NREM 345 Week 2, 2010 Reading assignment: Chapter. 4 and Sec. 5.1 to 5.2.4 Material covered this week contributes to the accomplishment of the following course goal: Goal 1: Develop the understanding and skills necessary for accurate measurement of direction, distance, area, and height from aerial photos Information obtained from these sessions, lab, and from your reading assignment will help set the stage for use of aerial photos in measuring distance, direction, areas and heights. After studying class notes and reading assignments, you should be able to: Describe and calculate nominal scale, point scale, and average scale. Describe what data is needed in order to calculate either nominal, point, or average scale. Select and use the best method for calculating scale given the information available in a particular situation. Describe how a change in camera focal length, flying height above mean sea level, or change in ground elevation will affect nominal scale or point scale of a photo. Explain Distance Correction Factor (DCF) and describe situations in which it must be applied Correctly apply DCF as needed when determining distance Correctly determine distances from vertical aerial photos Assess the impact of the combination of photo scale and measurement device on the level of accuracy obtainable. You may wish to look through the exercises at the end of Chapter 4 in Paine to help in your understanding of scale determination.
Aerial Photographs Enjoyable to look at Can spend hours exploring from office or home Can provide a very rapid visual assessment BWCA: 5 October 2011
Want to develop skill for several reasons Improves armchair exploration Give a more complete visual impression Much can be done in terms of measurement if photo geometry is understood
Understanding photo geometry Terminology First Fiducial Marks Index marks, rigidly connected with the camera, which form images on the negative. Optically projected as fine crosses, dots, half arrows, or other markings Located at either the side mid-points or corners of the aerial photographs. If one is trimming photos, must be careful to not clip fiducial marks off. Principal point (PP) Point on ground directly under the center of camera at time of exposure The geometric center of the photo, irrespective of tilt PP found at the intersection of imaginary lines connecting opposing fiducial marks (sides or corners). All distortion due to lens aberration is radial from the PP NADIR (N) The point on an aerial photograph that falls directly under (i.e., plumb line) the camera. Used for calculating topographic displacement. On perfectly vertical photos N & PP are the same point On oblique photos N & PP are two distinct points, where N may not be on the photo if tilt is too great. All distortion due to elevation (or depression) is radial from NADIR Isocenter (I) Point on photo that bisects the angle between a two lines: one perpendicular from the aerial camera to the ground and the other a plumb line from the aerial camera to the ground. In plan speak point on photo halfway between PP and NADIR All displacement due to tilt is radial from the isocenter On perfectly vertical aerial photos N, PP, and I are the same!! Parallax The apparent shift in position of and object when viewed from two exposure stations (Image separation distance or ISD). This is what allow one to see in stereo. Conjugate Principal Point (CPP) The geographic center of neighboring photo in a flight line that is visible on the first photo. Used to find exact flight direction and is the basis of all parallax measures of height and displacement.
Principal Point, Nadir, & Isocenter PP distortions due to lens (radiate) N origin of distortions due to terrain I origin of distortions due to tilt
Principal Point (PP) & Conjugate PP Flight line passes through the PPs of successive photos. Because of photo overlap (often 50%), we can see PP 1 on photo 2. PP 1 is known as the Conjugate PP on photo 2 or CPP. Used to properly align 2 successive photos prior to absolute parallax measurements.
Difference in Absolute Parallax Images of points lying at different elevations are topographically displaced by different amounts along the X-axis (flight direction) on successive, overlapping photographs. This difference in displacement is called: Difference in Absolute Parallax (dp) The absolute parallax (or X parallax) of a point on successive, overlapping photos is: X coordinate left photo X coordinate right photo X a - ( - X a ) X a + X a 1.47 + 0.66 = 2.13 Absolute Parallax: The algebraic difference measured parallel to the line of flight (x-axis) from the corresponding y-axis to the two images of the point on a stereoscopic pair of aerial photos. ASSUMES VERTICAL PHOTOS + Flight Direction
Vertical Exaggeration (VE) Trees, buildings, or topography is often seen stereoscopically to be exaggerated compared to ground distances. This has to do with airbase location when successive photo were taken. Each successive photo has 80% overlap, giving a VE of 2 time the horizontal scale. That is, heights appear 2 times greater than reality. If every other photo is used to see stereo, we have 60% overlap and the VE is 4. The displacement (due to increased distance between photo exposure centers) is greater.
