Download Automatic Calibration and Reconstruction for Active Vision by Beiwei Zhang PDF

By Beiwei Zhang

In this publication, the layout of 2 new planar styles for digital camera calibration of intrinsic parameters is addressed and a line-based technique for distortion correction is advised. The dynamic calibration of dependent gentle platforms, which encompass a digital camera and a projector can also be taken care of. additionally, the 3D Euclidean reconstruction by utilizing the image-to-world transformation is investigated. finally, linear calibration algorithms for the catadioptric digital camera are thought of, and the homographic matrix and basic matrix are generally studied. In those equipment, analytic suggestions are supplied for the computational potency and redundancy within the facts could be simply integrated to enhance reliability of the estimations. This quantity will as a result end up necessary and functional software for researchers and practioners operating in photograph processing and computing device imaginative and prescient and similar subjects.

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It is independent of the scene structure, and only depends on the camera’s internal parameters and relative pose. Mathematically, the fundamental matrix is a 3 × 3 matrix and the rank is 2. Since it is a singular matrix, there are many different parameterizations. For example, we can express one row (or column) of the fundamental matrix as the linear combination of the other two rows (or columns). As a result, there are many different approaches for estimating this matrix. We will next show a simple homogeneous solution.

Homogeneous Solution In this case, we can stack the Homography matrix into a 9-vector as h = (h1 , h2 , h3 , h4 , h5 , h6 , h7 , h8 , h9 )T . 12), given n(n ≥ 4) pairs of correspondences, we can obtain the following matrix equation: ⎡ u1 ⎢0 ⎢ ⎢ Where A = ⎢ ... 13) v1 0 .. 1 0 .. 0 u1 .. 0 v1 .. 0 1 .. −u 1 u1 −v 1 x1 .. −u 1 v1 −v 1 v1 .. un 0 1 0 0 un 0 vn 0 1 −u n un −v n un −u n vn −v n vn ⎤ −u 1 −v 1 ⎥ ⎥ .. ⎥. ⎥ ⎥ −u n ⎦ −v n Let Q = AT A. Using eigenvalue decomposition, the solution for the vector h can be determined by the eigenvector corresponding to the smallest eigenvalue of Q.

From the horizontal triplet (1, 3, 1), we get the vertical alias (a1 , a2 , a3 ) = (2, 1, 2). 1, the column index is j = 15. Consequently, the coordinates for the codeword is (6, 15). From the light pattern matrix, we can verify that it is correct. 1 Some Preliminaries Notations and Definitions I. Notations Π, Πk , . . , represent the projective planes: The image plane of the CCD camera is denoted by Π, and the k-th light stripe plane by Πk . F w , F Π , F 2Πk , F 3Πk , . . , represent the coordinate frames.

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