**3.1 Bundle adjustment for line segments**

In the case of feature points, the final position of the projected features relative to the camera poses is estimated throughout an optimization process. As a part of most SfM pipelines, bundle adjustment [14] is based on Levenberg-Marquardt, and it rearranges the poses of the cameras and 3D points. The cost function of this optimization process is engineered to find the minimum distance error between the reprojection of every 3D point onto each camera plane and their original observation. A limit value for the residual is usually set to stop the iterative process for the event of convergence, while another threshold is set to end the optimization when reaching a maximum number of iterations.

Along matched segments under a viewpoint change, the only point-to-point valid correspondences are their endpoints. Segment's endpoint location are noticeably less accurate than a rotation and scale invariant feature point. Employing line endpoints as the sole set of geometrical constraints in the adjustment might not be

#### **Figure 2.**

*Figure from [2]. Graphic representation of the 3D abstraction layer of the method. The different cameras are represented as drones.*

## *Build 3D Abstractions with Wireframes DOI: http://dx.doi.org/10.5772/intechopen.96141*

resembling the intersections is a sparse cloud, and it is denoted as R. Finally, and same as with the endpoints, the 3D intersections R enter the least-squares optimization. The SBA returns the new optimized estimations for ϒ, and the optimal 3D intersections R. The spatial line and camera pose estimations are corrected by forward projecting them from the newly estimated camera planes ϒ. This returns the final sketch {ϒ,Γ}. The high level diagram on **Figure 2** shows the process

In the case of feature points, the final position of the projected features relative to the camera poses is estimated throughout an optimization process. As a part of most SfM pipelines, bundle adjustment [14] is based on Levenberg-Marquardt, and it rearranges the poses of the cameras and 3D points. The cost function of this optimization process is engineered to find the minimum distance error between the reprojection of every 3D point onto each camera plane and their original observation. A limit value for the residual is usually set to stop the iterative process for the event of convergence, while another threshold is set to end the optimization when

Along matched segments under a viewpoint change, the only point-to-point valid correspondences are their endpoints. Segment's endpoint location are noticeably less accurate than a rotation and scale invariant feature point. Employing line endpoints as the sole set of geometrical constraints in the adjustment might not be

*Figure from [2]. Graphic representation of the 3D abstraction layer of the method. The different cameras are*

described in this section.

*Applications of Pattern Recognition*

**Figure 2.**

**50**

*represented as drones.*

**3.1 Bundle adjustment for line segments**

reaching a maximum number of iterations.

adequate to improve the 3D sketch. Some of the reasons for this are that recurrent segment mismatches, fragmentation or the inaccurate placement of counterparts may prevent the convergence of the optimization. It is possible to perform a linebased Bundle Adjustment by converting the primitives into Plücker coordinates [20, 21] within the cost function of the optimisation process. This allows a reduction in the number of parameters and the computational cost.
