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7 February 2018

Open Source and Independent Methods for Bundle Adjustment Assessment in Close-Range UAV Photogrammetry

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and
1
ICube Laboratory UMR 7357, Photogrammetry and Geomatics Group, National Institute of Applied Sciences (INSA), 24 Boulevard de la Victoire, 67084 Strasbourg, France
2
Department of Computing Science, Umeå University, 90187 Umeå, Sweden
3
Drone Alsace, 4 Rue Sainte-Catherine, 67000 Strasbourg, France
*
Author to whom correspondence should be addressed.
Drones2018, 2(1), 3;https://doi.org/10.3390/drones2010003
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Abstract

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.

1. Introduction

Improvements in sensor technologies, supported by developments in image processing algorithms, has renewed the interest in image-based 3D mapping of reality. In that regard, the method of close-range photogrammetry has been used many times to capture 3D information from 2D images (e.g., shape, position and size) [1]. Close-range photogrammetry has seen various applications, such as the modeling of facades [2], buildings [3,4], monuments [5,6], etc. Developments in imaging sensor technology have made this method a great alternative or complement to terrestrial laser scanners [7,8,9]. Furthermore, the use of low-cost sensors such as smartphone images has also increased [10].
In parallel with those developments, image processing algorithms have also seen a significant improvement in the past two decades. 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. Despite the presence of many open source solutions [16,17], commercial solutions remain very popular among users [18,19], especially outside the photogrammetric community. This is mainly due to the fact that commercial solutions tend to provide fairly accurate results with simpler and more streamlined user interfaces. A simplified workflow offers utility to a broad user base, but can hide the more complex functionality, which can be valuable to expert users. This is particularly important in projects that require detailed metrics such as high precision mapping, where the user often requires more control of the processing parameters. As far as geomatic requirements are concerned, it is still in the interest of the user to understand their results at a detailed enough level to be able to assess the quality of the results and determine if any part of the project may be improved.
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.
For the purposes of this paper, a UAV flight was conducted on the St-Paul church (Figure 1), located in the city of Strasbourg, France. The church is located in the Neustadt quarter, which was recently inscribed into the UNESCO list of World Heritage in the summer of 2017. The eastern facade of the church was then taken for the experiments regarding the quality of its bundle adjustment, by means of comparing the results generated by PhotoScan, DBAT and Apero.
Figure 1. The St-Paul neo-gothic church located in the UNESCO World Heritage site of Neustadt, in the city of Strasbourg, France. Imagery of the eastern facade was used for the experiments in this paper.

3. Data Acquisition and Research Design

In this paper, the UAV DJI Phantom 4 Professional was used to acquire the data. The Phantom 4 Professional was released in November 2016 and includes a 20-megapixel on-board still sensor. It is equipped with a three-axis stabilization gimbal and may fly for roughly 30 min for each flight. The sensor is a CMOS with a three-micron pixel size, with an 8.8-mm focal length. It is a multi-rotor type UAV with four rotors. The Phantom 4 sensor is integrated with the system; the image acquisitions were therefore performed using the on-board sensor, equipped with a standard frame camera lens, i.e., not a fish-eye lens. The UAV employs a global shutter as opposed to a rolling shutter.
The UAV was used to acquire the images of St-Paul’s church, a historic 19th century church located in the city of Strasbourg, France. The project therefore also serves as a 3D documentation for this particular cultural heritage. In terms of building material, the edifice was built using Alsatian red sandstone. This provides enough textures for the feature matching step and eventually the dense matching process. Both perpendicular and oblique photos were taken, following the same flight plan (Figure 3). It should be noted that UAV projects are strictly regulated by the French government. However, close-range photogrammetry projects such as the one performed in this research fit one of the scenarios set by the regulations, with an 8-kg limit on the UAV weight and a 100-m limit of operation between the pilot and the UAV [50].
Figure 3. Illustration of the flight plan, with perpendicular and oblique photos following the same vertical flight strip design. The flown path largely followed the original flight plan. However, some modifications were performed by the pilot based on the conditions in the field.

