Download e-book for kindle: 3D computer vision: efficient methods and applications by Christian Wöhler

By Christian Wöhler

ISBN-10: 3642017312

ISBN-13: 9783642017315

This ebook presents an advent to the rules of third-dimensional machine imaginative and prescient and describes contemporary contributions to the sphere. Geometric equipment contain linear and package deal adjustment established methods to scene reconstruction and digital camera calibration, stereo imaginative and prescient, aspect cloud segmentation, and pose estimation of inflexible, articulated, and versatile items. Photometric recommendations evaluation the depth distribution within the photograph to deduce three-d scene constitution, whereas real-aperture techniques 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 eventualities comprise business caliber inspection, metrology, human-robot-interaction, and distant sensing.

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67) for i = 2, . . , m, which corresponds to Ri = A−1 Bi − bi pT A1 . It follows from the i T orthonormality of the rotation matrices that RR = I and thus Ai ATi = Bi − bi pT A1 AT1 Bi − bi pT T . 68) A geometric entity which is important in this context is the absolute conic Ω∞ . 69) holds. Points x˜ = (X ,Y, Z,W )T on the absolute conic Ω∞ are situated on the plane at infinity π˜ ∞ . In a metric coordinate system we have π˜ ∞ = (0, 0, 0, 1)T , and points on Ω∞ satisfy the two relations X 2 + Y 2 + Z2 = 0 W = 0.

Geometrically, Q∗∞ is represented by the planes which are tangent to Ω∞ (the “envelope” of Ω∞ ). Algebraically, Q∗∞ is represented by a homogeneous 4× 4 matrix of rank 3, which in its canonical form in a metric coordinate system corresponds to Q∗∞ = I 0 . 71) The plane at infinity π˜ ∞ is the null-vector of Q∗∞ (Hartley and Zisserman, 2003). An important geometric entity in the context of self-calibration is the image of the absolute conic (IAC). Its determination requires knowledge about the projection from the plane at infinity π˜ ∞ to the image plane.

A problem with this approach is the fact that the fundamental matrix obtained from Eq. e. the eigenvectors belonging to the zero eigenvalues of F T and F, respectively. These do not exist if the rank of F is higher than 2. A convenient way to enforce the constraint that F is of rank 2 is to replace the solution found by the singular value decomposition of the coefficient matrix G as defined in Eq. 57) by the matrix F¯ which minimises the Frobenius norm F − F¯ F subject to the constraint det F¯ = 0.

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


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