María-Eugenia Polo

Analysis of Uncertainty and Repeatability of a Low-Cost 3D Laser Scanner

Portable 3D laser scanners are a valuable tool for compiling elaborate digital collections of archaeological objects and analysing the shapes and dimensions of pieces. Although low-cost desktop 3D laser scanners have powerful capacities, it is important to know their limitations. This paper performs an analysis of the uncertainty and repeatability of the NextEngine™ portable low-cost 3D laser scanner by scanning an object 20 times in two different resolution modes—Macro and Wide. Some dimensions of the object were measured using a digital calliper, and these results were used as the “true” or control data. In comparing the true and the scanned data, we verified that the mean uncertainty in the Macro Mode is approximately half that of the Wide Mode, at ±0.81 mm and ±1.66 mm, respectively. These experimental results are significantly higher than the accuracy specifications provided by the manufacturer. An analysis of repeatability shows that the successive replicates do not match in the same position. The results are better in Macro Mode than in Wide Mode; it is observed that the repeatability factor is slightly larger than the corresponding mode accuracy, with ±0.84 vs. ±0.81 mm in Macro Mode and ±1.82 vs. ±1.66 mm in Wide Mode. We suggest several improvements, such as adding an external reference scale or providing a calibrated object to allow for a self-calibration operation of the scanner.

Estimating the Uncertainty of Terrestrial Laser Scanner Measurements

At present, several papers discuss the accuracy and precision of terrestrial laser scanners (TLSs), but the research continues to focus on the behavior of the TLSs. The purpose of this paper is to propose a method to evaluate the uncertainty of a TLS (FARO Photon 80). A rigid and transportable aluminum structure with 28 black-and-white targets was designed for this purpose. The structure was scanned 12 times at several distances from 2 to 70 m, and the x, y, and z coordinates of the center of the targets were automatically identified. Data were analyzed by means of circular and spherical statistics using R modules programmed in our research group. Analysis reveals that 3-D spatial distribution has a stratified pattern in the Z-axis. Regardless of the scanner status, these results indicate that these analyses should be performed periodically because they can have an impact on some studies. The proposed methodology is robust and simple and can be performed with free software such as the R modules used in this work.

Positional Accuracy Analysis of Satellite Imagery by Circular Statistics

The proposed method in this paper uses circular statistics for the analysis of errors in the positional accuracy of geometric corrections satellite images using Independent Check Lines (ICL) instead of Independent Check Points (ICP). Circular statistics has been preferred because of the vectorial nature of the spatial error. A study case has been presented and discussed in detail. From the TERRA-ASTER images of Extremadura area (Spain), the Ground Control Point (GCP), ICP, and ICL data were acquired using differential GPS through field survey, and the planimetric positional accuracy was analyzed by both the conventional method (using ICP) and the proposed method (using 1CL). Comparing conventional and proposed methods, the results indicated that modulus statistics are similar (e.g., RMSE of Geometric Correction 1 were 17.5 for the conventional method and 17.2 m for proposed method). But as additional results, azimuthal component statistics was calculated (e.g., mean direction: 247.2° in Geometric Correction 1), and several tests were made which showed the error distribution are not uniform and normal.

VecStatGraphs2D, A Tool for the Analysis of Two-Dimensional Vector Data: An Example Using QuikSCAT Ocean Winds

Circular or directional data are used in disciplines such as meteorology, geomatics, biology, and geology. The analysis of angular data requires special methods that are available in some statistical packages. However, these tools analyze only the angular values and do not include the vector modules, assuming unit vectors in all cases. In this letter, an open-source graphic and statistical package, i.e., VecStatGraphs2D, is described. It works in the R environment and provides statistics and graphics for modules (linear) and azimuths (circular), as well as graphics for the joint analysis of modules and azimuths. QuikSCAT satellite wind data are used to demonstrate some features of the package. QuikSCAT data are non-unit-length vectors, where both azimuth and magnitude (speed) are derived from u and v vector components (vector projections over the x- and y-axes). The example is used to show the seasonal change of winds in the Intertropical Convergence Zone, a key area in the ocean bird migration from the North to South Atlantic oceans.

The Use of Spherical Statistics to Analyze Digital Elevation Models: An Example From LIDAR and ASTER GDEM

The use of spherical statistics for comparing and analyzing different digital elevation models (DEMs) is proposed in this letter by the new software package VecStatGraphs3D. Spherical data deal with angular data such as unit vector in 3-D space and are used in disciplines such as meteorology, geomatics, biology, and geology. Usually, the most common descriptor to analyze DEMs is the root-mean-square error (linear statistic), but this statistic itself cannot describe the error positional distributions. Comparing homologous points in two different DEMs generates 3-D vectors, which can be analyzed by means of spherical statistics. A 3-D vector is defined by its module (linear statistics) and colatitude and longitude (spherical statistics). While several graphical and statistical tools are available for the analysis of directional data in 3-D, these tools consider only the angular magnitude and work with unit vectors. In this letter, the open-source software package VecStatGraphs3D is described. It works in the R environment and provides statistics for modules (linear), colatitude and longitude (spherical), and graphics for the joint analysis of 3-D vectors. The spatial locations of singular points between two DEMs of different spatial resolution: LIDAR (5 m) and ASTER Global Digital Elevation Map (30 m) are compared as examples using VecStatGraphs3D. The interactive 3-D graphics reveal spatial patterns and assist in understanding the effect of the DEM resolution on the uncertainty of the spatial locations of relief.

Detection and Labeling of Sensitive Areas in Hydrological Cartography Using Vector Statistics

The recognition and delineation of hydrological stream lines has, traditionally, been a subjective manual task in cartography. However, digital elevation models (DEMs) are nowadays often employed to extract stream lines automatically, via the use of geographic information systems. Whereas the automatic generation of hydrological networks presents errors, their manual recognition can be almost arbitrary. In this paper, we propose a methodology with which to label potentially sensitive zones in the comparison of hydrological cartographic networks. Two different sources were analyzed: a conventional cartographic stream network, and one automatically extracted from a DEM. The 72 500 vectors of displacement, representing the spatial disagreement (or fit) between the stream networks, were also examined. A number of remarkable distributions of large errors were identified that were a cause for alarm; these errors are here denoted by “warnings” and are classified into six different groups. The displacement vectors were also analyzed in terms of modulus and azimuth, thereby allowing the analysis of the isotropy of the spatial displacements. We propose the use of all of the derived information as metadata for hydrological spatial quality, as well as the extension of the methodology to any other type of cartographic element (roads, cadastral, etc.) for which two different vector format information sources are compared.

Analysis of free image-based modelling systems applied to support topographic measurements

The image-based modelling systems create 3D models of objects using a set of overlapping photographs. Several applications are available that do not require a user expert or expensive equipment. In this paper, four free systems were applied in two cases: ReMake, which is a freemium software, CMP Web Service and Arc 3D, which are free web services, and Visual SfM, which is a free software. The purpose of this study is to evaluate the applications that support topographical measurements and to assess the potential for their use in accurate modelling. The results show that these systems can be an auxiliary technique for surveyors and can provide an advantage in some cases.