1. Photogrammetry DOQ of Mount Shasta

2. Introduction • Photogrammetry is … • “the art and science of making accurate measurements by means of aerial photography” (Jensen 2000) • Analog photogrammetry • performed visually using hard-copy data • Digital photogrammetry • computer-aided using digitized data

3. Some Potential Measurements • Analog photogrammetry of single vertical air photo • Photo scale • Object height, length, area, perimeter • Grayscale tone/color • Analog photogrammetry of stereoscopic air photos • All of the above • Precise planimetric (x, y) object location and height (z) • Digital photogrammetry of stereoscopic air photos • All of the above • Orthophotos • Digital elevation models (DEMs) • Bathymetric models

4. Flight Lines/ Strips of Vertical AP • Flight line • “Flight path” along which photos were acquired at specific exposure stations • (Nadir line: Flight line-equivalent on the ground, directly beneath the aircraft, during photo acquisition) • Intervalometer • Determines time b/w individual exposures • Setting depends on desired photo scale and aircraft speed • Stereoscopic overlap/endlap (~ 60%) • Sidelap (~ 20-30%) • Block of air photos: multiple flightlines with sidelap

5. Flight Lines/ Strips of Vertical AP Flight line Photo #1 Photo #2 Photo #3 60% overlap

6. Flight line #1 Flight line #2 Flight line #3 60% overlap Flight Lines/ Strips of Vertical AP Block of AP 20-30% sidelap

7. Flight line #3 Flight line #4 Flight Lines/ Strips of Vertical AP Exposure #6 Exposure #4 Exposure #5 Exposure #4 Exposure #6 Exposure #5

8. Flight Lines/ Strips of Vertical AP • Uncontrolled Photomosaic • Compiled from previously shown block of air photos

9. Fiducial marks Date: 03-30-1993 Flight line # 04 Scale: 1”=500’ Photo# 05 Fiducial Marks • Fiducial marks • Small targets on camera body, whose positions relative to the camera body are calibrated • Define image coordinate system, whereby the projection center position is known • Vary with manufacturer

10. Principal point (PP) Principal Point (PP) • Principal point • On the ground: Location where the camera’s optical axis was pointing during exposure • On air photo: Intersection of lines b/w opposite fiducial marks

11. Conjugate Principal Point (CPP) • Conjugate principal point (CPP) • Location of PP on adjacent photographs (after transfer) Flight line     PP3-4 PP3-5 CPP3-5 CPP3-4 60% Overlap

12. Conjugate Principal Point (CPP) • Note the 60% overlap area, which can be viewed stereoscopically • PP1 on Photo 1= CPP1 on Photo 2 • PP2 on Photo 2= CPP2 on Photo 1

13. Negative image space Optical axis Positive print +y +x Earth object space Sea level Vertical AP Geometry – Flat Terrain Negative image space (a’, b’, c’, d’)  Reversal in tone and geometry the Earth Earth object space (A B, C, D) x, y = Photographic coordinate axes

14. Scale Measurement • Three ways to express scale of air photos • Verbal/ Written scale • Representative fraction (RF)/ Fractional scale • Graphic scale/ Scale bar

15. Scale Measurement • Single Air Photo Over Nearly Level Terrain • Two main methods • Compare size of (a) objects in real world or from map with (b) same objects on air photo • Compute relationship b/w camera focal length (ƒ) and altitude of aircraft AGL (H) Both equations yield representative fractions (dimensionless)!!! Distance from point a/A to b/B  Scale proportional to f (image distance)  Scale inversely proportional to H (object distance)

16. Vertical AP Geometry – Variable Terrain • Problem: • Many scales • Lower elevations • smaller scales • land “moved away” from camera • Higher elevations • larger scales • land “moved closer” toward camera

17. ab AB Scale Measurement • Single Air Photo Over Variable Terrain Lb Lo s = scale (representative fraction) h = terrain elevation ASL H = flight altitude ASL LP LB = Average/ Nominal Scale

18. Object Height Measurement • Two methods: • Image relief displacement • Shadow length

19. Height Measurement • Method 1: Image relief displacement • Vertical displacement of objects that are above (radial displacement away from PP) or below (radial displacement toward PP) the local datum • Amount of displacement, d, is: • directly proportional to the difference in elevation, h, between the top of the object and the local datum (the greater h, the greater d) • directly proportional to the radial distance, r, between the top of the displaced image and the PP (the greater r, the greater d) • inversely proportional to the altitude, H, of the camera above the local datum (the greater H, the smaller d)

