12 A Cost Effective DIC System for Measuring Structural Vibrations 141 Fig. 12.2 Distortion of a rectangular reference image for different transform parameter subset points to be located on a plane element, the transform between the left (reference) and right stereo image can be given by the perspective projection [2] 0 @ ˛ xr ˛ yr ˛ 1 ADA.p/ 0 @ xl yl 1 1 A; A.p/ D 0 @ 1Ca11 a12 a13 a21 1Ca22 a23 a31 a32 1 1 A: (12.1) The unknown coefficientsaij of the transform matrixA(p) are collected in the parameter vector pD.a11; a12; a13; a21; a22; a23; a31; a32/ T. The unknown elements a13, a23 and a11, a12, a21, a22 denote the relative displacements as well as the strain and the shearing of the reference element in horizontal and vertical direction, respectively, see Fig. 12.2b–g. The perspective distortion is represented by a31, a32, see Fig. 12.2h–i. Equation (12.1) directly renders the pixel coordinates (xr, yr) xr D .1Ca11/xl Ca12yl Ca13 1Ca31xl Ca32yl ; yr D a21xl C.1Ca22/yl Ca23 1Ca31xl Ca32yl : (12.2) Although the reference pixel coordinates (xl, yl) are integer valued, the projected coordinates (xr, yr) are floating numbers, leading to the challenge of evaluating the right image at subpixel coordinates. This requires a two dimensional subpixel
RkJQdWJsaXNoZXIy MTMzNzEzMQ==