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: rules discusses and explains ways to extract 3-dimensional (3D) types from undeniable pictures. particularly, the 3D details is acquired from pictures for which the digicam parameters are unknown. the foundations 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 very important benefits. Then, the particular concept at the back of this line of analysis is given. The authors have attempted to maintain the textual content maximally self-contained, hence additionally heading off hoping on an intensive wisdom of the projective strategies that typically seem in texts approximately self-calibration 3D tools. really, mathematical causes which are extra amenable to instinct are given. the reason of the idea contains the stratification of reconstructions bought from snapshot pairs in addition to metric reconstruction at the foundation of greater than pictures mixed with a few extra wisdom in regards to 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 through an analogous authors. half II will specialise in more effective information regarding tips to enforce such uncalibrated structure-from-motion pipelines, whereas half III will define an instance pipeline with additional implementation concerns particular to this actual case, and together with a person advisor.

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Additional resources for 3D Reconstruction from Multiple Images

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Calibrating Radial Distortion Only For some computer vision tasks like object recognition, complete calibration of the camera is not necessary. However, radial distortion in the images makes these tasks more difficult. That is why one sometimes simply wants to remove the radial distortion in the images. In order to remove it, the parameters of the distortion need to be known. A simple but efficient way of retrieving the parameters without a full calibration is explained below. 10. The picture on the left shows a clearly distorted image and we want to undistort it.

27), viz κ K1 H = 0 T a K1 . 28) For the other images, where each is paired with the first, a similar set of equations can be derived. But as mentioned, we have to be careful in order to end up with the same projective distortion already resulting from the reconstruction based on the first two views. In order to achieve this, we ˆ j for each new view independently, but have to find a solution that holds cannot simply choose A for ˆ ρˆ1 m1 = M ˆj M ˆ + ej ρˆj mj = A and for j ∈ {2, . . , m} ˆ satisfy all reconstruction equations at once.

Apart from the generic case, special camera motions are considered as well. In particular, camera translation respectively rotation are discussed. These often occur in practice, but their systems of self-calibration equations or reconstruction equations become singular. Special attention is paid to the case of internally calibrated cameras and the important notion and use of the essential matrix is explored. 2 The 3D Reconstruction Problem The aim of passive 3D reconstruction is to recover the geometric structure of a (static) scene from one or more of its images: given a point m in an image, determine the point M in the scene of which m is the projection.

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