By Theo Moons, Luc van Gool, Maarten Vergauwen
3D Reconstruction from a number of pictures, half 1: rules discusses and explains how you can extract three-d (3D) types from simple pictures. particularly, the 3D details is bought from pictures for which the digicam parameters are unknown. the foundations underlying such uncalibrated structure-from-motion equipment are defined. First, a quick evaluation of 3D acquisition applied sciences places such equipment in a much wider context and highlights their very important benefits. Then, the particular thought at the back of this line of study is given. The authors have attempted to maintain the textual content maximally self-contained, consequently additionally heading off counting on an in depth wisdom of the projective strategies that typically seem in texts approximately self-calibration 3D equipment. really, mathematical reasons which are extra amenable to instinct are given. the reason of the idea comprises the stratification of reconstructions received from picture pairs in addition to metric reconstruction at the foundation of greater than photos mixed with a few extra wisdom concerning the cameras used. 3D Reconstruction from a number of photos, half 1: ideas is the 1st of a three-part Foundations and traits instructional in this subject written by means of an analogous authors. half II will specialize in simpler information regarding tips to 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 consultant.
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Additional info for 3D Reconstruction from Multiple Images, Part 1: Principles
11), viz. M = C1 + ρ1 R1 K−1 1 m1 . 12) of the second camera, yields T ρ2 m2 = ρ1 K2 RT2 R1 K−1 1 m1 + K2 R2 (C1 − C2 ). 14) The last term in this equation corresponds to the projection e2 of the position C1 of the ﬁrst camera in the second image: ρe2 e2 = K2 RT2 (C1 − C2 ). 15) e2 is called the epipole of the ﬁrst camera in the second image. 11) in the second image. 3 that R1 K−1 1 m1 is the direction vector of the projecting ray of m1 with respect to the world frame. In the camera-centered reference frame of the second camera, the coordinates of this vector are RT2 R1 K1 −1 m1 .
Hence a non-linear minimization algorithm like Levenberg–Marquardt is applied to these data. The algorithm is initialized with the distortion parameters set to zero. 3 The 3D Reconstruction Problem 329 ﬁtted. , the resulting error is close to zero). 5. 3 The 3D Reconstruction Problem The aim of passive 3D reconstruction is to recover the geometric structure of a (static) scene from one or more of its images: Given a point m in an image, determine the point M in the scene of which m is the projection.
The coordinates ¯ provide a 3D reconstruction of the scene point M up to an unknown M 3D similarity, as expected. We could have seen this additional scaling issue coming also intuitively. If one were to scale a scene together with the cameras in it, then this would have no impact on the images. In terms of the relative camera positions, this would only change the distance between them, not their relative orientations or the relative direction in which one camera is displaced with respect to the other.
3D Reconstruction from Multiple Images, Part 1: Principles by Theo Moons, Luc van Gool, Maarten Vergauwen