By Theo Moons, Luc van Gool, Maarten Vergauwen
3D Reconstruction from a number of photos, half 1: rules discusses and explains the right way to extract third-dimensional (3D) types from simple photos. specifically, the 3D info is got from pictures for which the digital camera parameters are unknown. the rules underlying such uncalibrated structure-from-motion equipment are defined. First, a brief evaluation of 3D acquisition applied sciences places such equipment in a much broader context and highlights their very important merits. Then, the particular thought in the back of this line of study is given. The authors have attempted to maintain the textual content maximally self-contained, as a result additionally warding off hoping on an in depth wisdom of the projective recommendations that sometimes look in texts approximately self-calibration 3D equipment. relatively, mathematical motives which are extra amenable to instinct are given. the reason of the speculation contains the stratification of reconstructions received 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 pictures, half 1: ideas is the 1st of a three-part Foundations and traits educational in this subject written by way of an identical authors. half II will specialise in simpler information regarding how one can enforce such uncalibrated structure-from-motion pipelines, whereas half III will define an instance pipeline with extra implementation concerns particular to this actual case, and together with a consumer advisor.
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Extra info for 3D Reconstruction from Multiple Images, Part 1: Principles
A reconstruction which is correct up to an unknown 3D aﬃne transformation. It suﬃces to know A and e2 in order to compute an aﬃne reconstruction of the scene. 2 and in more detail in Section 4, e2 can be extracted from F, and F can be derived — up to a non-zero scalar factor — from corresponding points between the images. Since e2 is in the left nullspace of F, an unknown scalar factor on F does not prevent the extraction of e2 , however. Unfortunately, determining A is not that easy in practice.
18 based on symmetry considerations. 1 ﬁrst. The matrix A is deﬁned algebraically as A = K2 RT2 R1 K−1 1 , but it also has a clear geometrical interpretation: the matrix A transfers vanishing points of directions in the scene from the ﬁrst image to the second one. Indeed, consider a line L in the scene with direction vector V ∈ R3 . 12. Parameter equations of this line are M = C1 + τ V with τ a scalar parameter, and the projection of every point M on this line in the ﬁrst image is given by K1 RT1 (X − C1 ) = τ K1 RT1 V.
For the determination of all parameters one often uses the term complete calibration. Traditional 3D passive reconstruction techniques had a separate, explicit camera calibration step. As highlighted before, the diﬀerence with selfcalibration techniques as explained in this tutorial is that in the latter 328 Principles of Passive 3D Reconstruction Fig. 6 Calibration objects: 3D (left) and 2D (right). the same images used for 3D scene reconstruction are also used for camera calibration. , a set of 3D coordinates with corresponding 2D coordinates in the image for their projections.
3D Reconstruction from Multiple Images, Part 1: Principles by Theo Moons, Luc van Gool, Maarten Vergauwen