By Beiwei Zhang
In this booklet, the layout of 2 new planar styles for digital camera calibration of intrinsic parameters is addressed and a line-based strategy for distortion correction is advised. The dynamic calibration of established mild platforms, which include a digicam and a projector can be handled. 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 primary matrix are commonly studied. In those tools, analytic strategies are supplied for the computational potency and redundancy within the information may be simply integrated to enhance reliability of the estimations. This quantity will hence turn out beneficial and sensible instrument for researchers and practioners operating in picture processing and desktop imaginative and prescient and similar subjects.
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Extra info for Automatic Calibration and Reconstruction for Active Vision Systems
5. 3 Plane-Based Homography According to the projective geometry, the term plane-based Homography refers to the plane-to-plane transformation in the projective space, which maps a point on one plane to a point on the other. The Homography arises when a planar surface is imaged or two views of the planar surface are obtained. 12 shows one of the cases, in which M represents a space point on the plane π, mc , and mp denote its corresponding projections. g. H = ⎣h4 h5 h6 ⎦. Under the perspective projection, the corresponding h7 h8 h9 ˜c are related by ˜p and m points m ˜p = λH m ˜c m where λ is a scale factor.
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. Assuming an arbitrary point M in the scene, the corresponding image pixels are denoted by mc and mp in Fig.
It is a fixed conic under projective transformation. Algebraically, the absolute conic corresponds to a conic with matrix ω∞ = I, such that for an arbitrary point M ∞ on the conic, the identity M T∞ ω∞ M ∞ = 0 always holds. Let M ∞ be the homogeneous representation of M ∞ , which means M ∞ = [x y z 0]T if we set M ∞ = [x y z]T . Let m∞ be its corresponding imaged point. Let the intrinsic and extrinsic parameters of the camera be respectively K c and R c , t c . 2) The above equation describes the relationship between M ∞ and its image point m∞ .
Automatic Calibration and Reconstruction for Active Vision Systems by Beiwei Zhang