## 2 Related Work
### Calibration Methods
#### 2.4.4 Multi-Camera Calibration  
Algorithms for performing calibration on a set of many cameras were proposed by [PERSON] and [PERSON] [48], [PERSON] et al. [49] and [PERSON] [50]. As far as calibration of stereo cameras is concerned there is a commonly used technique available in the OpenCV library [41]. OpenCV provides a calibration based on the Hartley's rectification method [51]. This method was also adapted by authors of this paper for performing calibration on the EBCA array. As opposed to pairwise stereo calibration like the standard openCV method, which usually requires one _central_ camera to which all other cameras are calibrated; the work in [8] showed a multi-camera array calibration pipeline that fulfills all associated requirements. Figure 2: AIT’s dot pattern calibration target with 3-dot central element (**left**: abstract representation, **right**: actual acquisition with one of EBCA’s cameras). Note that this pattern is the smallest possible asymmetric configuration on a regular grid and three distinct marks (the different color is for illustration only) suffice to estimate an affine transformation, which approximates the more general perspective transformation needed to unwarp the image, c.f. [46] for details. The bundle adjustment [7] is a nonlinear method for refining extrinsic and intrinsic camera parameters, as well as the structure of the scene. For a set of \(n\) cameras with index \(i\), it is characterized by minimizing the reprojection error by a standard least-squares approach  
\[E(\mathbf{C},\mathbf{P})=\sum_{i=1}^{n}\sum_{w}dist(p_{iw},C_{i}(P_{w})))^{2}, \tag{3}\]  
where \(C_{i}(P_{w})=C(A_{i},T_{i},d_{i},P_{w})\) is the _reprojected point_ as defined in Equation (2), i.e., the image of a point \(P_{w}\) as observed by the \(i\)-th camera, which depends on the intrinsic matrix \(A_{i}\), the camera pose \(T_{i}\) and the distortion parameters \(d_{i}\). Furthermore, \(p_{iw}\) is the corresponding detected point of the calibration pattern and \(dist(p_{iw},C_{i})\) is the point's reprojection error. For the details on this approach, please refer to the work in [8], where it is shown that the minimization of Equation (3) yields better reprojection errors and thus a higher 3D reconstruction quality than standard pairwise stereo approaches. Bundle adjustment is designed for retrieving camera poses for the purpose of processing images with the use of multi-view stereo or structure from motion methods described in Section 2.1[7]. Similarly as in camera calibration and rectification methods, in bundle adjustment points representing the same parts of objects are identified on different images. The identification of corresponding points is based on descriptors such as SIFT. However, bundle adjustment has a different application than stereo camera calibration and rectification, because bundle adjustment is foremost performed to identify in a common 3D space camera poses from which images were taken. It is used when images are taken from different points of view located around viewed object and there is no need to make cameras parallel to each other. In the MVS technology, there is also a problem of taking images from proper positions. [PERSON] et al. addressed this issue in a case in which the number of images taken for the purpose of processing them using MVS is redundant [52]. They proposed a method for selecting suitable images. Bundle adjustment generates some error in estimating camera poses in 3D space. This error needs to be considered in relation to distances between cameras. The impact of the error is not critical when cameras are not adjacent to each other. However, in case of using adjacent cameras such as those in a stereo camera it is crucial to perform calibration with higher precision using predefined patterns such as chessboards.