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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 Lucas–Kanade method ： ウィキペディア英語版 Lucas–Kanade method In computer vision, the Lucas–Kanade method is a widely used differential method for optical flow estimation developed by Bruce D. Lucas and Takeo Kanade. It assumes that the flow is essentially constant in a local neighbourhood of the pixel under consideration, and solves the basic optical flow equations for all the pixels in that neighbourhood, by the least squares criterion.〔 B. D. Lucas and T. Kanade (1981), ''(An iterative image registration technique with an application to stereo vision. )'' Proceedings of Imaging Understanding Workshop, pages 121--130 〕〔Bruce D. Lucas (1984) ''(Generalized Image Matching by the Method of Differences )'' (doctoral dissertation) 〕 By combining information from several nearby pixels, the Lucas–Kanade method can often resolve the inherent ambiguity of the optical flow equation. It is also less sensitive to image noise than point-wise methods. On the other hand, since it is a purely local method, it cannot provide flow information in the interior of uniform regions of the image. == Concept == The Lucas–Kanade method assumes that the displacement of the image contents between two nearby instants (frames) is small and approximately constant within a neighborhood of the point ''p'' under consideration. Thus the optical flow equation can be assumed to hold for all pixels within a window centered at ''p''. Namely, the local image flow (velocity) vector $(V\_x,V\_y)$ must satisfy :$I\_x(q\_1)\; V\_x\; +\; I\_y\; (q\_1)\; V\_y\; =\; -I\_t(q\_1)$ :$I\_x(q\_2)\; V\_x\; +\; I\_y\; (q\_2)\; V\_y\; =\; -I\_t(q\_2)$ :$\backslash vdots$ :$I\_x(q\_n)\; V\_x\; +\; I\_y\; (q\_n)\; V\_y\; =\; -I\_t(q\_n)$ where $q\_1,q\_2,\backslash dots,q\_n$ are the pixels inside the window, and $I\_x(q\_i),I\_y(q\_i),I\_t(q\_i)$ are the partial derivatives of the image $I$ with respect to position ''x'', ''y'' and time ''t'', evaluated at the point $q\_i$ and at the current time. These equations can be written in matrix form $A\; v\; =\; b$, where :$A\; =\; \backslash begin$ I_x(q_1) & I_y(q_1) \\() I_x(q_2) & I_y(q_2) \\() \vdots & \vdots \\() I_x(q_n) & I_y(q_n) \end, \quad\quad v = \begin V_x\\() V_y \end, \quad \mbox\quad b = \begin -I_t(q_1) \\() -I_t(q_2) \\() \vdots \\() -I_t(q_n) \end This system has more equations than unknowns and thus it is usually over-determined. The Lucas–Kanade method obtains a compromise solution by the least squares principle. Namely, it solves the 2×2 system :$A^T\; A\; v=A^T\; b$ or :$$ 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「Lucas–Kanade method」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.