By Theo Moons, Luc van Gool, Maarten Vergauwen

ISBN-10: 1601982844

ISBN-13: 9781601982841

3D Reconstruction from a number of photos, half 1: ideas discusses and explains how you can extract third-dimensional (3D) versions from undeniable photographs. particularly, the 3D info 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 wider context and highlights their vital merits. Then, the particular thought at the back of this line of analysis is given. The authors have attempted to maintain the textual content maximally self-contained, for this reason additionally keeping off hoping on an in depth wisdom of the projective ideas that sometimes seem in texts approximately self-calibration 3D tools. fairly, mathematical causes which are extra amenable to instinct are given. the reason of the speculation comprises the stratification of reconstructions received from picture 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 tendencies instructional in this subject written by means of a similar authors. half II will concentrate on more effective 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 consumer consultant.

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Additional resources for 3D Reconstruction from Multiple Images, Part 1: Principles

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Notice that this also shows that the infinite homography A maps the epipole e1 in the first image onto the epipole e2 in the second image. , 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. , 1 FT m2 . By interchanging the role of the two images in the reasoning leading up to the epipolar relation derived above, one easily sees that the epipolar line 1 in the first image corresponding to a point m2 in the second image is the line through the epipole e1 in the first image and the vanishing point A−1 m2 in the first image of the projecting ray of m2 in the second camera.

5 Two Image-Based 3D Reconstruction Up-Close 347 could be a candidate for the unknown matrix A. Unfortunately, as both the fundamental matrix F and [e2 ]× have rank 2, the matrix [e2 ]× F is not invertible as A ought to be. But, recall from the previous section that two matrices A1 and A2 satisfying F = [e2 ]× A1 and F = [e2 ]× A2 are related by A1 = A2 + e2 aT for some three-vector a ∈ R3 . This implies that the unknown matrix A must be of the form A = −(1 / e2 2 ) [e2 ]× F + e2 aT for some three-vector a ∈ R3 .

Right: The same image after removal of the radial distortion. Straight lines in the scene now appear as straight lines in the image as well. Radial distortion is a non-linear effect and is typically modeled using a Taylor expansion. , the effect is symmetric around the center. The effect takes place in the lens, hence mathematically the radial distortion should be between the external and internal parameters of the pinhole model. The model we will propose here follows this strategy. Let us define   mux ρ mu = muy  = RT (M − C) , 1 where M = (X, Y, Z)T are the coordinates of a scene point with respect to the world frame.

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3D Reconstruction from Multiple Images, Part 1: Principles by Theo Moons, Luc van Gool, Maarten Vergauwen


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