Measurement of Direction: Bearing vs. Azimuth

Transcription

1 Week 5 Monday

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3 Measurement of Direction: Bearing vs. Azimuth Bearing Is an angle of 90 o or less Measured from either North or South in easterly & westerly directions. North 22 o West, South 89 o West, North 53 o East, South 45 o East Azimuth Angles from o that are always measured clockwise from NORTH BEARINGS AZIMUTHS

4 Measurement of Direction Say you wish to find your way to a field plot that you located on an aerial photo. However, because of the absence of photo-specific detail on the map It s not possible to pinpoint the field plot s location on the map. What to do 1) Need to establish a distance-bearing line from some reference point (that is visible on both the photo and the map) to field plot s location on the photo. 2) Then, to get the bearing to the field plot, establish a baseline on the photo for which azimuth or bearing are easily determined (e.g., east-west road etc.). 3) Then, the direction of your distance-bearing line is found by measuring the angle between it and the known baseline.

5 Measurement of Direction 3 Point of Interest 2 1 Road Intersection reference point visible on both photo & map 1) Determine the road s bearing from the map. 2) Orient a compass at same angle with center at the road intersection. 3) Read the final bearing to your Point of Interest

6 Measurement of Direction Is this photo tilted? Any topographic variation? Can you rely on photo-measured bearings or azimuths?

7 Measurement of Direction: Cautions Photo TILT has an effect on bearings measured on photos similar to the effect on photo scale In the past: Photo rectification could fix direction & distortion problems associate with tilt Way too expensive for a whole mission almost never done. Because tilt displacement radiates form isocenter (typically close to PP), bearings that passing through (or near) PP are affected little by tilt. More Recently: If one has the camera calibration coefficient file (f, H, photo format, fiducial marks, GPS ephemeris, etc.) much of the process can be automated ERDAS (OrthoBase) ERMAPPER OrthoMapper (Dr. Frank Scarpace, UW-Madison) All very similar Photo missions increasingly use large-format digital cameras. All photogrammetry laws and procedures still apply However, it is now relatively easy to geo-rectify the resulting images to remove distortion 1 st to 2 nd order polynomial regression tip, tilt, yaw 3 rd order polynomial regressions Earth curvature & lens distortion Orthorectification (terrain correction) using DEM

8 Measurement of Direction Measurement of direction on aerial photos is the same as measurement of direction on maps. However.. - Points above Nadir elev. are displaced away from nadir Correction inward adjustment - Points below Nadir elev. are displaced toward nadir Correction outward adjustment Plane Alt. = 6000 MSL E = Nadir Elev = 1000 f or CFL = 6 A B = Photo Baseline H = 5000 ( ) h A = 560 ( ) h B = ( ) r A = 3.81 r B = 2.60 d = rh H d A = 3.81" ( 560 ) 5000 = 0.43 Correction = 0.43 farther from nadir (A ) Bearing A-B (meas. in field) = N 78 o E Bearing A-B (meas. on photo) = N 87 o E Bearing = 9 o d B = 2.60" (450 ) 5000 = Correction = 0.23 closer to nadir (B )

9 Measurement of Direction: Final Notes Errors in photo-measured bearings caused by terrain displacement are Non-existent (i.e. photo bearing = ground bearing) under these cases: 1) If bearing line passes through NADIR displacement is radial to point if interest. 2) if Nadir & both ends of the bearing line are at same elevation 3) If both ends of a bearing line are at same elevation and are same distance from Nadir, but ELEV bearing line ELEV Nadir Think of these when establishing your photo base-lines To avoid having to correct bearing measurements

10 Parallax Measurement So far, we have discussed single-photo displacement for height calculation Handy in many cases, but can t be used to calculate topographic elevation differences Doesn t take advantage of Vertical Exaggeration (VE) For your eyes, the farther they are apart (exposure distance), the better you perceive depth. VE is the same deal the farther photo exposure stations are apart. the more vertical detail is exaggerated compared to horizontal scale (PSR) Example: 80 % Here, each photo is 80% overlapped on the next Exposure stations close together VE 2 time horizontal scale Every other photo (green) has 60% overlap Exposure stations farther apart VE 4 times horizontal scale 60 %

11 Vertical Exaggeration (VE) VE with the ratio of dist. btwn photo centers flying height VE = AB H AVD EB AB = Air Base distance (photo centers) H = height above ground EB = Eye Base or dist. between you eyes AVD = apparent stereo view dist. (~17 ) AVD = is estimated at ~17 IPD for average adult = /17 ratio of 0.15 EB = 0.15 * 12 = 1.8 /foot Example: VE = AB H AVD EB FMT = 9 photos (in flight direction) %E = 55% endlap CFL = 12 (1 ft.) H = 20,000 ft. EB = eye base of 1.8 VE = 1 %E FMT" PSR H VE = " , " 1 12" = VE is 2.25 time greater than horizontal photo distances Height determination by parallax solves these problems!!

