In this dissertation, two problems of 3D structure and camera motion recovery are addressed. The first problem is the 3D reconstruction problem using multiple images. Particularly, in this dissertation, the line estimation using multiple views is researched. The second addressed problem of 3D structure and camera motion recovery is the line-based bundle adjustment. A novel cost function for line based bundle adjustment is proposed.
For the line based 3D structure and camera motion recovery, the first problem is the 3D line estimation which provides an initial solution for the bundle adjustment process. In order to facilitate this I represent the 3D line by its Plücker coordinates. A typical requirement of this representation is the use of the Plücker constraint. I leverage the state of art by waiving the Plücker constraint and propose two streamlined solutions to 3D line estimation problem. The first proposed 3D line estimation model is based on the preservation of coincidence in the dual projective space. The second method is based on the averaging of a set of 3D lines which are generated by the intersection of the back-projection planes from multiple images viewing the estimated 3D line.
The second component of my proposal is to develop a new bundle adjustment model. More precisely, a new line-based cost function that defines a geometric error in the object space is proposed. The proposed cost function is derived by using the equivalence between the image plane and the unit Gaussian sphere with its center positioned at the optical center of the image plane. Particularly, the geometric error is defined as the integrated squared distance between the projection plane of a 3D line estimate and point on the perimeter of the circular sector equivalent to the image of the 3D line estimate.