal gnomonic projections, with the advantage on our side that the algorithms are not limited to distances below 10000 km. This results in our algorithm being the only general solution for the problem of minimum distance from a point to a geodesic on the ellipsoid.Baselga Moreno, S.; Martínez Llario, JC. (2018). Intersection and point-to-line solutions for geodesics on the ellipsoid. Studia Geophysica et Geodaetica. 62(3):353-363. https://doi.org/10.1007/s11200-017-1020-zS353363623JaVaWa, 2017. JAVAWA GPS Tools. (http://www.javawa.nl/coordcalc_en.html).Karney C.F.F., 2011a. Geodesics on an Ellipsoid of Revolution. Technical Report. SRI International (http://arxiv.org/abs/1102.1215v1).Karney C.F.F., 2011b. Intersection between Two Geodesic Lines. (https://sourceforge.net/p/geographiclib/discussion/1026621/thread/21aaff9f).Karney C.F.F., 2013. Algorithms for geodesics. J. Geodesy, 87, 43–55.Karney C.F.F., 2017. GeographicLib, version 1.47. (http://geographiclib.sourceforge.net).Patrikalakis N.M., Maekawa T. and Cho W., 2009. Shape Interrogation for Computer Aided Design and Manufacturing. (http://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/mathe.html).PostGIS Development Group, 2017. PostGIS 2.3.3dev Manual. (http://postgis.net/docs/index.html).Sjöberg L.E., 2002. Intersections on the sphere and ellipsoid. J. Geodesy, 76, 115–120.Sjöberg L.E., 2006. Direct and indirect geodetic problems on the ellipsoid. Z. Vermess., 131, 35–39.Sjöberg L.E., 2008. Geodetic intersection on the ellipsoid. J. Geodesy, 82, 565–567.Sjöberg L.E., 2009. New solutions to classical geodetic problems on the ellipsoid. In: Sideris M.G. (Ed.), Observing our Changing Earth. International Association of Geodesy Symposia 133, 781–784, Springer-Verlag, Berlin, Germany.Sjöberg L.E. and Shirazian M, 2012. Solving the direct and inverse geodetic problems on the ellipsoid by numerical integration. J. Surv. Eng., 138, 9–16.Todhunter I., 1886. Spherical Trigonometry, 5th Edition. MacMillan and Co., London, U.K. (http://www.gutenberg.org/ebooks/19770).Vincenty T., 1975. Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations. Surv. Rev., 23, 88–93

Accurate Algorithms for Spatial Operations on the Spheroid in a Spatial Database Management System

[EN] Some of the most powerful spatial analysis software solutions (Oracle, Google Earth Engine, PostgreSQL + PostGIS, etc.) are currently performing geometric calculations directly on the ellipsoid (a quadratic surface that models the earth shape), with a double purpose: to attain a high degree of accuracy and to allow the full management of large areas of territory (countries or even continents). It is well known that both objectives are impossible to achieve by means of the traditional approach using local mathematical projections and Cartesian coordinates. This paper demonstrates in a quantitative methodological way that most of the spatial analysis software products make important deviations in calculations regarding to geodesics, being the users unaware of the magnitude of these inaccuracies, which can easily reach meters depending on the distance. This is due to the use of ellipsoid calculations in an approximate way (e.g., using a sphere instead of an ellipsoid). This paper presents the implementation of two algorithms that solve with high accuracy (less than 100 nm) and efficiently (few iterations) two basic geometric calculations on the ellipsoid that are essential to build more complex spatial operators: the intersection of two geodesics and the minimum distance from a point to a geodesic.Martínez Llario, JC.; Baselga Moreno, S.; Coll-Aliaga, E. (2021). Accurate Algorithms for Spatial Operations on the Spheroid in a Spatial Database Management System. Applied Sciences. 11(11):1-21. https://doi.org/10.3390/app11115129121111

Application of a combination of digital image processing and 3D visualization of graffiti in heritage conservation

[EN] In recent years, heritage documentation processes have largely benefited from the application of both 2D imagery analysis and 3D techniques for recording and visualization of assets. In this paper, a combined 2D-3D methodological workflow, especially helpful for the documentation of graffiti on closed and narrow spaces, is presented. It is proposed, firstly, the use of structure from motion software to obtain the 3D model and texture information. Then, the use of decorrelation stretching algorithms is used to obtain enhanced textures. This study found that the performance of the algorithms usually recommended for enhancement of the different colours is sometimes suboptimal. Finally, the integration of 2D and 3D information into Blender, a powerful 3D open-source tool, allows for a detailed exploration of the areas containing graffiti. Additionally, it allows high quality rendition of the resulting model that helps to better understand and record heritage resources. This methodological approach has been applied to the military defense heritage site of Puig-Carassols trench line in Spain.Palomar-Vázquez, J.; Baselga Moreno, S.; Viñals Blasco, MJ.; García-Sales, C.; Sancho-Espinós, I. (2017). Application of a combination of digital image processing and 3D visualization of graffiti in heritage conservation. Journal of Archaeological Science Reports. 12:32-42. doi:10.1016/j.jasrep.2017.01.021S32421

