3D computer vision: efficient methods and applications by Christian Wöhler

By Christian Wöhler

This publication offers an creation to the rules of third-dimensional machine imaginative and prescient and describes contemporary contributions to the sector. Geometric tools contain linear and package adjustment established methods to scene reconstruction and digicam calibration, stereo imaginative and prescient, element cloud segmentation, and pose estimation of inflexible, articulated, and versatile gadgets. Photometric suggestions evaluation the depth distribution within the photograph to deduce third-dimensional scene constitution, whereas real-aperture methods make the most the habit of the purpose unfold functionality. it really is proven how the mixing of a number of equipment raises reconstruction accuracy and robustness. functions situations contain commercial caliber inspection, metrology, human-robot-interaction, and distant sensing.

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44) To compute the homography H, Zhang (1999a) proposes a nonlinear optimisation procedure which minimises the Euclidean backprojection error of the scene points projected into the image plane. The column vectors of H are denoted by h1 , h2 , and h3 . 45) where λ is an arbitrary scale factor. It follows from Eq. 45) that r1 = (1/λ )A−1 h1 and r2 = (1/λ )A−1h2 with λ = 1/ A−1h1 = 1/ A−1h2 . 46) as constraints on the intrinsic camera parameters. In Eq. 46), the expression A−T −1 is an abbreviation for AT .

45) that r1 = (1/λ )A−1 h1 and r2 = (1/λ )A−1h2 with λ = 1/ A−1h1 = 1/ A−1h2 . 46) as constraints on the intrinsic camera parameters. In Eq. 46), the expression A−T −1 is an abbreviation for AT . 47) 26 1 Geometric Approaches to Three-dimensional Scene Reconstruction which can alternatively be defined by a six-dimensional vector b = (B11 , B12 , B22 , B13 , B23 , B33 ). 48) where the six-dimensional vector vi j corresponds to vi j = hi1 h j1 , hi1 hi2 + h j1 , hi2 h j2 , hi3 h j1 + hi1 h j3 , hi3 h j2 + hi2 h j3 , hi3 h j3 T .

2. This procedure immediately allows to compute a projective reconstruction of the scene based on the camera projection matrices P1 and P2 which can be computed with Eqs. 22). Given a sufficient number of point correspondences S1 x˜ , S2 x˜ (seven or more), the fundamental matrix F can be computed based on Eq. 20). We express the image points S1 x˜ and S2 x˜ in normalised coordinates by the vectors (u1 , v1 , 1)T and (u2 , v2 , 1)T . Each point correspondence generates one linear equation in the unknown matrix elements of F according to u1 u2 F11 + u2v1 F12 + u2 F13 + u1 v2 F21 + v1 v2 F22 + v2 F23 + u1 F31 + v1 F32 + F33 = 0.

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