12 Height by Parallax Difference Measurement Most useful photo-based method for measuring heights, but requires A stereo-pair of aerial photos Interpreter must have good depth perception Vertical photos Tilt = height errors, but if tilt is < 3 o not too bad Forms of the height equation Mountainous terrain equation valid for mountainous & level terrain Level terrain equation Elevation of the object s base must = average(pp1 elev & PP2 elev ) Short-cut equation Can approximate mountainous or level terrain. Never completely appropriate Is the implest of the height equations Can be used with previously prepared tables

13 Height by Parallax Difference Measurement Similar Triangles ABC & ADE Hence, h = dp H h P P h = dpp H h P h = dp H dp h P h + dp h = dp H h P + dp = dp H h = H(dP) P + dp H = Fly Height AG f(psr) P = parallax of PP 1 & PP 2 P left = PP right - CPP right P right = PP left - CPP left Because the plane may bounce around between exposure stations, P left P right So, we use the average P

14 Height by Parallax Difference Measurement Absolute Parallax of point a and of the baseline, x or x Flight Direction (x) + + Absolute parallax of object "a" is: x a x a, or x a + x a Absolute parallax of the baseline is: (x b + x b)/2 If "a" is at same elevation as baseline, then: x a + x a (x b + x b)/2 = dp = 0 To have a difference in absolute parallax we need different elevations Top & Bottom of a Tree! The absolute parallax (P) of a tree then is the P top P bottom

15 Height by Parallax Difference Measurement On the left photo, x coordinate of the TOP OF TREE is +(x t ) and BOTTOM OF TREE is + x b On the right photo, x coordinate of the TOP OF TREE is (x t ) and BOTTOM OF TREE is (x b ) With PPs & CPPs perfectly aligned, absolute parallax of TREE TOP = x t x t x t + x t The absolute parallax of TREE BOTTOM = x b + x b Difference in absolute parallax, dp, between TREE TOP & BOTTOM dp = x t + x t (x b + x b ) dp = x t x b + x t x b = d c = dp 1 + dp 2 How dp is actually measured on a stereo pair d c Height of object then h = dp" H P" + dp" Level Terrain Equation

16 Devices to Measure dp on a Stereo Photo Pair Engineer s scale If careful can do pretty well Nearest 0.01 Stereoplotter Most accurate and most expensive. Parallax Bar Align photo so PPs and CPP are in line, with separation similar to the P-Bar Two measurements: top_top & bottom_bottom (FLOATING DOT) Not actually reading distance between the images its an arbitrary reading The difference (top_top) (bot_bot) is the true dp Parallax Wedge Whole series of parallax bars set at fixed dps Used in stereo vision (FLOATING DOT)

17 Height by Parallax: Mountainous Terrain Equation h = H dp P b + dp = P + P H dp ± E H + dp Where Pb must = P + P ± E H Why two equations? One may be more applicable than the other depending on the info you have at hand. h = height of the object being measured H = flying height above the base of the object dp = difference in absolute parallax between the top & bottom of the object P = average absolute parallax of the two ends of the baseline (measured as the average distance between PP and CPP in the stereo pair) P b = absolute parallax at the base of the object (distance between the PPs of the two photos minus the distance between the images of the base of the object on the 2 photos when properly aligned for measurement of dp) ± E = difference in elevation base of object [0. 5 PP 1 + PP 2 ] (+ if higher and if lower)

18 Height by Parallax: Level-Terrain Equation Mountainous Terrain Level Terrain Only valid when E = 0 However, when terrain not perfectly flat Level Terrain Equation can be used if Elev object_base (Elev PP2 + Elev PP1 ) 1 2 < H 0.05

19 Height by Parallax: Short-Cut Equation DFP Neither is totally valid ignores dp in denominator Error in height estimates are small if dp is a small proportion of P or Pb Substituting f PSR for H h = f PSR dp Pb

20 Short-Cut EQ: Differential Parallax Factor (DPF) Tables DFP Substituting f PSR for H h = f PSR dp Pb Substituting DPF for f/pb (DPF is constant for a stereo pair) h = (DPF)(PSR)(dP)

21 Parallax Cautions Things to consider when using parallax to measure heights High points are displaced radially outward in the amount: d = rh H On vertical photos, Nadir & PP are same point Apparent depth exaggeration in stereo stretches objects vertically 21:2 to 31:2 times normal There are two parallaxes: X and Y parallax Y-parallax will introduce large h errors Avoid Y-parallax by carefully aligning photos PP CPP CPP PP

22 Example Parallax Problem Flying height is ft. above datum Average photo base is 3.17 in. If distance from base-to-base is 4 in. and from tip-to-tip is 3.98 in. How tall is the object? H = dp = P = = H = " 3.17" " = 86.2 ft. dp = difference in absolute parallax between the top & bottom of the object P = average absolute parallax of the two ends of the baseline