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By Theo Moons, Luc van Gool, Maarten Vergauwen

3D Reconstruction from a number of photos, half 1: ideas discusses and explains ways to extract 3-dimensional (3D) versions from simple pictures. specifically, the 3D info is bought from photographs for which the digicam parameters are unknown. the foundations underlying such uncalibrated structure-from-motion equipment are defined. First, a quick evaluate of 3D acquisition applied sciences places such equipment in a much wider context and highlights their vital merits. Then, the particular idea in the back of this line of study is given. The authors have attempted to maintain the textual content maximally self-contained, consequently additionally warding off counting on an intensive wisdom of the projective recommendations that typically seem in texts approximately self-calibration 3D tools. particularly, mathematical factors which are extra amenable to instinct are given. the reason of the speculation contains the stratification of reconstructions acquired from photo pairs in addition to metric reconstruction at the foundation of greater than photographs mixed with a few extra wisdom in regards to the cameras used. 3D Reconstruction from a number of photos, half 1: rules is the 1st of a three-part Foundations and traits instructional in this subject written by way of a similar authors. half II will concentrate on more effective information regarding how you can 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 consumer consultant.

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4. Given a point m1 in the first image, the homogeneous coordinates of the epipolar line 2 in the second image corresponding to m1 are 2 Fm1 . Recall that the epipolar relation mT2 F m1 = 0 expresses the geometrical observation that the point m2 in the second image, which corresponds to m1 , lies on the line 2 through the epipole e2 and the point Am1 , which by definition is the epipolar line in the second image corresponding to m1 . This proves the claim. 5. Similarly, given a point m2 in the second image, the homogeneous coordinates of the epipolar line 1 in the first image corresponding to m2 are 1 FT m2 .

Here, however, we are interested in the question which information can be salvaged in cases where our knowledge about the camera configuration is incomplete. As will be seen, depending on what is still known about the camera setup, the geometric uncertainty about the 3D reconstruction can range from a Euclidean motion up to a 3D projectivity. 1 Euclidean 3D Reconstruction Let us first assume that we don’t know about the cameras’ position and orientation relative to the world coordinate frame, and that we only know the position and orientation of the second camera relative to the first.

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. A flexible technique has been described by Zhang [86]. A 2D calibration object is moved several times and an image is taken by the camera every time. The internal camera calibration is easily extracted from these images. Jean-Yves Bouguet has made a Matlab implementation of this algorithm available on the Internet [9].

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3D Reconstruction from Multiple Images by Theo Moons, Luc van Gool, Maarten Vergauwen

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