20. Displacement d r b a H B Obj. h PP Local datum A Height Measurement • Method 1: Image relief displacement

21. Height Measurement • Method 1: Image relief displacement × Radial distance, r × Relief displacement, d

22. Height Measurement • Method 2: Shadow length a = Suns’s elevation angle h = object height L = Shadow length • Sun’s elevation angle, a: • Solar ephemeris table • Empirically for known object

23. Height Measurement • Method 2: Shadow length

24. Single vs. Multiple Air Photos • Single air photo • Shows objects from a specific vantage point at specific point in time • Multiple air photos • Show an object from a number of vantage points at different points in time, because the aircraft moves between exposures • In a succession of air photos, the position of a specific object will move from the left to the right (if the flight the line was from the left to the right)

25. Multiple Air Photos • Stereoscopic parallax • Change in position of an object with height, from one photo to the next relative to its background • Caused by aircraft’s motion

26. Parallax • Parallax • Apparent displacement in the position of an object, with respect to a frame of reference, caused by a shift in the position of observation  Basis for stereoscopic viewing • Differential parallax • Differences in the parallax of various objects of interest • Basis for most planimetric (x, y) and topographic (x, y, z) maps

27. Fundamentals of Human Stereoscopy • Stereoscopy • Science of perceiving depth using two eyes • Binocular vision • Vision as a result of both eyes working as a team • Eye base/ Interpupillary distance • Distance between the eyes’ optical axes (63-69 mm) • Parallactic angle () • Angle formed by the two optical axes of the eyes as they converge on a point of interest • Decreases with increasing distance

28. Fundamentals of Human Stereoscopy • Depth perception • Result of changing parallactic angles with distance • Increases with increasing interpupillary distance • For distances up to 1,000 m • Hyperstereoscopy • Stereoscopic viewing in which the relief effect is noticeably exaggerated (e.g., by increasing interpupillary distance or extending the camera base)

29. Stereoscopy & Aerial Photography • 3D-viewing of terrain on air photos is possible, b/c: • Overlapping air photos contain stereoscopic parallax • Hyperstereoscopy allows us to view overlapping photos as if we were present at both exposure stations at the instant of exposure

30. Methods of Stereoscopic Viewing • Keeping the lines of sight parallel with the aid of a stereoscope • Keeping the lines of sight parallel without the aid of a stereoscope • Crossing the eyes and reversing the order of the stereoscopic images • Using anaglyphic or polarizing glasses

31. Stereoscopes • Stereoscope • Binocular viewing system initially developed for the analysis of terrestrial stereoscopic photos (mid-1800s) • Stereo World • Magazine published by the National Steroscopic Association (http://www.stereoview.org/stereoworld.html) • Stereoscopes for air photos • Same principles as used in original stereoscopes

32. Stereoscopes Terrestrial stereogram of the temple in Salt Lake City, UT (1899) (Source: Jensen 2000) Brewster’s lens stereoscope (1849) (Source: Jensen 2000) Vintage stereo camera (Source: Jensen 2000)

33. Pocket Lens Stereoscopes • “Handheld” • Two convex lenses mounted on metal/ plastic frame • Helps keep lines of view parallel • Magnifies the photography

34. Mirror Stereoscopes • Allows entire overlapping area of air photo stereo pair to be seen at once • Various magnification options

35. Stereoscopic Aerial Photography • Air base • Distance b/w two exposure stations • Becomes stretched eye base, which causes exaggerated third dimension when viewing stereoscopically • X-parallax • Change in object position from one photo to the next due to aircraft’s motion • Hypothetical example: • Objects A + B in the real world are recorded as points a + b in exposure L1 and a’ + b’ in exposure L2.

36. Stereoscopic Aerial Photography • Superposition • Vertical lines running through each of the photo’s PPs are superimposed on top one another • Parallax of point a: pa = xa – xa’ • Directly related to a point’s elevation above mean terrain • Greater for high elevations than low elevations Differential parallax • Example: Object A (the taller building) has greater x-parallax (pa) than Object B (pa)

37. Stereoscopic Aerial Photography Differences in the parallax between any two points facilitates the determination of elevation differences using stereoscopic parallax equations • A = arbitrary point at a lower elevation • B = arbitrary point at a higher elevation • a1, b1 = points "A" and "B" as imaged on the left image • a2, b2 = points "A" and "B" as imaged on the right image • Xa = ground X-parallax b/c the elevation of point "A" is above the reference plane • Xb = ground X-parallax b/c the elevation of point "B" is above the reference plane • ha = height of point "A" above the reference plane • hb = height of point "B" above the reference plane • Source: Natural Resources Canada (2004). http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/stereosc/chap4/chapter4_3_e.html.

