18-Geom-A4 Photogrammetry · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, May 2014 — 3 hours, closed book (any non-communicating calculator permitted). SEVEN questions constitute a complete paper: Part A answer all of #1–#5, Part B answer one of #6/#7, Part C answer one of #8/#9. Marks are shown in brackets. All nine questions (including both alternatives in Parts B and C) are solved below for completeness.
Reference texts: Wolf, Dewitt & Wilkinson, Elements of Photogrammetry with Applications in GIS (4th ed., McGraw-Hill, 2014); Mikhail, Bethel & McGlone, Introduction to Modern Photogrammetry (Wiley, 2001); Kraus, Photogrammetry: Geometry from Images and Laser Scans (2nd ed., de Gruyter, 2007); Ghilani & Wolf, Elementary Surveying (15th ed.). Canadian mapping practice (NRCan / Canadian Geodetic Survey) throughout.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
8.1 Nodal points. The two points on the optical axis of a lens (the front and rear nodal points) with the property that a ray directed at the front nodal point emerges from the rear nodal point travelling parallel to its original direction (zero angular deviation). The rear nodal point is effectively the perspective centre of the image side; the perpendicular distance from it to the focal plane is the focal length, making the nodal points the reference for the camera's projective geometry.
8.2 Relief displacement. The radial shift in the image position of an object caused by its elevation (relief) above or below the datum: on a vertical photo any point higher than the datum is displaced radially outward from the principal point (and lower points inward). Its magnitude is $d=\dfrac{r\,h}{H}$, where $r$ is the radial distance of the image from the principal point, $h$ the object height above datum and $H$ the flying height above datum. Relief displacement is what leans buildings outward and is exactly what orthorectification removes (and what allows heights to be measured from a single photo).
8.3 Interior orientation. Reconstruction of the internal geometry of the camera/bundle of rays that existed at exposure — i.e. recovering the position of the perspective centre relative to the image. It is defined by the calibrated focal length, principal-point coordinates, and lens-distortion parameters (plus fiducial/pixel-frame definition), and it re-establishes each image ray in the camera coordinate system. In digital work it also includes the transformation from pixel to image (fiducial) coordinates.
8.4 Exterior orientation. The position and attitude of the camera in the object (ground) coordinate system at the instant of exposure — the six parameters: three coordinates of the perspective centre $(X_L,Y_L,Z_L)$ and three rotation angles $(\omega,\phi,\kappa)$. Exterior orientation places each already-reconstructed bundle of rays correctly in ground space; it is recovered by space resection, relative+absolute orientation, aerotriangulation, or direct georeferencing.
8.5 Direct georeferencing. Determining the exterior-orientation parameters of each image directly from onboard sensors — a GNSS receiver (perspective-centre position) integrated with an inertial measurement unit (IMU, giving the attitude $\omega,\phi,\kappa$) — rather than by aerotriangulation from ground control. After boresight/lever-arm calibration between the camera, GNSS antenna and IMU, the six EO parameters are available for every exposure with little or no ground control, enabling immediate orthorectification and rapid mapping.
