Least-squares 3D reconstruction from one or more views and geometric clues

Bundle adjustment with additional constraints applied to imagery of the Dunhuang wall paintings

“…Different types of geometric constraints can be applied in case of redundancy in bundle adjustment, which include topology constraints (e.g., object point constraint, object line constraint, and coplanarity) and object constraints (e.g., parallelism, perpendicularity, and symmetry) (van den Heuvel, 1998). Least-squares estimates of the 3D points, camera position orientation are recovered precisely by exploiting planes, alignments, symmetries, orthogonalities, and other forms of geometrical regularity (Grossmann and Santos-Victor, 2005). The integration of parallelism constraint on planes and line-photogrammetric bundle adjustment results in a valid polyhedral description of the object, which offers the advantage of processing a model without real control points on the condition that the exterior orientation parameters are approximately known (Hrabácek and van den Heuvel, 2000).…”

3D surface models by geometric constraints propagation

“…Constraint-based methods [1,3,7,8,10,21] are more flexible, as they do not rely on a-priori models but use simple primitives like points and lines. Geometric information, such as orthogonality, parallelism, or planarity, is given in the form of constraints on 3D points and reconstruction is obtained as the solution of an optimization process.…”

“…[1,8,10,20], the constraints detection phase requires the user to provide a geometrical description of the model, which can be very timeconsuming. In other cases [3,7], geometric constraints are detected automatically thanks to prior knowledge about the model to reconstruct.…”

Error Analysis of Stereo Calibration and Reconstruction

“…The reconstruction of the 3D scene is the process of recovering unknown 3D coordinates from K ≥ 2 2D images of the scene made from different points of view. We assume at least two calibrated cameras are used to take pictures of the scene, and the calibration stage performed for each of the cameras has yielded the projection matrices P (1) , P (2) , ...,…”

“…Another approach is presented in [9], where the method of bounding boxes is used in the uncertainty analysis of 3D reconstruction. The sensitivity of 3D reconstruction of a specific kind of scene is analyzed in [2]. Hartley and Zisserman [3] analyzed the uncertainties in identifying a homography between two 2D images based on given points, using the best approximation in terms of the Mahalanobis distance between given and reconstructed coordinates.…”