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 photos, half 1: ideas discusses and explains how you can extract third-dimensional (3D) versions from undeniable photographs. particularly, the 3D details is got from photos for which the digicam 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 wider context and highlights their very important merits. Then, the particular conception in the back of this line of study is given. The authors have attempted to maintain the textual content maximally self-contained, as a result additionally keeping off counting on an intensive wisdom of the projective techniques that typically look in texts approximately self-calibration 3D tools. quite, mathematical reasons which are extra amenable to instinct are given. the reason of the idea comprises the stratification of reconstructions got from photo pairs in addition to metric reconstruction at the foundation of greater than photographs 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 tendencies instructional in this subject written by way of a similar authors. half II will specialise in simpler information regarding the right way to 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 consultant.

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Additional info for 3D Reconstruction from Multiple Images

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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.

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. Formulated in this way, passive 3D reconstruction is seen as solving the following problem : Given two images I1 and I2 of a (static) scene and a set of corresponding image points m1 ∈ I1 and m2 ∈ I2 between these images, determine a calibration matrix K1 , a position C1 and an orientation R1 for the first camera and a calibration matrix K2 , a position C2 and an orientation R2 for the second camera, and for every pair of corresponding image points m1 ∈ I1 and m2 ∈ I2 compute world coordinates (X, Y, Z) of a scene point M such that ρ1 m1 = K1 RT1 ( M − C1 ) and ρ2 m2 = K2 RT2 ( M − C2 ) .

These objects all have in common that easily recognizable markers are applied to them. 9. Measure the 3D positions of the markers on this object. • Take one or more (depending on the algorithm) pictures of the object with the camera to be calibrated. • Extract and identify the markers in the image. • Fit a linearized calibration model to the 3D-2D correspondences found in the previous step. • Improve the calibration with a non-linear optimization step. Tsai’s and Zhang’s methods As mentioned, both 2D and 3D calibration objects can be used to perform the calibration.

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