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Derivative-based Optimization: Lie Algebra Method
Published in Kenichi Kanatani, 3D Rotations, 2020
Bundle adjustment described in Sec. 6.8 is a process of adjusting the bundle of rays, or lines of sight, that start from the camera viewpoint, i.e., the lens center, and piece through the points we are viewing in such a way that the camera imaging geometry of perspective projection is satisfied. This term originates from photogrammetry for computing the 3D topography for map making from aerial photographs. Its origin dates back to the invention of photography and has been extensively studied mainly in Germany. Since the advent of computers in the second half of the 20th century, its algorithm has been produced by computer vision researchers. Today, various program codes are available on the Web. The best known is the SBA of Lourakis and Argyros [33]. Snavely et al. (39; 40) combined it with image correspondence extraction process and offered a tool called bundler. The procedure described in Sec. 6.8 is a modification of SBA for explicitly using the Lie algebra method for camera rotation optimization [29]; in most of currently available open software, the quaternion representation of rotations is used.
Algorithmic approaches to BIM modelling from reality
Published in Yusuf Arayici, John Counsell, Lamine Mahdjoubi, Gehan Nagy, Soheir Hawas, Khaled Dewidar, Heritage Building Information Modelling, 2017
Ebenhaeser Joubert, Yusuf Arayici
Bundle adjustment is the minimization of the re-projection error between the locations of observed image points, which is then equated as the sum of squares of a large number of nonlinear, real-valued functions. Nonlinear least-squares algorithms are used to perform the minimization. Due to the ease of implementation and the use of a dampening strategy, the Levenberg–Marquardt algorithm is one of the most successful. Normal equations are solved to iteratively linearize the function to be minimized in the neighbourhood of the current estimate. A sparse block structure is obtained by the normal equations due to the lack of interaction between parameters for different 3D points. Employing a sparse variant of the Levenberg–Marquardt algorithm, the above statement can be used to gain computational benefits which explicitly take advantage of the normal equations zeros pattern, avoiding storing and operating on zero elements (Triggs et al., 1999).
Photogrammetry
Published in Toru Yoshizawa, Handbook of Optical Metrology, 2015
When we measure with more than one picture, we combine bundle adjustment to the process. As the measuring method that uses the more images gets the more discrepancy, we minimize the discrepancy by bundle adjustment. Bundle adjustment process is the process to determine simultaneously, by least-squares method, both the exterior orientation parameters (the 3D position of the camera and the inclination of three axes) and the interior orientation parameters (lens distortion, principal distance, principal point, and others) of each picture, identifying control point, tie point, and pass point of the same object photographed on each different picture (or in the light bundle of each picture).
Structure SLAM with points, planes and objects
Published in Advanced Robotics, 2022
Benchun Zhou, Maximilian Gilles, Yongqi Meng
Bundle adjustment is an optimization process to jointly optimize camera poses , cuboids , planes and feature points . It can be formulated as a nonlinear least squares problem: where is a covariance matrix of different error measurements. The measurement error between different landmarks is represented by and will be explained in Subsubsection 3.2.2. The problem can be solved by Gauss–Newton or Levenberg–Marquardt algorithm available in many libraries, such as g2o [33]. Huber robust cost function [31] is applied to all measurement errors to improve the robustness.
Volumetric monitoring of cutaneous leishmaniasis ulcers: can camera be as accurate as laser scanner?
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2019
Omar Zenteno, Eduardo González, Sylvie Treuillet, Braulio M. Valencia, Benjamin Castaneda, Alejandro Llanos-Cuentas, Yves Lucas
So called Structure-from-Motion (SfM) algorithm consists in modelling a scene observed in a series of images taken from different points of view. The camera parameters, positions and 3D scene geometry are automatically carried out by iterative bundle adjustment from similar features identified and matched in different images. 3D modelling by SfM can be done from images taken with any commercial camera. The scene is assumed to be rigid. The trajectory of the camera needs to include largely separated points of views for better triangulation. On the other hand, it is necessary to obtain good quality overlapping images to compute precise 3D coordinates of points and camera positions. Figure 1(a) shows an example of 3D point cloud computed from a series of images. Colour texture can also be mapped onto the 3D model.
Multi-frame optimisation for active stereo with inverse renderingto obtain consistent shape and projector-camera posesfor 3D endoscopic system
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2023
Ryo Furukawa, Michihiro Mikamo, Ryusuke Sagawa, Yuki Okamoto, Shiro Oka, Shinji Tanaka, Hiroshi Kawasaki
To deal with such problems in passive-stereo systems, multi-frame global optimisations are often used for correcting scaling mismatches and shape distortions, and also for widening the measurement areas, i.e., SfM or SLAM using only a camera. In general, such systems are often based on optimisation techniques of multi-frame information called bundle adjustment (BA), where 3D feature points and the camera positions are optimised from 2D observations of the 3D points by minimising a loss function that represents the sum of reprojection errors, i.e., the errors between the 2D observations and the projections of the 3D points onto the camera images.