3D Reconstruction and Camera Calibration from Circular-Motion Image Sequences

This dissertation, "3D Reconstruction and Camera Calibration From Circular-motion Image Sequences" by Yan, Li, 李燕, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled "3D Reconstruction and Camera Calibration from Circular-Motion Image Sequences" Submitted by Li Yan for the degree of Doctor of Philosophy at The University of Hong Kong in December 2005 This thesis investigates the problem of 3D reconstruction from circular motion image sequences. The problem is normally resolved in two steps: projective reconstruction and then metric reconstruction by self-calibration. A key question considered in this thesis is how to make use of the circular motion information to improve the reconstruction accuracy and reduce the reconstruction ambiguity. The information is previously utilized by identifying the fixed image entities (e.g. the image of the rotation axis, vanishing line of the motion plane, etc). These fixed entities, however, only exist in constant intrinsic parameter sequences. In this thesis, circular motion constraints, which are valid for varying intrinsic parameter (e.g. zooming/refocusing) cameras, are formulated from the movement of camera center and principal plane. Based on the constraints, several novel algorithms are developed for each step of the whole 3D reconstruction procedure. For image sequences with known rotation angles, a circular projective reconstruction algorithm is proposed. We first formulate the circular motion constraints in the Euclidean frame, and then deduce the most general form of reconstruction in a projective frame that satisfies the circular motion constraints. The constraints are gradually enforced during an iterative process, resulting in a circular projective reconstruction. This approach can be used to deal with both cases of constant and varying intrinsic parameters. It is proved that the circular projective reconstruction retrieves metric reconstruction up to a two-parameter ambiguity representing a projective distortion along the rotation axis of the circular motion. Based on the circular projective reconstruction, a hierarchical self-calibration algorithm is proposed to estimate the remaining two parameters. Closed-form expressions of the absolute conic and its image are deduced in terms of the two parameters, which are then determined with zero-skew and unit aspect ratio assumptions. Alternatively, starting from a general (rather than circular) projective reconstruction, a stratified self-calibration algorithm is proposed to upgrade the projective reconstruction directly to a metric one. In this case, the plane at infinity is first identified with (i) the circular motion constraint on camera center and (ii) zero-skew and unit aspect ratio assumptions. With the knowledge of the plane at infinity, the camera calibration matrices can be readily obtained. All the above algorithms assume that the rotation angles are known. In the case if the angles are unknown, we provide two novel rotation angle recovery methods. For constant intrinsic parameter sequences, rotation angles can be recovered by using the fixed image entities. For varying intrinsic parameter sequences, it is shown that the movements of the camera center and principal plane form two concentric circles on the motion plane. By identifying the corresponding conic loci in 3D projective frame, the geometry of circular motion on the motion plane can be recovered. Compared with existing methods, the new method is more flexible in that it allows the intrinsic parameters to vary, and is simpler by avoi