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

By Christian Wöhler

This booklet offers an advent to the principles of 3-dimensional computing device imaginative and prescient and describes fresh contributions to the sphere. Geometric equipment contain linear and package adjustment dependent methods to scene reconstruction and digicam calibration, stereo imaginative and prescient, aspect cloud segmentation, and pose estimation of inflexible, articulated, and versatile items. Photometric suggestions review the depth distribution within the snapshot to deduce 3-dimensional scene constitution, whereas real-aperture ways make the most the habit of the purpose unfold functionality. it really is proven how the combination of numerous equipment raises reconstruction accuracy and robustness. purposes situations comprise commercial caliber inspection, metrology, human-robot-interaction, and distant sensing.

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L11 . Radial and tangential distortions introduce offsets ∆u and ∆v with respect to the position of the image point expected according to the pinhole model. Using the polynomial laws defined in Eqs. 29) (Kwon, 1998). The additional parameters L12 . . L14 describe the radial and L15 and L16 the tangential lens distortion, respectively. By replacing in Eq. 27) the values of u by u + ∆u and v by v + ∆v and defining the abbreviation Qi = L9 xi + L10 yi + L11 zi + 1, where xi , yi and zi denote the world coordinates of scene point i (i = 1, .

Incorporating orthonormality constraints into the DLT scheme would require nonlinear optimisation methods instead of the simple iterative linear solution scheme defined by Eq. 32). Another drawback is the fact that the optimisation scheme is not equivalent to bundle adjustment. While bundle adjustment minimises the backprojection error in the image plane, Eq. 30) illustrates that the DLT method minimises the error of the backprojected scaled pixel coordinates (ui /Qi , vi /Qi ). It is not guaranteed that this somewhat arbitrary error measure is always a reasonable choice.

52) (Zhang, 1998). 4 Geometric Calibration of Single and Multiple Cameras 27 r1 = λ A−1 h1 r2 = λ A−1 h2 r3 = r1 × r2 t = λ A−1 h3 . 53) The matrix R computed according to Eq. 53), however, does not generally satisfy the orthonormality constraints imposed on a rotation matrix. For initialisation of the subsequent nonlinear bundle adjustment procedure, Zhang (1998) therefore describes a method to estimate the rotation matrix which is closest to a given 3 × 3 matrix in terms of the Frobenius norm.

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