By Kenichi Kanatani, Yasuyuki Sugaya, Yasushi Kanazawa
This classroom-tested and easy-to-understand textbook/reference describes the state-of-the-art in 3D reconstruction from a number of photographs, making an allowance for all features of programming and implementation. not like different desktop imaginative and prescient textbooks, this advisor takes a distinct strategy during which the preliminary concentration is on useful program and the strategies essential to truly construct a working laptop or computer imaginative and prescient method. The theoretical heritage is then in brief defined afterwards, highlighting how you can quick and easily receive the specified end result with no realizing the derivation of the mathematical element. positive aspects: reports the basic algorithms underlying laptop imaginative and prescient; describes the most recent concepts for 3D reconstruction from a number of photos; summarizes the mathematical thought in the back of statistical errors research for basic geometric estimation difficulties; offers derivations on the finish of every bankruptcy, with options provided on the finish of the ebook; offers extra fabric at an linked website.
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Additional resources for Guide to 3D Vision Computation: Geometric Analysis and Implementation
20) 38 3 Fundamental Matrix Computation Multiplying the matrix Pk from the left means replacing the third component of the vector by 0. The following identity can be confirmed by substituting Eq. 3) to the left-hand side. (θ, V0 [ξ α ]θ) = f 02 Pk Fxα 2 + Pk F xα 2 . 21) Here, V0 [ξ α ] is the normalized covariance matrix in Eq. 12), where x¯α , y¯α , x¯α , and y¯α are replaced by xα , yα , xα , and yα , respectively. Because (ξ α , θ) = f 02 (xα , Fxα ) holds from the definition of ξ and θ in Eq.
2 Method of Fitzgibbon et al. A well-known method for fitting only ellipses is the following method of Fitzgibbon et al. ) 1. Compute the 6 × 6 matrices M= 1 N ⎛ N α=1 ξ αξ α , 0 0 ⎜ 0 −2 ⎜ ⎜1 0 N=⎜ ⎜0 0 ⎜ ⎝0 0 0 0 10 00 00 00 00 00 0 0 0 0 0 0 ⎞ 0 0⎟ ⎟ 0⎟ ⎟. 55) 2. 56) and return the unit generalized eigenvector θ for the generalized eigenvalue λ of the smallest absolute value. 24 2 Ellipse Fitting N Comments This is an algebraic method, minimizing the algebraic distance α=1 2 2 (ξ α , θ) subject to AC − B = 1 such that Eq.
Stat. Data Anal. 52(2), 1208–1222 (2007) 14. K. Kanatani, Y. S. (2008) 15. K. Kanatani, Y. Sugaya, Unified computation of strict maximum likelihood for geometric fitting. J. Math. Imaging Vis. 38(1), 1–13 (2010) 32 2 Ellipse Fitting 16. K. Kanatani, Y. Sugaya, Hyperaccurate correction of maximum likelihood for geometric estimation. IPSJ Trans. Comput. Vis. Appl. 5, 19–29 (2013) 17. K. Kanatani, Y. Sugaya, K. Kanazawa, Ellipse Fitting for Computer Vision: Implementation and Applications (Morgan and Claypool, San Rafael, 2016) 18.
Guide to 3D Vision Computation: Geometric Analysis and Implementation by Kenichi Kanatani, Yasuyuki Sugaya, Yasushi Kanazawa