3.1. Project Planning

Before the image acquisition was performed, a topographical survey was conducted around the object of interest using a Trimble S8 robotic total station. Traverse points were measured around the church, from which detail points on the facade were measured. Some of the detail points were used as Ground Control Points (GCP), while others were used as Check Points (CP). The whole traverse network was attached to the French national cartographic projection system using a GNSS receiver and the RTK (Rapid Time Kinematic) method. Two traverse points were fixed in planimetric coordinates, while the altitude of one of the two points was fixed. The altitude values of the points were measured by GNSS, as no leveling benchmark was found near the building. Each GCP and CP was measured twice from two stations, in order to enable a spatial intersection computation on their coordinates. 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. A rough flight plan was designed beforehand to ensure enough overlap and side-lap between the images and strips, respectively, and given to the pilot. The final flight configuration resembled the designed one, although some modifications needed to be performed in the field. Furthermore, additional flights were carried out to capture more complex parts of the edifice, such as the central spire.
The project was planned to homogenize the lighting conditions and the resulting image texture as much as possible. Thus, flights were performed during the morning or the afternoon to avoid hard sunlight around noon. Cloudy days were preferred for flights over sunny days. In terms of geometric planning, the UAV was flown at an approximate camera-to-object distance of between 5 and 10 m. This corresponds to a theoretical average GSD of 2 mm. In total, three separate flights were performed to photograph the entire building. However, in this paper, only one flight over the eastern facade of the building will be discussed.

3.2. Experiments

The images were processed using the standard PhotoScan pipeline, from the tie point generation, bundle adjustment and self-calibration, up to the creation of 3D models. In this paper, we focus on the bundle adjustment results for the 485 images of the eastern facade of the church. A total of 29 marked points (see Figure 4) was measured manually. Sixteen points were used as GCP. The remaining thirteen were used as CP. The distribution of GCP followed the classical photogrammetric convention that control points should be placed at the object’s perimeters in order to ensure a uniform 3D transformation of the model [51].
Figure 4. Distribution of the ground control points and the check points on the eastern facade of St-Paul’s church. Green triangles denote GCPs while orange triangles denote Check Points (CPs).
The experiments were designed to assess and compare the bundle adjustment results from PhotoScan with DBAT and Apero. DBAT was used to reprocess the bundle adjustment computations of the PhotoScan project. Thus, DBAT computations used the same 2D point measurements and 3D GCP control measurements as PhotoScan to reprocess the project and provide detailed bundle adjustment diagnostics. In contrast, the Apero comparison was performed using only the same images as input. Thus, the Apero computations were based on measurements of different tie points rather than those generated by PhotoScan.
A graphical representation of the conducted experiments is shown in Figure 5. GCP and CP residuals were compared between PhotoScan and DBAT in Experiment 1 and PhotoScan and Apero in Experiment 2. This method of bundle adjustment assessment is often used in the literature [52,53,54]. After the comparisons were performed and the results validated, metrics from the open source algorithms were then used to perform a quality assessment of the project. The objective of the quality assessment was to investigate whether improvements and error detection can be performed on PhotoScan projects by the open source solutions, to potentially enable a more precise photogrammetric end product.
Figure 5. Flowchart of the conducted experiments involving PhotoScan, DBAT and Apero. Two experiments were performed in order to compare PhotoScan to DBAT and Apero, respectively, followed by a project quality control based on the bundle adjustment metrics reported by open source solutions.
The GCP standard deviation values obtained from the topographic survey were used as weighting factors. Furthermore, the manual marking error was set to 0.3 pixels, and the automatic tie point error was set to one pixel. The weightings of the observations in the bundle adjustment were therefore dictated by the a priori values. Identical weighting settings were used for all three algorithms (PhotoScan, DBAT and Apero) in order to compare their results under similar computing conditions.
DBAT provides more metrics than PhotoScan at the end of the computation. This may be exploited further in order to detect potential errors or outliers in the project, and thus, in this regard, DBAT can be used as a quality control tool. An example to this use of DBAT as a quality control tool will be further elaborated in Section 4.2. In the event that an unknown error comes with the project, this may be useful for the user to find these errors, which otherwise may not be detectable in PhotoScan alone.
The goal of Experiment 2 was to reprocess the original images independently. Thus, in this experiment, each software detected its own set of tie points from the same input images. Furthermore, the control points were measured manually in each software. As in Experiment 1, the observation weights for both the automatic and manual tie point measurements were set to be identical in both software in order to assess the bundle adjustment process in similar conditions. In Apero, this was regulated by using the Campari command to perform a block bundle adjustment with pre-assigned weights.

4. Results and Discussions

4.1. Bundle Adjustment Assessment

All three algorithms succeeded in computing the orientation parameters of all images in the project. Results from PhotoScan were reprocessed in DBAT using the Gauss–Newton–Armijo method, while Apero performed the bundle adjustment based on tie points provided by Pastis. A visual representation of the orientation results of the three algorithms can be seen in Figure 6.
Figure 6. Results of the external orientation process showing the positions and attitudes of each camera station, together with the sparse point clouds generated from the respective feature matching process. PhotoScan and DBAT processed the same tie point measurements. Apero generated its own set of tie point measurements from the same input images as PhotoScan. (a) PhotoScan; (b) DBAT; (c) Apero.
In PhotoScan proper, the reported 3D GCP RMS error was 5.3 mm. This is close to the expected result, considering that the theoretical GSD was around 2 mm and the GCP precision was 5 mm. The 3D CP RMS error was slightly higher, 6.3 mm.

