3.3 Pose estimation
Figure 3.7 A marker is tracked by centring the ROI containing the image around the centroid after each frame. If a marker image moves outside of the bounds of the ROI then the marker will no longer be tracked. sm x is the maximum movement in the marker position that can be tracked using a ROI of this size.
adjustment , camera calibration , pose estimation [53–55], space resection , and the perspective-n-point problem .
Multiview geometry is a broad term describing problems in geometric reconstruction us- ing multiple camera views. Structure from motion (also known as structure and motion) covers problems in refining 3D structure given a number of 2D image sequences. Bundle adjustment is part of this refining process and the estimate of camera pose is one of the out- puts of a bundle adjustment algorithm. Bundle adjustment is described in more detail in Section 3.3.1. Camera calibration often produces the extrinsic parameters of a camera (the camera’s pose) as a by-product of calculating the intrinsic parameters required for calibra-
tion. Pose estimation, space resection, and the perspective-n-point problem are all terms that describe the problem of determining the pose of a calibrated camera given known ref- erence points . Recent development in these areas includes work by Snavely, Seitz, and Szeliski [57, 58] on reconstructing 3D scenes using multiple images available from public internet galleries such as Flickr .
Within the pose estimation literature there are methods based on analytic solutions. These are solutions to what is termed the perspective-3-point [56, 60, 61], perspective-4-point [30, 56], and perspective-n-point problems . Quan and Lan  note that the pose es- timation problem can be solved with only three known markers but that four markers are required to produce a unique solution.
There are also numerical methods for solving this pose problem based around minimising some sort of cost function. Usually these methods are presented as a minimisation of an error residual in a least mean squares sense [53–55, 62]. If there are outliers in the data then convergence can be compromised. Methods are available to pre-process the data and remove outliers [53, 63]. Each of these pose estimation methods assumes that the model points are known to infinite precision. It is unrealistic to assume this accuracy but the positions of markers can be surveyed to reasonable accuracy and this can then be used to provide a basic pose estimate.