By Kenichi Kanatani, Yasuyuki Sugaya, Yasushi Kanazawa
This classroom-tested and easy-to-understand textbook/reference describes the cutting-edge in 3D reconstruction from a number of photos, bearing in mind all features of programming and implementation. in contrast to different computing device imaginative and prescient textbooks, this advisor takes a different method during which the preliminary concentration is on sensible program and the methods essential to truly construct a working laptop or computer imaginative and prescient approach. The theoretical history is then in brief defined afterwards, highlighting how you can fast and easily receive the specified outcome with out realizing the derivation of the mathematical aspect. positive factors: experiences the basic algorithms underlying computing device imaginative and prescient; describes the newest strategies for 3D reconstruction from a number of pictures; summarizes the mathematical idea at the back of statistical mistakes research for normal geometric estimation difficulties; offers derivations on the finish of every bankruptcy, with recommendations provided on the finish of the e-book; offers extra fabric at an linked website.
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Extra resources for Guide to 3D Vision Computation: Geometric Analysis and Implementation
Chernov, Y. Sugaya, Renormalization returns: hyperrenormalization and its applications, in Proceedings of 12th European Conference on Computer Vision, Firenze, Italy, October 2012 10. K. Kanatani, A. Al-Sharadqah, N. Chernov, Y. Sugaya, Hyper-renormalization: nonminimization approach for geometric estimation. IPSJ Trans. Comput. Vis. Appl. 6, 143–159 (2014) 11. K. Kanatani, P. Rangarajan, Hyper least squares fitting of circles and ellipses. Comput. Stat. Data Anal. 55(6), 2197–2208 (2011) 12. K.
5) by considering the noise properties described by the covariance matrices V [ξ α ]. Mathematically, this is the same problem as ellipse fitting. Therefore the algebraic methods described there (least squares, the Taubin method, HyperLS, iterative reweight, renormalization, and hyper-renormalization) can be directly applied. 1. 1 (Least squares) 1. Compute the 9 × 9 matrix M= 1 N N α=1 ξ αξ α . 13) 2. Solve the eigenvalue problem Mθ = λθ , and return the unit eigenvector θ for the smallest eigenvalue λ.
Let J be the value of Eq. 23) for F . 14. Unless J < J or J ≈ J , let c ← 10c and go back to Step 10. 15. If F ≈ F, return F and stop. Else, let F ← F , U ← U , V ← V , φ ← φ , and c ← c/10, and go back to Step 3. 5(1)): ∇θ J = 1 N N α=1 2(ξ α , θ)ξ α 1 − (θ , V0 [ξ α ]θ) N = 2(M − L)θ = 2Xθ . 46) Here, M and L are the matrices defined by Eq. 38), and X is the matrix in Eq. 39). Using Eq. 46), we search for the values of U, V, and φ in Eq. 35) that minimize Eq. 23). The main point is the update of U and V.