4.1.1. Experiment 1: Reprocessing of PhotoScan Using DBAT

In the first experiment, the PhotoScan project was reprocessed using DBAT. The main objective of Experiment 1 was to investigate whether DBAT can recreate the PhotoScan results. Diagnostics from DBAT can then be used to assess the quality of the project. The evaluation was based on the GCP and CP residual RMS. The GCP and CP residuals are shown in Table 1 and Table 2, respectively.
Table 1. GCP residuals for PhotoScan and DBAT.
Table 2. CP residuals for PhotoScan and DBAT.
Overall, the DBAT residual RMS values for the GCP and CP have differences of 0.0–0.5 mm from those of PhotoScan. These slight differences are virtually negligible, since they correspond to 0.2 pixels when the GSD is taken into account. As the manual marking error was assumed to be 0.3 pixels, an error of this magnitude falls largely within the marking tolerance (hypothesized to be 1.96 σ for a 95% confidence level).
The largest disparity between 3D residuals was for Points 123 and 126, with a difference of 3.5 mm between DBAT and PhotoScan. However, the results suggest that DBAT is able to reproduce PhotoScan’s results to a reasonable degree and within the expected tolerance, thus validating the results given by PhotoScan.

4.1.2. Experiment 2: Independent Check Using Apero

In the second experiment, a similar comparison was performed between PhotoScan and Apero. The number of tie points used by PhotoScan and Apero was on average 4,000 points per image and 15,000 points per image, respectively. The GCP and CP residuals are shown in Table 3 and Table 4.
Table 3. GCP residuals for PhotoScan and Apero.
Table 4. CP residuals for PhotoScan and Apero.
The Apero GCP residuals were higher than that of PhotoScan, 8.0 mm. This is higher than the theoretical GSD of 2 mm, which roughly represents the lowest geometric value attainable by an observation on an image. However, it is still within the tolerance when considering the 5-mm GCP precision. The Apero CP residual RMS was similar to the the ones generated by the PhotoScan/DBAT results. The observed difference in residual size may be due to the different processes used to detect and filter tie points. Especially, a less aggressive tie point filtering strategy in Apero might explain the elevated residuals. An alternate hypothesis is that PhotoScan employs a better blunder detection algorithm for the automatic tie points. Nevertheless, the Apero results show that millimetric result can be obtained from this dataset.

4.2. Quality Control

Conclusions from Experiments 1 and 2 can be used to validate PhotoScan’s results. Experiment 1 showed that using the same initial values and under similar weighting conditions, PhotoScan’s results can be recreated by DBAT. Meanwhile, Experiment 2 showed that a similar order of precision can be achieved independently using Apero. In terms of computing time, DBAT took 1 h and 13 min and Apero 54 min to finish the bundle adjustment process, using a computer with a 24-core Intel(R) Xeon(R) 2.4-GHz processor and 50 GB of RAM. It should be noted that much of this computing time is used to calculate the covariance matrix for the observations, which means that projects with more observations would typically require longer computing time. In total, 485 images, 16 manual GCPs and 192,814 automatic tie points were processed. The bundle adjustment analysis provided by PhotoScan is limited to the GCP and CP residuals, as well as the image residuals of the observations, internal parameter correlations and standard deviations. However, both DBAT and Apero generate other metrics related to the quality of the result of their respective bundle adjustment processes.
The metrics presented by DBAT include the image coverage, the number of automatic tie points for each image, the overall tie point residuals for each image, as well as the standard deviations for the positions and rotational attitudes of each camera station. The DBAT statistics are presented graphically in Figure 7. The statistics generated by Apero include the overall tie point residuals, the number of automatic tie points and the percentage of points deemed useful for the bundle adjustment. A graphical representation of the Apero statistics can be seen in Figure 8.
Figure 7. Project statistics generated by DBAT related to the quality of the images and their exterior orientation parameters. Large point residuals or high standard deviations of the exterior parameters provide clues to problematic areas within the project, as does low image coverage, point count or ray angles.
Figure 8. Project statistics generated by Apero related to the quality of tie points used in the bundle adjustment process.
An analysis of Figure 7 reveals some interesting results. For example, some spatial standard deviation values of the camera stations reach 2 cm. This correlates with the low point count for those particular images, sometimes also with a decrease in camera ray angles. In some cases, the rotational standard deviation peaked to more than 0.01 degrees, something that may be due to a lower number of tie points, although the connection is less clear. Nevertheless, the correlation between the number of tie points in an image and the precision of its exterior orientation parameters is expected, as fewer observations will generate lower precision due to a lower redundancy. In addition, the image coverage correlates with the number of tie points in the images. Overall, the statistics provide clues as to what parts of the model would benefit from adding more measurements and/or images.
The metrics generated by Apero provide similar information, although with less obvious conclusions of where to improve the model. The Apero plots do show that the number of automatic points is much higher than that generated by PhotoScan. It should be noted that in both experiments, no post-bundle adjustment filtering of tie points were carried out. The number of detected points can also be used as an indication of image quality, since images with worse quality, e.g. blurred or not focused, have fewer features available for detection during the image matching step. Indeed, the number of tie points detected by Apero seems to be correlated to the percentage of tie points used in the bundle adjustment process. Figure 8 also shows that in general, Apero takes more than 90% of the detected tie points for the bundle adjustment, with a small part of the images where less than 90% were used. This can also be an indication of the quality of the images. Finally, in terms of the RMS point residuals, both DBAT and Apero gave an average value of around one pixel, which corresponds to the assumed precision of the automatically-detected tie points. In terms of posterior manual marking precision, the mean value of 0.28 pixels was obtained. This corresponds also to the expected prior value of 0.3 pixels set in the start of the bundle adjustment process.
Even though the exact algorithm used by PhotoScan remains difficult to ascertain due to its black-box nature, these approaches may help users to better understand the results they receive and eventually improve them. Indeed, with the lack of more metrics, some problems in the dataset cannot be detected within PhotoScan, as has been shown in this section.