An attempt to analyse Iterative Data Snooping and L1-norm based on Monte Carlo simulation in the context of leveling networks

[EN] The goal of this paper is to evaluate the outlier identification performance of iterative Data Snooping (IDS) and L-1-norm in levelling networks by considering the redundancy of the network, number and size of the outliers. For this purpose, several Monte-Carlo experiments were conducted into three different levelling networks configurations. In addition, a new way to compare the results of IDS based on Least Squares (LS) residuals and robust estimators such as the L-1-norm has also been developed and presented. From the perspective of analysis only according to the success rate, it is shown that L-1-norm performs better than IDS for the case of networks with low redundancy ((r) over bar < 0.5), especially for cases where more than one outlier is present in the dataset. In the relationship between false positive rate and outlier identification success rate, however, IDS performs better than L-1-norm, independently of the levelling network configuration, number and size of outliers.Klein, I.; Suraci, SS.; De Oliveira, LC.; Rofatto, VF.; Matsuoka, MT.; Baselga Moreno, S. (2022). An attempt to analyse Iterative Data Snooping and L1-norm based on Monte Carlo simulation in the context of leveling networks. Survey Review. 54(382):70-78. https://doi.org/10.1080/00396265.2021.187833870785438

Performance comparison of least squares, iterative and global L1 Norm minimization and exhaustive search methods for outlier detection in leveling networks

[EN] Different approaches have been proposed to determine the possible outliers existing in a dataset. The most widely used consists in the application of the data snooping test over the least squares adjustment results. This strategy is very likely to succeed for the case of zero or one outliers but, contrary to what is often assumed, the same is not valid for the multiple outlier case, even in its iterative application scheme. Robust estimation, computed by iteratively reweighted least squares or a global optimization method, is other alternative approach which often produces good results in the presence of outliers, as is the case of exhaustive search methods that explore elimination of every possible set of observations. General statements, having universal validity, about the best way to compute a geodetic network with multiple outliers are impossible to be given due to the many different factors involved (type of network, number and size of possible errors, available computational force, etc.). However, we see in this paper that some conclusions can be drawn for the case of a leveling network, which has a certain geometrical simplicity compared with planimetric or three-dimensional networks though a usually high number of unknowns and relatively low redundancy. Among other results, we experience the occasional failure in the iterative application of the data snooping test, the relatively successful results obtained by both methods computing the robust estimator, which perform equivalently in this case, and the successful application of the exhaustive search method, for different cases that become increasingly intractable as the number of outliers approaches half the number of degrees of freedom of the network.Baselga Moreno, S.; Klein, I.; Suraci, SS.; Castro De Oliveira, L.; Matsuoka, MT.; Rofatto, VF. (2020). Performance comparison of least squares, iterative and global L1 Norm minimization and exhaustive search methods for outlier detection in leveling networks. Acta Geodynamica et Geomaterialia. 17(4):425-438. https://doi.org/10.13168/AGG.2020.003142543817

Global Optimization of Redescending Robust Estimators

[EN] Robust estimation has proved to be a valuable alternative to the least squares estimator for the cases where the dataset is contaminated with outliers. Many robust estimators have been designed to be minimally affected by the outlying observations and produce a good fit for the majority of the data. Among them, the redescending estimators have demonstrated the best estimation capabilities. It is little known, however, that the success of a robust estimation method depends not only on the robust estimator used but also on the way the estimator is computed. In the present paper, we show that for complicated cases, the predominant method of computing the robust estimator by means of an iteratively reweighted least squares scheme may result in a local optimum of significantly lower quality than the global optimum attainable by means of a global optimization method. Further, the sequential use of the proposed global robust estimation proves to successfully solve the problem of M-split estimation, that is, the determination of parameters of different functional models implicit in the data.Baselga Moreno, S.; Klein, I.; Sampaio Suraci, S.; Castro De Oliveira, L.; Tomio Matsuoka, M.; Francisco Rofatto, V. (2021). Global Optimization of Redescending Robust Estimators. Mathematical Problems in Engineering. 2021:1-13. https://doi.org/10.1155/2021/9929892S113202

Evaluation of Long-Range Mobile Mapping System (MMS) and Close-Range Photogrammetry for Deformation Monitoring. A Case Study of Cortes de Pallás in Valencia (Spain)

none8openDi Stefano, Francesco; Cabrelles, Miriam; García-Asenjo, Luis; Lerma, José Luis; Malinverni, Eva Savina; Baselga, Sergio; Garrigues, Pascual; Pierdicca, RobertoDi Stefano, Francesco; Cabrelles, Miriam; García-Asenjo, Luis; Lerma, José Luis; Malinverni, Eva Savina; Baselga, Sergio; Garrigues, Pascual; Pierdicca, Robert