By Theo Moons, Luc van Gool, Maarten Vergauwen
3D Reconstruction from a number of photos, half 1: rules discusses and explains the way to extract three-d (3D) types from undeniable photographs. particularly, the 3D details is acquired from photographs for which the digicam parameters are unknown. the foundations underlying such uncalibrated structure-from-motion equipment are defined. First, a quick overview of 3D acquisition applied sciences places such tools in a much broader context and highlights their very important benefits. 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, for that reason additionally averting counting on an intensive wisdom of the projective techniques that typically look in texts approximately self-calibration 3D tools. fairly, mathematical motives which are extra amenable to instinct are given. the reason of the speculation comprises the stratification of reconstructions got 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 photographs, half 1: rules is the 1st of a three-part Foundations and traits educational in this subject written through an analogous authors. half II will concentrate on simpler information regarding easy methods to enforce such uncalibrated structure-from-motion pipelines, whereas half III will define an instance pipeline with extra implementation matters particular to this actual case, and together with a consumer advisor.
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Extra info for 3D Reconstruction from Multiple Images, Part 1: Principles
Indeed, consider a line L in the scene with direction vector V ∈ R3 . 12. Parameter equations of this line are M = C1 + τ V with τ a scalar parameter, and the projection of every point M on this line in the ﬁrst image is given by K1 RT1 (X − C1 ) = τ K1 RT1 V. The vanishing L oo image l1 v1 C1 Fig. 12 The vanishing point v1 in the ﬁrst image of the projection 1 of a line L in the scene is the point of intersection of the line through the center of projection C1 and parallel to L with the image plane.
1 ﬁrst. The matrix A is deﬁned algebraically as A = K2 RT2 R1 K−1 1 , but it also has a clear geometrical interpretation: the matrix A transfers vanishing points of directions in the scene from the ﬁrst image to the second one. Indeed, consider a line L in the scene with direction vector V ∈ R3 . 12. Parameter equations of this line are M = C1 + τ V with τ a scalar parameter, and the projection of every point M on this line in the ﬁrst image is given by K1 RT1 (X − C1 ) = τ K1 RT1 V. The vanishing L oo image l1 v1 C1 Fig.
Observe that this pinhole image actually is the photo-negative image of the scene. The photo-positive image one observes when watching a photograph or a computer screen corresponds to the projection of the scene onto a hypothetical plane that is situated in front of the camera obscura at the same distance from the hole as the opposite wall on which the image is actually formed. In the sequel, the term image plane will always refer to this hypothetical plane in front of the camera. This hypothetical plane is preferred to avoid sign reversals in the computations.