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One of the major quality control parameters in bundle adjustment arethe posterior estimates of the covariance of the estimated parameters. Posterior covariance computations have been part of the open source Damped Bundle Adjustment Toolbox in Matlab (DBAT) since its first public release. However, for large projects, the computation of especially the posterior covariances of object points have been  time consuming.

The non-zero structure of the normal matrix depends on the ordering of the parameters to be estimated. For some algorithms, the ordering of the parameters highly affect the computational effort needed to compute the results. If the parameters are ordered to have the object points first, the non-zero structure of the normal matrix forms an arrowhead.

In this paper, the legacy DBAT posterior computation algorithm was compared to three other algorithms: The Classic algorithm based on the reduced normal equation, the Sparse Inverse algorithm by Takahashi, and the novel Inverse Cholesky algorithm. The Inverse Cholesky algorithm computes the explicit inverse of the Cholesky factor of the normal matrix in arrowhead ordering.

The algorithms were applied to normal matrices of ten data sets of different types and sizes. The project sizes ranged from 21 images and 100 object points to over 900 images and 400,000 object points. Both self-calibration and non-self-calibration cases were investigated. The results suggest that the Inverse Cholesky algorithm is the fastest for projects up to about 300 images. For larger projects, the Classic algorithm is faster. Compared to the legacy DBAT implementation, the Inverse Cholesky algorithm provides a performance increase by one to two orders of magnitude. The largest data set was processed in about three minutes on a five year old workstation.

The legacy and Inverse Cholesky algorithms were implemented in Matlab. The Classic and Sparse Inverse algorithms included codes written in C. For a general toolbox as DBAT, a pure Matlab implementation is advantageous, as it removes any dependencies on,e.g., compilers. However, for a specific lab with mostly large projects, compiling and using the classic algorithm will give improved performance. Nevertheless, the Inverse Cholesky algorithm is a significant addition to DBAT as it enables a relatively rapid computation of more statistical metrics, further reinforcing its application for reprocessing bundle adjustment results of black-box solutions.

The main purpose of this article is to show that photogrammetric bundle-adjustment computations can be sequentially organized into modules. Furthermore, the chain rule can be used to simplify the computation of the analytical Jacobians needed for the adjustment. Novel projection models can be flexibly evaluated by inserting, modifying, or swapping the order of selected modules. As a proof of concept, two variants of the pinhole projection model with Brown lens distortion were implemented in the open-source Damped Bundle Adjustment Toolbox and applied to simulated and calibration data for a nonconventional lens system. The results show a significant difference for the simulated, error-free, data but not for the real calibration data. The current flexible implementation incurs a performance loss. However, in cases where flexibility is more important, the modular formulation should be a useful tool to investigate novel sensors, data-processing techniques, and refractive models.

The Damped Bundle Adjustment Toolbox (DBAT) is a free, open-source, toolbox for bundle adjustment. The purpose of DBAT is to provide an independent, open-source toolkit for statistically rigorous bundle adjustment computations. The capabilities include bundle adjustment, network analysis, point filtering, forward intersection, spatial intersection, plotting functions, and computations of quality indicators such as posterior covariance estimates and parameter correlations. DBAT is written in the high-level Matlab language and includes several processing example files. The input formats have so far been restricted to PhotoModeler export files and Photoscan (Metashape) native files. Fine-tuning of the processing has so far required knowledge of the Matlab language.

This paper describes the development of a scripting language based on the XML (eXtensible Markup Language) language that allow the user a fine-grained control over what operations are applied to the input data, while keeping the needed programming skills at a minimum. Furthermore, the scripting language allows a wide range of input formats. Additionally, the XML format allows simple extension of the script file format both in terms of adding new operations, file formats, or adding parameters to existing operations. Overall, the script files will in principle allow DBAT to process any kind of photogrammetric input and should extend the usability of DBAT as a scientific and teaching tool for photogrammetric computations.

In this study we have investigated why diameters of tree stems, which are approximately cylindrical, are often overestimated by mobile laser scanning. This paper analyzes the physical processes when using ground-based laser scanning that may contribute to a bias when estimating cylinder diameters using circle-fit methods. A laser scanner simulator was implemented and used to evaluate various properties, such as distance, cylinder diameter, and beam width of a laser scanner-cylinder system to find critical conditions. The simulation results suggest that a positive bias of the diameter estimation is expected. Furthermore, the bias follows a quadratic function of one parameter - the relative footprint, i.e., the fraction of the cylinder width illuminated by the laser beam. The quadratic signature opens up a possibility to construct a compensation model for the bias.

