Leica Photogrammetry Suite Project Manager

Figure 13: Pixel Coordinate System vs. Image SpaceCoordinate SystemYa-fileYo-fileXa-fileXo-fileaxayaΘfiducial markUsing a 2D affine transformation, the relationship between the pixelcoordinate system and the image space coordinate system isdefined. The following 2D affine transformation equations can beused to determine the coefficients required to transform pixelcoordinate measurements to the corresponding image coordinatevalues:x = a 1+ a 2X + a 3Yy = b 1 + b 2 X+b 3 YThe x and y image coordinates associated with the calibrated fiducialmarks and the X and Y pixel coordinates of the measured fiducialmarks are used to determine six affine transformation coefficients.The resulting six coefficients can then be used to transform each setof row (y) and column (x) pixel coordinates to image coordinates.The quality of the 2D affine transformation is represented using aroot mean square (RMS) error. The RMS error represents the degreeof correspondence between the calibrated fiducial mark coordinatesand their respective measured image coordinate values. Large RMSerrors indicate poor correspondence. This can be attributed to filmdeformation, poor scanning quality, out-of-date calibrationinformation, or image mismeasurement.The affine transformation also defines the translation between theorigin of the pixel coordinate system (x a-file and y a-file ) and the imagecoordinate system (x o-file and y o-file ). Additionally, the affinetransformation takes into consideration rotation of the imagecoordinate system by considering angle Θ (theta). A scanned imageof an aerial photograph is normally rotated due to the scanningprocedure.The degree of variation between the x- and y-axis is referred to asnonorthogonality. The 2D affine transformation also considers theextent of nonorthogonality. The scale difference between the x-axisand the y-axis is also considered using the affine transformation.LPS Project ManagerInterior Orientation / 30