Vertical Exaggeration (VE) VE increases with the ratio of the distance between exposure stations (photo centers) over Hg (flying height above ground). VE = AB AVD Hg EB AB = photo center distance Hg = 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 = 2.6 2.6 /17 ratio of 0.15 EB = 0.15 * 12 = 1.8 /foot Example: FMT = 9 photos (in flight direction) %E = 55% endlap CFL = 12 (1 ft.) Hg = 20,000 ft. EB = eye base of 1.8 VE = AB AVD Hg EB VE = 1 %E FMT" PSR Hg VE = 0.45 9" 20000 20,000 1.8" 1 12" 1 0.15 = 2. 25 VE is 2.25 time greater than horizontal photo distances
Back to Horizontal Distances Problem is this You need to know the ground distances between several points that can be seen on photo 25. Think about the steps you would go through to determine those distances. The first thing one must do is to determine the photo scale. More on this in a bit
Scale is the most important aspect of photogrammetry Need to know scale before one can make useful measurements on a map, drawing, or photo Scale indicates the size of the map, photo, drawing, etc. in relation to the size of the physical object it represents Architects may use a scale of 1/8 = 1 foot for a floor plan of a house Engineer might use a scale of 1 = 50 feet for a highway construction project Maps may use a scale of 1 = 50 miles In Photogrammetry scale is a unitless representative fraction (RF) showing the relation between 1 unit on the photo and X units on the ground 1/15840 or 1:15840 1:20000 1:40000 1:63360 In the Paine text all calculations use the inverse of RF, which is known as Photo Scale Reciprocal (PSR) 15840 20000 40000 63360
Scale is the most important aspect of photogrammetry While there is no clear break between large scale photos and small scale photos, some are larger scale than others. 1:15840 is a larger scale than 1:20000 A larger fraction (e.g., 1/15840) = larger scale In a large scale photo, objects (buildings, trees, buffalo) appear photographically LARGER than when the RF is a smaller fraction (e.g., 1/63360) VS. Photo scale may vary depending on the ground being photo graphed VS. Larger Scale Flat Mountainous Smaller Scale
Determining Photo Scale Method for scale determination Scale from ratio of ground measurement to photo measurement RF: 1 X = d D OR PSR: X = D d Where: d = distance between 2 points on a photo (aka PD) D = distance between same 2 points on the ground (aka GD) The 2 points used should be near NADIR and on opposite sides to reduce displacement errors Wouldn t have to do this if you knew 2 things: 1) that the ground was perfectly flat & level (same elevation) everywhere 2) that the photo was, indeed, perfectly vertical Fantasy!!! d should be measured at least to the nearest 100 th inch (½ marks on 50 scale) The larger the photo distant, the less chance for error May use map distance rather than measured ground distance.
Determining Photo Scale d = distance between 2 points on a photo D = distance between same 2 points on the ground RF: 1 X = d D OR PSR: X = D d Using MAP rather than GROUND distance to determine RF or PSR EXAMPLE: - photo distance (PD or d) between two county roads is 3.17 - Map shows roads to be 1 mile apart 1 = 3.17 X (12)(5280) X = (12)(5280) 3.17 = 63360 3.17 = 20000
