By Theo Moons, Luc van Gool, Maarten Vergauwen
3D Reconstruction from a number of pictures, half 1: rules discusses and explains easy methods to extract three-d (3D) versions from undeniable photos. specifically, the 3D details is acquired from pictures for which the digital camera parameters are unknown. the rules underlying such uncalibrated structure-from-motion tools are defined. First, a quick overview of 3D acquisition applied sciences places such tools in a much broader context and highlights their vital benefits. Then, the particular thought in the back of this line of analysis is given. The authors have attempted to maintain the textual content maximally self-contained, as a result additionally heading off counting on an intensive wisdom of the projective ideas that sometimes look in texts approximately self-calibration 3D equipment. fairly, mathematical factors which are extra amenable to instinct are given. the reason of the idea comprises the stratification of reconstructions bought from picture pairs in addition to metric reconstruction at the foundation of greater than pictures mixed with a few extra wisdom in regards to the cameras used. 3D Reconstruction from a number of photos, half 1: ideas is the 1st of a three-part Foundations and developments educational in this subject written by means of a similar authors. half II will concentrate on simpler information regarding tips to enforce such uncalibrated structure-from-motion pipelines, whereas half III will define an instance pipeline with additional implementation matters particular to this actual case, and together with a person advisor.
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Improve the calibration with a non-linear optimization step. Tsai’s and Zhang’s methods As mentioned, both 2D and 3D calibration objects can be used to perform the calibration. In his seminal article Tsai  describes an algorithm to calibrate a camera with either 2D or 3D calibration objects. He follows the procedure explained above. Using his technique it is possible to retrieve not only the intrinsic but also the extrinsic parameters of the camera. Using the 2D 32 CHAPTER 2. 9: Calibration objects in 3D (left) and 2D (right) calibration object, some degenerate setups can appear however, the most important one consisting of the calibration plane being parallel to the image plane.
That this will not automatically amount from a pairwise reconstruct-and-then-combine procedure will be explained a bit further shortly. In any case, the workaround is to solve all equations as one larger system. 3. 4. 3D RECONSTRUCTION EQUATIONS UP-CLOSE 51 ˆ2 = ˆ and thus are also unknown) and A where ρˆ1 and ρˆ2 are non-zero scalars (which depend on M 2 ˆ ˆ (−1/ e2 ) [e2 ]× F12 with F12 an estimate of the fundamental matrix between the first two images ˆ constitute a 3D reconstruction as computed from point correspondences.
Awareness of this stratification might be useful when additional information on the scene is available, because by exploiting this information it sometimes is possible to upgrade the geometric structure of the reconstruction to one with less uncertainty. Illustrations of this will be given in the sequel. In the first instance, the conclusion of this section — viz. that without additional information about the (internal and external) camera parameters the 3-dimensional structure of the scene only can be recovered from two images up to an unknown projective transformation — might come as a disappointment.
3D Reconstruction from Multiple Images by Theo Moons, Luc van Gool, Maarten Vergauwen