By Theo Moons, Luc van Gool, Maarten Vergauwen
3D Reconstruction from a number of photographs, half 1: ideas discusses and explains how you can extract three-d (3D) types from simple pictures. specifically, the 3D info is bought from photographs for which the digital camera parameters are unknown. the rules underlying such uncalibrated structure-from-motion tools are defined. First, a brief evaluation of 3D acquisition applied sciences places such equipment in a much wider context and highlights their very important benefits. Then, the particular idea at the back of this line of analysis is given. The authors have attempted to maintain the textual content maximally self-contained, accordingly additionally keeping off hoping on an in depth wisdom of the projective options that typically seem in texts approximately self-calibration 3D tools. relatively, mathematical causes which are extra amenable to instinct are given. the reason of the speculation contains the stratification of reconstructions received from snapshot pairs in addition to metric reconstruction at the foundation of greater than photos 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 traits instructional in this subject written by means of a similar authors. half II will concentrate on simpler information regarding the right way to enforce such uncalibrated structure-from-motion pipelines, whereas half III will define an instance pipeline with additional implementation concerns particular to this actual case, and together with a person consultant.
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Additional resources for 3D Reconstruction from Multiple Images, Part 1: Principles
2 The camera-centered reference frame is ﬁxed to the camera and aligned with its intrinsic directions, of which the principal axis is one. 1), are given with respect to the principal point p in the image. 2 Image Formation and Camera Model 319 the origin and the scene point M has coordinates ρ (X, Y, Z) for some real number ρ. The point of intersection of this line with the image plane must satisfy the relation ρ Z = f , or equivalently, ρ = Zf . Hence, the image m of the scene point M has coordinates (u, v, f ), where Y X and v = f .
5 Two Image-Based 3D Reconstruction Up-Close 339 point v1 of the line 1 in the ﬁrst image thus satisﬁes the equation ρv1 v1 = K1 RT1 V for some non-zero scalar ρv1 . Similarly, the vanishing point v2 of the projection 2 of the line L in the second image is given by ρv2 v2 = K2 RT2 V for some non-zero scalar ρv2 . Conversely, given a vanishing point v1 in the ﬁrst image, the corresponding direction vector V in the scene is V = ρv1 R1 K−1 1 v1 for some scalar ρv1 , and its vanishing point in the second image is given by ρv2 v2 = ρv1 K2 RT2 R1 K−1 1 v1 .
8 Given two images of a static scene, the location of the scene point M can be recovered from its projections m1 and m2 in the respective images by means of triangulation. duced in Section 1. As already noted there, the 3D reconstruction problem has not yet been solved, unless the internal and external parameters of the cameras are known. 10) where M = (X, Y, Z)T are the coordinates of the scene point M with respect to the world frame, m1 = (x1 , y1 , 1)T are the extended pixel coordinates of its projection m1 in the ﬁrst image, K1 is the calibration matrix of the ﬁrst camera, C1 is the position and R1 is the orientation of the ﬁrst camera with respect to the world frame, and ρ1 is a positive real number representing the projective depth of M with respect to the ﬁrst camera.
3D Reconstruction from Multiple Images, Part 1: Principles by Theo Moons, Luc van Gool, Maarten Vergauwen