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.
9.1 Depth of field. The range of object distances (nearest to farthest) within which objects appear acceptably sharp in the image for a given focus setting. It increases as the aperture is stopped down (smaller aperture, larger $f$-number), with shorter focal length, and with greater focusing distance; it is bounded by the circle of confusion criterion for acceptable sharpness. In aerial mapping the object distance is effectively infinite so depth of field is rarely limiting; in close-range/terrestrial work it is a key exposure consideration.
9.2 Vanishing points. The point in the image plane at which the projected images of a set of parallel object-space lines appear to converge (the image of their common point at infinity). Lines parallel to the photo plane have their vanishing point at infinity (they stay parallel in the image); a horizontal set images to a vanishing point on the horizon line. Vanishing points encode direction information and are used in analytical and close-range photogrammetry (e.g. to recover camera rotation or rectify façades).
9.3 Camera self-calibration. A technique in which the interior-orientation / calibration parameters (focal length, principal point, and lens-distortion coefficients) are recovered simultaneously with the exterior orientation and object points as additional unknowns in the bundle adjustment (via extra “additional parameters”), rather than from a separate laboratory calibration. It requires a suitably strong, redundant network geometry (varied images, convergent and rolled photos) and is standard in close-range and UAV photogrammetry, where the camera is not metric.
9.4 Absolute orientation. The step that transforms a relatively oriented stereo-model (or free-network model, in its arbitrary model coordinate system) into the ground/object coordinate system: a 3-D similarity (conformal) transformation with seven parameters — three translations, three rotations and one scale — determined from ground control points. It fixes the model's position, orientation and scale in the real world (levelling and scaling the model).
9.5 Space resection. Determining the exterior orientation (the six parameters $X_L,Y_L,Z_L,\omega,\phi,\kappa$) of a single photograph from the measured image coordinates of a number of points whose ground coordinates are known (control). It is solved from the collinearity equations (a minimum of three well-distributed control points, normally more for a least-squares solution) and is the classical way to recover a photo's pose — the inverse of intersection.
