Comparison of form measurement results for optical aspheres and freeform surfaces

Comparing form measurement data for aspheres and freeform surfaces is an important tool for ensuring the quality and functionality of the devices used to take such measurements and may also allow the underlying measurement methods to be evaluated. However, comparing the highly accurate form measurements of such complex surfaces is a demanding task. It is difficult to analyze measurement results whose accuracies are in the range of several tens of nanometers root-mean-square, especially when comparing data with different, and anisotropic distributions of the 3D measurement points on the surface under test. In this paper, we investigate eight different 3D measurement point distributions that are typical of highly accurate measurement systems currently in use and demonstrate the effects of these distributions on the comparison results by using virtually generated data and applying different evaluation strategies. The results show that, for the examples investigated, the different 3D measurement point distributions can yield different levels of accuracy for the comparison. Furthermore, an improved evaluation procedure is proposed and recommendations on how to significantly reduce the influence of the different 3D measurement point distributions on the comparison result are given. A method of employing virtually generated test data is presented that may be generalized in order to further improve and validate future comparison methods.

Experimental Study on 3D Measurement Accuracy Detection of Low Altitude UAV for Repeated Observation of an Invariant Surface

Low-altitude unmanned aerial vehicle (UAV) photogrammetry combined with structure-from-motion (SFM) algorithms is the latest technological approach to imaging 3D stereo constructions. At present, derivative products have been widely used in landslide monitoring, landscape evolution, glacier movement, volume measurement, and landscape change detection. However, there is still a lack of research into the accuracy of 3D data positioning based on the structure-from-motion of unmanned aerial vehicle (UAV-SFM) technology, itself, which can affect the measurable effectiveness of the results in further applications of this technological approach. In this paper, validation work was carried out for the DJI Phantom 4 RTK UAV, for earth observation data related to 3D positioning accuracy. First, a test plot with a relatively stable surface was selected for repeated flight imaging observations. Specifically, three repeated flights were performed on the test plot to obtain three sorties of images; the structure from motion and multi-view stereo (SFM-MVS) key technology was used to process and construct a 3D scene model, and based on this model the digital surface model (DSM) and digital orthophoto map (DOM) data of the same plot with repeated observations were obtained. In order to check the level of 3D measurement accuracy of the UAV technology itself, a window selection-based method was used to sample the point cloud set data from the three-sortie repeat observation 3D model. The DSM and DOM data obtained from three repeated flights over the surface invariant test plots were used to calculate the repeat observation 3D point errors, taking into account the general methodology of redundant observation error analysis for topographic surveys. At the same time, to further analyze the limits of the UAV measurement technique, possible under equivalent observation conditions with the same processing environment, a difference model (DOD) was constructed for the DSM data from three sorties, to deepen the overall characterization of the differences between the DSMs obtained from repeated observations. The results of the experimental study concluded that both the analysis of the 3D point set measurements based on window sampling and the accuracy evaluation using the difference model were generally able to achieve a centimeter level of planimetric accuracy and vertical accuracy. In addition, the accuracy of the surface-stabilized hardened ground was better, overall, than the accuracy of the non-hardened ground. The results of this paper not only probe the measurement limits of this type of UAV, but also provide a quantitative reference for the accurate control and setting of an acquisition scheme of the UAV-based SfM-MVS method for geomorphological data acquisition and 3D reconstruction.

Studies on Three-Dimensional (3D) Accuracy Optimization and Repeatability of UAV in Complex Pit-Rim Landforms As Assisted by Oblique Imaging and RTK Positioning

Unmanned Aerial Vehicles (UAVs) are a novel technology for landform investigations, monitoring, as well as evolution analyses of long−term repeated observation. However, impacted by the sophisticated topographic environment, fluctuating terrain and incomplete field observations, significant differences have been found between 3D measurement accuracy and the Digital Surface Model (DSM). In this study, the DJI Phantom 4 RTK UAV was adopted to capture images of complex pit-rim landforms with significant elevation undulations. A repeated observation data acquisition scheme was proposed for a small amount of oblique-view imaging, while an ortho-view observation was conducted. Subsequently, the 3D scenes and DSMs were formed by employing Structure from Motion (SfM) and Multi-View Stereo (MVS) algorithms. Moreover, a comparison and 3D measurement accuracy analysis were conducted based on the internal and external precision by exploiting checkpoint and DSM of Difference (DoD) error analysis methods. As indicated by the results, the 3D scene plane for two imaging types could reach an accuracy of centimeters, whereas the elevation accuracy of the orthophoto dataset alone could only reach the decimeters (0.3049 m). However, only 6.30% of the total image number of oblique images was required to improve the elevation accuracy by one order of magnitude (0.0942 m). (2) An insignificant variation in internal accuracy was reported in oblique imaging-assisted datasets. In particular, SfM-MVS technology exhibited high reproducibility for repeated observations. By changing the number and position of oblique images, the external precision was able to increase effectively, the elevation error distribution was improved to become more concentrated and stable. Accordingly, a repeated observation method only including a few oblique images has been proposed and demonstrated in this study, which could optimize the elevation and improve the accuracy. The research results could provide practical and effective technology reference strategies for geomorphological surveys and repeated observation analyses in sophisticated mountain environments.

Accuracy of image-free navigation in intraoperative leg length change from total hip arthroplasty using evaluations from 2D and 3D measurements

Background Leg length discrepancy is one of the most common problems after total hip arthroplasty (THA). The aim of this study was to investigate the accuracy of image-free navigation in intraoperative leg length change (LLC) using evaluations from anteroposterior radiographs (2D measurement) and 3D bone models using CT data (3D measurement). Methods One hundred THAs with cementless cups and stems were performed using an image-free navigation system in our hospital. We evaluated the accuracy of image-free navigation based on LLC from 2D and 3D measurements. Furthermore, we also investigated error in absolute value and correlations between 2D and 3D measurements in LLC. Results The accuracy of image-free navigation based on 2D measurement was 94% within 5 mm and 76% within 3 mm. The accuracy of image-free navigation based on 3D measurement was 92% within 5 mm and 81% within 3 mm. The error in absolute value in LLC between 2D and 3D measurements was 1.7 ± 1.4 mm (range, 0 to 6 mm). A strong correlation was observed between 2D and 3D measurements in the LLC. Conclusions In the present study, good accuracy of image-free navigation in intraoperative LLC was confirmed for both evaluation methods from 2D and 3D measurements. In addition, the error in absolute value in the LLC between 2D and 3D measurements was very small, and we observed a strong correlation between 2D and 3D measurements. Based on these results, evaluation of LLC from radiographs was considered sufficient if radiographs can be taken accurately.