Download 3D Reconstruction from Multiple Images, Part 1: Principles by Theo Moons, Luc van Gool, Maarten Vergauwen PDF
By Theo Moons, Luc van Gool, Maarten Vergauwen
3D Reconstruction from a number of photographs, half 1: ideas discusses and explains easy methods to extract third-dimensional (3D) types from undeniable pictures. specifically, the 3D details 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 tools in a much wider context and highlights their vital 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, accordingly additionally heading off hoping on an in depth wisdom of the projective thoughts that typically look in texts approximately self-calibration 3D tools. quite, mathematical factors which are extra amenable to instinct are given. the reason of the idea contains the stratification of reconstructions bought 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 pictures, half 1: rules is the 1st of a three-part Foundations and developments instructional in this subject written by way of an analogous authors. half II will specialize in simpler information regarding tips on how 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 consultant.
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Extra info for 3D Reconstruction from Multiple Images, Part 1: Principles
Observe that [a]× has rank 2 if a is non-zero. 4 The Epipolar Relation Between 2 Images of a Static Scene 335 Fig. 11 All projecting rays of the ﬁrst camera originate from its center of projection. , at the epipole. The epipolar relation states that, for a point m1 in the ﬁrst image, its corresponding point m2 in the second image must lie on the line through the epipole e2 and the vanishing point A m1 . Algebraically, this is expressed by demanding that the three-vectors m2 , e2 , and Am1 representing homogeneous coordinates of the corresponding image points are linearly dependent (cf.
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. 5 Two Image-Based 3D Reconstruction Up-Close 339 point v1 of the line 1 in the ﬁrst image thus satisﬁes the equation ρv1 v1 = K1 RT1 V for some non-zero scalar ρv1 . Similarly, the vanishing point v2 of the projection 2 of the line L in the second image is given by ρv2 v2 = K2 RT2 V for some non-zero scalar ρv2 .
A detailed discussion on this important optical component is out of the scope of this tutorial, however. 2 Projection Equations for a Camera-Centered Reference Frame To translate the image formation process into mathematical formulas we ﬁrst introduce a reference frame for the 3D environment (also called the world ) containing the scene. The easiest is to ﬁx it to the camera. 2 shows such a camera-centered reference frame. It is a righthanded and orthonormal reference frame whose origin is at the center of projection.