38. Measurement of Parallax • Parallax Equation ho = Object height H-h = Altitude of aircraft above-ground-level (AGL) P = absolute stereoscopic parallax at the base of the object of interest dp = differential parallax • Equation yields correct only if: • Vertical air photos have  3º • Adjacent photos are exposed from approx. the same altitude AGL • The PPs of both photos are at approx. the same elevation AGL • The base of the objects of interest are at approx. the same elevation as that of the PPs

39. Measurement of Parallax • Parallax Equation • Requires three measurements on stereoscopic photos: • Determine altitude of aircraft AGL (H – h) • (Locate the principal point PP on each of the photos) • (Locate the conjugate principal point CPP on each of the photos) • (Position photographs along flight line by aligning PP and CPP of each photo ( Line of flight) • Determine the average photo air base (absolute stereoscopic parallax, P): • Measure distance between PP1 and CPP2 on Photo1 (= A-base1) • Measure distance between PP2 and CPP1 on Photo2 (= A-base2) • Mean of A-bases = average photo air base b/w two exposure stations = absolute stereoscopic parallax, P H – h P

40. A A CPP2 PP1 PP2 CPP1 B B A-base2 A-base1 Measurement of Parallax • Parallax Equation • Continued: • Measurement of absolute stereoscopic parallax, P • Absolute stereoscopic parallax, P = (A-base1 + A-base2)/2 L2 L1 Profile view of Photo 2 Profile view of Photo 1 P b’ o a b a’ o

41. Measurement of Parallax • Parallax Equation • Continued: • Measure the differential parallax, dp, between the location of the base and the location of the top of the building: • Ruler • Measurement using fiducial lines • Measurement based on superposition • Measurement using a parallax bar (stereometer) dp

42. xb’ A-base2 Fiducial line of Photo 1 Flight line PP1 CPP2 xb Fiducial line xa xa’ Measurement of Parallax • Parallax Equation • Continued: • Measurement of the differential parallax, dp, using fiducial lines • Photo 1 dp Plan view of Photo 1 Photo 1 y-axis x-axis b = base a = top

43. xb’ PP2 A-base2 Flight line xb’ CPP1 Fiducial line of Photo 2 xa’ xa’ Fiducial line Measurement of Parallax • Parallax Equation • Continued: • Measurement of the differential parallax, dp, using fiducial lines • Photo 2 dp Plan view of Photo 2 Photo 2 b’ a’

44. Measurement of Parallax • Parallax Equation • Continued: • Measurement of the differential parallax, dp, using fiducial lines • Example: • xa-parallax (top) on Photo 1: -3.82 in from the fiducial line • xb-parallax (base) on Photo 1: -3.606 in from the fiducial line • xa’-parallax (top) on Photo 2: -0.270 in from the fiducial line • xb’-parallax (top) on Photo 2: -0.267 in from the fiducial line • Absolute value of x-parallax of the top of the building:pa = |(-3.82 in)-(-0.270 in)| = 3.55 in • Absolute value of x-parallax of the base of the building:pb = |(-3.606 in)-(-0.267 in)| = 3.339 in • Differential parallax, dp = 3.55 – 3.339 = 0.211 in dp

45. Measurement of Parallax • Parallax Equation • Continued: • Measurement of the differential parallax, dp, using superposition • Align top and base of building parallel with the line of flight (distance b/w photos not important) • x-parallax of the top/ base of the building = Distance b/w the top/ base of the building on Photo 1 and the same top/ base corner of Photo 2 • Differential parallax, dp = |top-x-parallax – base-x-parallax| dp

46. Measurement of Parallax • Parallax Equation • Continued: • Measurement of the differential parallax, dp, using superposition dp pb pa

47. Measurement of Parallax • Parallax Equation • Continued: • Measurement of the differential parallax, dp, using a parallax bar (stereometer) • Parallax bar • Useful for deriving elevation changes and mapping contour lines dp

48. Area Measurement • Area measurement from unrectified air photos • Only if terrain is level (< 5% of flight altitude) or if the area is carefully stratified into zones of roughly the same scale (e.g., valleys, ridges) • Area measurement of well-known shapes • Measure, length, width, diameter, etc. and use straightforward mathematical relationships for circles (pr2), squares (s2), rectangles (lw), etc. • Area measurement of irregularly shaped polygons • Compensating polar planimeter • Dot grids • On-screen digitization

49. Area Measurement • Area measurement of irregularly shaped polygons • On-screen digitization 5-level land use map compiled from 1996 digital orthophotos. Source: Great Lakes Environmental Center 2003. www.glec-online.com

50. ? Any questions ?