Scale from: Focal Length & Flying Height See that 1 = f X Hg is the scale or RF Must know the camera focal length, f, and flying height above ground, Hg Example: Plane flying at altitude ( A ) 15000 ft above MSL ground elevation ( E ) is 1250 ft above MSL camera focal length ( f ) = 8.25 or 0.6875 RF = 1 X = 0.6875 15000 1250 = 0.6875 13750 = 0.00005 = 1 20000 OR PSR = x = 13750 0.6875 = 20000 Many times, all that is given is altitude (A) above mean sea level (MSL) and Hg is not known. Can use a 7.5 topoquad or a DEM to estimate E Hg = A E where E is elevation of terrain
Magnitude of change in scale determination Change in elevation without a change in flying height above MSL leads to changes in PSR Camera Height Change in Photo Change in Focal Above Height Above Scale Photo Scale Length (ft.) Ground Ground Reciprocal Reciprocal Aerial cam. CFL 10,000 10,000 1.00 100 100 10,100 10,100 Aerial cam. CFL 10,000 14,545 0.6875 68.75 100 10,068.75 14,645 Aerial cam. CFL 10,000 20,000 0.50 50 100 10,050 20,100 35 mm cam. CFL 10,000 55,432 0.1804 18.04 100 10,018.04 55,532 PSR = Hg CFL Hence, PSR = Hg CFL Hg = X * CFL which result in: PSR = X CFL = Hg PSR X = Hg CFL
Two General Types of Photo Scale: Average Scale & Point Scale Average scale have to be careful!! Can refer to 2 different things: Average Project Scale Nominal Scale Nominal Scale: that scale specified in the contract & the goal of the aerial photo mission. Least reliable: rarely exactly the same as the actual scale on an individual photo. 1 = CFL PRS Hg Average single photo scale PRS = Hg CFL Hg = PRS * CFL Between two points on a photo Average for a small part of the photo Average of entire photo almost always varies photo to photo due to changes in: 1. tilt, 2. flying height, & 3. terrain between exposure stations PRS = Photo Scale Reciprocal CFL = Camera Focal Length Hg = Specified mission flying height above ground 1 X = d" D" X = D" d" D = PRS * d Except in flat terrain, average photo scale only approximates actual scale at all points on the photo
Two General Types of Photo Scale: Average Scale & Point Scale Point Scale is the most exact type of scale Scale at a finite point on the ground at a given elevation Most reliable Uses the exact ground elevation at a point, which can vary across a photo Only reliable/accurate at one specific point If another point has a different elevation it has a different Point Scale Range in point scales depends on Focal length of the camera Amount of variation in terrain elevation on a given photo
Magnitude of change in scale determination Camera Focal Length (CFL) f = 8.25 inch 0.6875 feet ELEVATION (E) ABOVE MSL (Feet) Flying Altitude above MSL A = 10890 feet 250 x 250 meter grid of DEM data 411.7 409.4 405.6 403.1 400.4 397.8 394.9 393.6 391.9 388.9 386.5 383.7 377.4 368.3 364.6 362.7 361.2 361.3 362.2 363.2 365.0 368.3 372.7 377.3 379.8 385.2 411.7 409.3 405.5 403.1 400.2 397.6 394.3 392.6 391.6 388.9 386.1 383.2 376.4 367.5 364.2 362.5 361.2 361.3 362.2 363.2 365.3 369.1 373.6 378.1 380.8 386.4 411.5 408.9 405.4 403.1 399.7 396.8 394.1 392.1 391.0 388.5 385.6 382.3 375.2 367.2 364.0 362.4 361.4 361.5 362.3 363.3 365.3 369.6 374.2 378.7 381.3 386.8 410.8 408.2 405.2 403.0 399.6 396.8 394.0 391.4 389.9 387.5 385.6 380.6 373.1 367.2 364.2 362.6 361.8 361.9 362.6 363.6 365.3 369.6 374.0 378.9 381.6 386.8 409.8 407.4 405.1 403.4 400.4 397.7 394.4 390.3 388.3 386.5 385.4 378.3 370.5 367.0 364.2 362.7 362.1 362.3 363.1 364.5 366.2 369.7 373.1 378.5 382.0 386.7 409.2 407.4 405.5 404.3 401.6 398.7 395.1 389.8 387.2 385.6 383.5 375.9 368.9 366.3 363.8 362.5 362.0 362.5 363.9 365.8 368.2 371.1 373.9 379.1 383.0 386.7 409.9 408.4 406.5 405.1 402.6 399.1 395.3 390.2 387.0 383.5 379.7 373.5 368.5 365.6 363.3 362.2 361.7 362.3 364.2 