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.
6.1 True orthophoto. An orthophoto is an aerial image that has been differentially rectified so that it has the uniform scale and geometry of a map: relief and tilt displacements are removed and every ground point is shown in its correct planimetric position, so distances and areas can be measured directly. An ordinary orthophoto corrects only the terrain (bare-earth DTM) and therefore still leans and hides ground behind tall objects — buildings and bridges remain displaced and cast “lean.” A true orthophoto goes further: it uses a full surface model (DSM) that includes buildings, bridges and other above-ground features, so those objects too are placed in their correct plan position (roof directly over footprint), and the occlusions they create are detected and filled from neighbouring overlapping images. The result has no relief displacement for any object, above or on the ground — essential in dense urban mapping and for overlaying vector utilities/cadastre.
6.2 Input data required for a digital orthoimage. Four ingredients are needed: (i) the digital image(s) themselves (scanned or native-digital, radiometrically corrected); (ii) the interior orientation / camera calibration (focal length, principal point, lens-distortion parameters) so image rays can be reconstructed; (iii) the exterior orientation of each photo (the six EO parameters $X_L,Y_L,Z_L,\omega,\phi,\kappa$, obtained from aerotriangulation or direct georeferencing with GNSS/IMU); and (iv) a digital elevation model — a DTM for a conventional orthophoto, or a DSM (buildings + terrain) for a true orthophoto. Ground control (or GNSS/IMU) underpins the exterior orientation.
6.3 Approach for orthoimage generation. Digital orthorectification is normally done by indirect (backward) resampling: the empty output ortho-grid is created first, and for each output pixel the process works back into the source image. (1) Define the output grid in ground coordinates at the chosen ground-sample distance. (2) For each ground cell $(X,Y)$, read its elevation $Z$ from the DEM. (3) Project that ground point into the source image through the collinearity equations using the interior and exterior orientation, giving a (generally sub-pixel) image location $(x,y)$. (4) Resample the image radiometry there (nearest-neighbour, bilinear or cubic) and write the value into the output cell. (5) For a true orthophoto, add visibility analysis: use the DSM to detect which cells are occluded in that image and fill them from another overlapping photo, then mosaic and radiometrically balance the images (feathering seamlines). Working backward from the output grid guarantees every ortho pixel is filled exactly once with no holes or overlaps.