5. Conclusions

This paper aims to demonstrate how open source solutions can be used to provide valuable survey diagnostics for bundle adjustment results generated by a commercial software, in this case PhotoScan. The experiments were conducted using a close-range UAV dataset. The relatively complex network configuration of a close-range UAV dataset compared to classical aerial photogrammetry, the inconsistent nature of its overlaps and intersecting angles, as well as the varying average GSD make it more important and difficult to detect weak parts of the network.
Two open source packages were used to provide a comparison of the bundle adjustment results. The DBAT toolbox processed the same tie point measurements as PhotoScan, whereas a comparison with the Apero package provided a case where different tie points from the same image set were used.
The results show that for this particular project, PhotoScan generated bundle adjustment results that are of the same millimetric order as the theoretical GSD. This was validated by both DBAT and Apero, which produced similar precision as estimated by the GCP and CP residuals. The results were achieved under the same weighting conditions. A downside of PhotoScan is the relative lack of detailed metrics for its orientation computation. This lack may mask potential problems in the dataset. In this paper, the DBAT results suggest that some improvements on the project can be made, particularly by adding more overlapping photos for some zones with lower exterior orientation precision. The Apero results provide some indication of the image quality that might be used for similar reasons.
Overall, this paper shows that an objective assessment of photogrammetric results is important. Errors may be hidden within the project, which limits the potential of the photogrammetric data. If the generated precision is within the project requirement, this may not be an issue. However, when problems occur within a dataset, bundle adjustment metrics, such as those provided by DBAT and, to a lesser degree, Apero, can be very helpful to detect the error. Unfortunately, this has yet to be integrated fully into commercial software such as PhotoScan. In this case, open source methods may be used to check the validity of the projects and to analyze the results in more detail. However, with the ever-increasing use of commercial photogrammetry/SfM software for mapping purposes, we have seen many improvements in this regard. If the recent addition of internal orientation errors and correlations in PhotoScan is anything to go by, open source solutions might lead the commercial software authors in the right direction. This will be a very welcome development for photogrammetrists and UAV users alike.

Acknowledgments

The project was conducted in collaboration with the Drone Alsace company (www.drone-alsace.fr), which provided the UAV images. The research also benefits from the Indonesian Endowment Fund for Education (LPDP), Republic of Indonesia. The authors would also like to thank Yi-Chou Lu for his help in performing the topographical survey.

Author Contributions

Arnadi Murtiyoso and Pierre Grussenmeyer conceived and designed the experiments. Arnadi Murtiyoso performed the experiments and analysed the data. Niclas Börlin worked on the version of DBAT used in this research. Julien Vandermeerschen and Tristan Freville were in charge of data acquisition and archiving. Julien Vandermeerschen contributed in the data pre-processing and PhotoScan processing. Arnadi Murtiyoso, Pierre Grussenmeyer, and Niclas Börlin wrote the paper.

Conflicts of Interest

The authors declare no conflict of interest. The sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

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Sample Availability: The 3D model of the St-Paul church resulting from this project can be consulted through the following Sketchfab link: https://skfb.ly/6vtQT (accessed on 20 December 2017).

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Acknowledgement to Reviewers of Drones in 2017
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