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

By Christian Wöhler

This booklet presents an advent to the rules of third-dimensional machine imaginative and prescient and describes fresh contributions to the sector. Geometric equipment contain linear and package adjustment dependent methods to scene reconstruction and digital camera calibration, stereo imaginative and prescient, aspect cloud segmentation, and pose estimation of inflexible, articulated, and versatile gadgets. Photometric concepts evaluation the depth distribution within the picture to deduce 3-dimensional scene constitution, whereas real-aperture techniques make the most the habit of the purpose unfold functionality. it truly is proven how the mixing of numerous equipment raises reconstruction accuracy and robustness. purposes eventualities comprise business caliber inspection, metrology, human-robot-interaction, and distant sensing.

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Otherwise, the pseudoinverse of M does not exist. A reduced, two-dimensional DLT can be formulated by setting z = 0 in Eq. 27) for scene points situated on a plane in three-dimensional space. In this special case it is always possible to choose the world coordinate system such that z = 0 for all regarded scene points. The DLT method is a simple and easy-to-use camera calibration method, but it has two essential drawbacks. The first one is that the computed elements of the matrix R do not form an orthonormal matrix, as it would be expected for a rotation matrix.

Eq. 78) is termed Kruppa equation; due to its algebraic form, however, this formulation cannot be easily applied in practice. 4 Geometric Calibration of Single and Multiple Cameras 37 where ui and vi are the column vectors of the matrices U und V obtained by singular value decomposition of the fundamental matrix F according to F = UDV T , with D as a diagonal matrix, and σi are the singular values. In Eq. 79) the DIACs ω1∗ and ω2∗ are not assumed to be identical in the two images. Cross-multiplication of both sides of the equation yields two quadratic equations in the parameters of ω1∗ and ω2∗ .

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, . . , N), an equation for determining the parameters L1 . . L16 is obtained according to  x1 y1 z1 1 −u1 x1 −u1 y1 −u1 z1 Q1 Q1 Q1 Q1 0 0 0 0 Q1 Q1 Q1  0 0 0 0 x1 y1 z1 1 −v1 x1 −v1 y1 −v1 z1  Q1 Q1 Q1 Q1 Q1 Q1 Q1  .

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