An underwater imaging system with camera and lens behind a flat port does not behave as a standard pinhole camera with additional parameters. Indeed, whenever the entrance pupil of the lens is not in contact with the flat port, the standard photogrammetric model is not suited anymore and an extended mathematical model that considers the different media would be required. Therefore, when dealing with flat ports, the use of the classic photogrammetric formulation represents a simplification of the image formation phenomenon, clearly causing a degradation in accuracy. Furthermore, flat ports significantly change the characteristics of the enclosed imaging device and negatively affect the image quality, introducing heavy curvilinear distortions and optical aberrations. With the aim of mitigating the effect of systematic errors introduced by a combination of (i) image quality degradation, induced by the flat ports, and (ii) a non-rigorous modelling of refraction, this paper presents a stochastic model for image observations that penalises those that are more affected by aberrations and departure from the pinhole model. Experiments were carried out at sea and in pools showing that the use of the proposed stochastic model is beneficial for the final accuracy with improvements up to 50 %.

In this paper we investigate how the residuals in bundle adjustmentcan be split into a composition of simple functions. According to thechain rule, the Jacobian (linearisation) of the residual can be formedas a product of the Jacobians of the individual steps. Whenimplemented, this enables a modularisation of the computation of thebundle adjustment residuals and Jacobians where each component haslimited responsibility. This enables simple replacement of componentsto e.g. implement different projection or rotation models byexchanging a module. The technique has previously been used toimplement bundle adjustment in the open-source package DBAT (Borlinand Grussenmeyer, ¨ 2013) based on the Photogrammetric and ComputerVision interpretations of Brown (1971) lens distortion model. In thispaper, we applied the technique to investigate how affine distortionscan be used to model the projection of a tilt-shift lens. Two extendeddistortion models were implemented to test the hypothesis that theordering of the affine and lens distortion steps can be changed toreduce the size of the residuals of a tilt-shift lens calibration.Results on synthetic data confirm that the ordering of the affine andlens distortion steps matter and is detectable by DBAT. However, whenapplied to a real camera calibration data set of a tilt-shift lens, nodifference between the extended models was seen. This suggests thatthe tested hypothesis is false and that other effects need to bemodelled to better explain the projection. The relatively lowimplementation effort that was needed to generate the models suggestthat the technique can be used to investigate other novel projectionmodels in photogrammetry, including modelling changes in the 3Dgeometry to better understand the tilt-shift lens.

Close-range photogrammetry as a technique to acquire reality-based 3D data has, in recenttimes, seen a renewed interest due to developments in sensor technologies. Furthermore, the strong democratization of UAVs (Unmanned Aerial Vehicles) or drones means that close-rangephotogrammetry 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 AdjustmentToolbox) 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.

Photogrammetry has recently seen a rapid increase in many applications, thanks to developments in computing power and algorithms. Furthermore with the democratisation of UAVs (Unmanned Aerial Vehicles), close range photogrammetry has seen more and more use due to the easier capability to acquire aerial close range images. In terms of photogrammetric processing, many commercial software solutions exist in the market that offer results from user-friendly environments. However, in most commercial solutions, a black-box approach to photogrammetric calculations is often used. This is understandable in light of the proprietary nature of the algorithms, but it may pose a problem if the results need to be validated in an independent manner. In this paper, the Damped Bundle Adjustment Toolbox (DBAT) developed for Matlab was used to reprocess some photogrammetric projects that were processed using the commercial software Agisoft Photoscan. Several scenarios were experimented on in order to see the performance of DBAT in reprocessing terrestrial and UAV close range photogrammetric projects in several configurations of self-calibration setting. Results show that DBAT managed to reprocess PS projects and generate metrics which can be useful for project verification.

We propose a novel photogrammetric method for field plot inventory, designed for simplicity and time efficiency on-site. A prototype multi-camera rig was used to acquire images from field plot centers in multiple directions. The acquisition time on-site was less than two minutes. From each view, a point cloud was generated using a novel, rig-based matching of detected SIFT keypoints. Stems were detected in the merged point cloud, and their positions and diameters were estimated. The method was evaluated on 25 hemi-boreal forest plots of a 10-m radius. Due to difficult lighting conditions and faulty hardware, imagery from only six field plots was processed. The method performed best on three plots with clearly visible stems with a 76% detection rate and 0% commission. Dieameters could be estimated for 40% of the stems with an RMSE of 2.8-9.5 cm. The results are comparable to other camera-based methods evaluated in a similar manner. The results are inferior to TLS-based methods. However, our method is easily extended to multiple station image schemas, something that could significantly improve the results while retaining low commission errors and time on-site. Furthermore, with smaller hardware, we believe this could be a useful technique for measuring stem attributes in the forest.

The aim of this paper is to investigate whether the Matlab-based Damped Bundle Adjustment Toolbox (DBAT) can be used to provide independent verification of the BA computation of two popular software—PhotoModeler (PM) and PhotoScan (PS).

For frame camera data sets with lens distortion, DBAT is able to reprocess and replicate subsets of PM results with high accuracy. For lens-distortion-free data sets, DBAT can furthermore provide comparative results between PM and PS. Data sets for the discussed projects are available from the authors.

The use of an external verification tool such as DBAT will enable users to get an independent verification of the computations of their software. In addition, DBAT can provide computation of quality parameters such as estimated standard deviations, correlation between parameters, etc., something that should be part of best practice for any photogrammetric software. Finally, as the code is free and open-source, users can add computations of their own.