By Theo Moons, Luc van Gool, Maarten Vergauwen
3D Reconstruction from a number of pictures, half 1: ideas discusses and explains the right way to extract third-dimensional (3D) types from simple pictures. specifically, the 3D info is got from photographs for which the digital camera parameters are unknown. the rules underlying such uncalibrated structure-from-motion tools are defined. First, a quick assessment of 3D acquisition applied sciences places such equipment in a much broader context and highlights their very important merits. Then, the particular thought in 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 warding off counting on an intensive wisdom of the projective thoughts that typically seem in texts approximately self-calibration 3D equipment. fairly, mathematical motives which are extra amenable to instinct are given. the reason of the idea comprises the stratification of reconstructions acquired from photograph 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 developments educational in this subject written through an analogous authors. half II will specialise in simpler information regarding find out how 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 person advisor.
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Extra resources for 3D Reconstruction from Multiple Images
Similarly, the vanishing point v2 of the projection 2 of this line L in the second image is given by ρv2 v2 = K2 RT2 V . Given the vanishing point v1 in the first image, the direction vector V of the line L in the scene is V = ρv1 R1 K−1 1 v1 and its projection in the second image −1 T is ρv2 v2 = ρv1 K2 RT2 R1 K−1 v . As A = K R this relation between the vanishing 1 2 2 R1 K1 1 42 CHAPTER 3. PRINCIPLES OF PASSIVE 3D RECONSTRUCTION points v1 and v2 can be simplified to ρ v2 = A v1 , where ρ = ρρv2 is a non-zero scalar factor.
3 Affine 3D Reconstruction A last step towards our goal of 3D reconstruction from the image data alone is to give up on knowledge of the internal camera parameters as well. o. 4. 3D RECONSTRUCTION EQUATIONS UP-CLOSE 45 the digital images into pure perspective projections of the scene, as was done in the previous section. The next step to take therefore seems to be to include this lack of knowledge about the calibration matrix K1 in the geometric uncertainty about the 3D scene. 15) by M M . 3. This system can be solved as in the metric case.
This explains why the matrix A is called the infinite homography in the computer vision literature. 2, the aim of passive 3D reconstruction was described as to recover the geometric structure of a (static) scene from one or more images of it. If the internal and external parameters of the cameras are known, such 3D reconstruction can be achieved from two images by triangulation. 2, is not directly applicable. From an algebraic point of view, triangulation can be interpreted as solving the projection equations for the scene point M.