16 J. Slavicˇ et al. Fig. 2.1 Multiview measurement setup 2.3 Image Based 2D Displacement Measurement Acquired images were processes by the Simplified gradient-based optical flow method [9] to identify the 2D displacements for each video sequence. The points to be analyzed in each image were selected by projecting a rectangular grid of 30×30 points onto each of the three object planes, totaling 2700 points per image. A rectangular region of interest of 11×11pixels with the grid node in the middle was analyzed for each of the selected points. 2.4 Multiview Geometry and Triangulation Each camera position in a multiview imaging setup (Fig. 2.1) can be defined by a transformation matrix that projects the coordinates of a point Xin space into the image plane: x =PX (2.1) wherexdenotes the coordinates of a point in an image andP=K[R| t] is a projective transform matrix, composed of a 3×3 matrix of intrinsic camera parameters K, 3×3 rotation matrixRanda 3×1 translation vector t [2]. By matching the position of a point in an imagexto the position of the same real-world point in another image, x , the3D position of the original point in a chosen global coordinate frame is triangulated by solving the following system of equations for three unknown coordinates inX[10]: x =P1X x =P2X (2.2) Each camera view adds another matrix equation to the already overdetermined system of algebraic equations, which was solved in a least-squares sense using singular value decomposition in our case.
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