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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Eight-point algorithm ： ウィキペディア英語版 Eight-point algorithm The eight-point algorithm is an algorithm used in computer vision to estimate the essential matrix or the fundamental matrix related to a stereo camera pair from a set of corresponding image points. It was introduced by Christopher Longuet-Higgins in 1981 for the case of the essential matrix. In theory, this algorithm can be used also for the fundamental matrix, but in practice the normalized eight-point algorithm, described by Richard Hartley in 1997, is better suited for this case. The algorithm's name derives from the fact that it estimates the essential matrix or the fundamental matrix from a set of eight (or more) corresponding image points. However, variations of the algorithm can be used for fewer than eight points. == Coplanarity constraint == One may express the epipolar geometry of two cameras and a point in space with an algebraic equation. Observe that, no matter where the point $P$ is in space, the vectors $\backslash overline$, $\backslash overline$ and $\backslash overline$ belong to the same plane. Call $X\_L$ the coordinates of point $P$ in the left eye's reference frame and call $X\_R$ the coordinates of $P$ in the right eye's reference frame and call $R,\; T$ the rotation and translation between the two reference frames s.t. $X\_R\; =\; R\; (X\_L-T)$ is the relationship between the coordinates of $P$ in the two reference frames. The following equation always equals to zero because the vector generated from $T\; \backslash wedge\; X\_L$ is orthogonal to both $T$ and $X\_L$ : :$$ X_L^T T \wedge X_L - T^T T \wedge X_L = (X_L-T)^T T \wedge X_L = 0 Because $I\; =\; R^T\; R$, we get :$$ (X_L-T)^T R^T R T \wedge X_L = 0 . Replacing $(X\_L-T)^TR^T$ with $X\_R^T$, we get :$$ X_R^T R T \wedge X_L = X_R^T R S X_L = X_R^T E X_L = 0 Observe that $T\; \backslash wedge$ may be thought of as a matrix; Longuet-Higgins used the symbol $S$ to denote it. The product $R^T\; T\; \backslash wedge\; =\; R\; S$ is often called essential matrix and denoted with $E$. The vectors $\backslash overline,\; \backslash overline$ are parallel to the vectors $\backslash overline,\; \backslash overline$ and therefore the coplanarity constraint holds if we substitute these vectors. If we call $y,\; y\text{'}$ the coordinates of the projections of $P$ onto the left and right image planes, then the coplanarity constraint may be written as :$$ y'^T \mathbf y = 0 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Eight-point algorithm」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.