Download e-book for kindle: 3D Reconstruction from Multiple Images by Theo Moons, Luc van Gool, Maarten Vergauwen

By Theo Moons, Luc van Gool, Maarten Vergauwen

3D Reconstruction from a number of photographs, half 1: ideas discusses and explains ways to extract three-d (3D) versions from undeniable pictures. specifically, the 3D details 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 quick evaluate 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 averting hoping on an intensive wisdom of the projective ideas that typically seem in texts approximately self-calibration 3D equipment. relatively, mathematical causes which are extra amenable to instinct are given. the reason of the speculation comprises the stratification of reconstructions received from snapshot pairs in addition to metric reconstruction at the foundation of greater than pictures mixed with a few extra wisdom concerning the cameras used. 3D Reconstruction from a number of pictures, half 1: ideas is the 1st of a three-part Foundations and developments instructional in this subject written by means of an analogous authors. half II will specialize 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 resources for 3D Reconstruction from Multiple Images

Example text

Unfortunately, the relation F = [ e2 ]× A does not define the matrix A uniquely. Indeed, suppose A1 and A2 are 3 × 3-matrices such that F = [ e2 ]× A1 and F = [ e2 ]× A2 . Then [ e2 ]× ( A1 − A2 ) = 0. e. [ e2 ]× v = e2 × v for all v ∈ R3 , the columns of A1 and A2 can differ by a scalar multiple of e2 . In particular, A1 = A2 + e2 aT for some 3-vector a ∈ R3 . Hence, we conclude that we cannot extract A from correspondences alone. So, what other image information can then be used to determine A?

This term reflects that the transformations higher up in the list are special types (subgroups) of the transformations lower down. Obviously, the uncertainty about the reconstruction goes up when going down the list, as also corroborated by the number of degrees of freedom in these transformations. Awareness of this stratification might be useful when additional information on the scene is available, because by exploiting this information it sometimes is possible to upgrade the geometric structure of the reconstruction to one with less uncertainty.

Since the camera matrix K1 is known, the Euclidean reconstruction M of M will be established if the unknown scalar factor ρ1 can be found. 3. 4 in chapter 2) and this relative orientation of the cameras is assumed to be known here. 3 can be computed. 13) gives the position of the first camera in the camera-centered reference frame of the second one; and this relative position of the cameras is assumed to be known here as well. 13) gives a system of 3 linear equations from which the two unknown scalar factors ρ1 and ρ2 can be computed.

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


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