366.8 370.3 374.1 377.4 382.0 384.9 387.1 411.1 409.6 407.6 406.0 403.3 399.7 395.5 390.4 386.6 381.4 377.1 372.0 367.3 364.9 362.7 361.8 361.5 362.3 364.2 367.4 371.3 377.2 380.9 384.6 386.6 388.3 411.7 410.3 408.2 406.3 403.8 399.5 395.9 390.7 386.5 380.8 376.5 371.3 366.6 364.5 362.5 361.6 361.5 362.2 364.3 367.7 372.0 379.1 382.9 385.5 387.9 389.5 412.0 410.7 408.7 406.7 404.0 399.9 396.3 390.9 386.6 380.8 375.7 371.0 366.4 364.2 362.2 361.3 361.1 361.9 364.2 367.9 372.4 379.9 384.5 386.7 389.1 390.5 412.4 411.3 409.4 407.3 404.4 400.3 397.0 391.1 386.7 381.4 375.6 370.7 366.5 363.7 361.7 360.8 360.8 361.6 363.8 368.0 372.7 379.9 385.6 388.7 390.9 392.0 412.7 411.8 410.0 407.8 405.0 400.9 397.1 391.5 386.9 381.5 375.7 370.9 366.1 363.5 361.3 360.5 360.4 361.3 363.6 368.4 373.7 381.6 387.0 391.3 393.8 394.6 413.0 412.2 410.6 408.3 405.6 401.3 397.3 391.9 387.2 381.7 375.9 371.0 365.9 363.1 361.0 360.1 360.0 361.0 363.4 368.8 374.9 382.9 389.0 393.7 396.8 397.3 413.1 412.2 410.6 408.1 405.5 401.4 397.7 392.6 387.8 382.4 376.3 371.4 366.0 362.9 360.8 359.8 359.8 360.8 363.3 369.3 375.8 383.9 390.4 395.1 398.3 398.8 413.0 412.0 410.1 407.4 404.9 401.2 398.0 393.4 388.6 383.4 377.0 371.9 366.2 362.9 360.7 359.8 359.8 360.8 363.3 369.7 376.3 384.5 391.2 395.5 398.4 398.9 412.8 411.6 409.5 406.5 404.1 401.0 398.3 394.2 389.5 384.4 377.7 372.4 366.5 363.0 360.7 359.8 359.7 360.9 363.4 369.9 376.8 384.8 391.5 395.5 398.1 398.4 412.2 410.9 408.8 405.9 403.7 401.0 398.5 394.8 390.1 385.0 378.2 372.8 366.7 363.0 360.6 359.4 359.5 360.9 363.8 370.2 377.0 384.7 391.4 395.1 397.6 397.7 411.3 410.0 408.1 405.5 403.6 401.1 398.6 395.1 390.2 385.2 378.4 373.0 366.9 362.9 360.3 358.9 359.0 361.0 364.1 370.4 377.1 384.1 390.6 394.3 396.6 396.7 410.5 409.1 407.5 405.2 403.5 401.1 398.6 395.1 390.2 385.3 378.5 373.1 367.1 362.8 360.0 358.3 358.5 360.8 364.1 370.2 376.7 383.2 389.5 393.1 395.4 395.5 409.7 408.3 406.8 404.8 403.2 400.9 398.4 395.1 390.1 385.4 378.7 373.4 367.6 363.0 359.9 358.0 358.2 360.3 363.6 369.4 375.8 381.8 388.1 391.6 394.0 394.1 409.2 407.8 406.4 404.4 402.8 400.6 398.1 394.9 390.0 385.4 379.0 373.7 368.0 363.3 360.2 358.1 357.9 359.7 362.8 368.2 374.6 380.5 386.8 390.3 392.6 392.9 408.8 407.4 406.0 404.1 402.4 400.2 397.6 394.5 389.8 385.4 379.2 374.0 368.5 363.6 360.5 358.1 357.6 359.0 361.7 366.6 373.0 378.8 385.1 388.7 391.2 391.7 408.3 406.9 405.6 403.6 401.8 399.6 396.8 393.8 389.4 385.4 379.6 374.4 369.1 364.0 360.8 358.2 357.3 358.2 360.5 364.8 370.9 376.4 382.8 386.9 389.8 390.5 407.9 406.5 405.2 403.3 401.3 398.9 395.8 393.0 389.0 385.3 379.9 374.8 369.7 364.4 361.1 358.2 357.0 357.4 359.3 362.9 368.6 373.9 380.7 385.4 388.9 390.0 407.3 405.9 404.6 402.7 400.5 398.0 394.7 392.0 388.4 385.1 380.1 375.0 370.0 364.7 361.2 358.1 356.7 356.7 358.1 361.1 366.2 371.2 378.3 383.6 387.7 389.3 406.5 404.8 403.5 401.5 399.2 396.6 393.4 390.9 387.7 384.6 380.0 374.7 369.7 364.3 360.8 357.7 356.3 356.0 357.2 359.6 364.1 368.6 375.4 380.9 385.3 387.5 PSR = (A - E) / f = 15840 (when E = 0) Multiple Point Scales in one Photo (Assuming vertical photography) 15241 15245 15250 15254 15258 15261 15266 15268 15270 15274 15278 15282 15291 15304 15310 15312 15315 15314 15313 15312 15309 15304 15298 15291 15288 15280 15241 15245 15250 15254 15258 15262 15266 15269 15270 15274 15278 15283 15293 15305 15310 15313 15315 15314 15313 15312 15309 15303 15297 15290 15286 15278 15242 15245 15250 15254 15259 15263 15267 15270 15271 15275 15279 15284 15294 15306 15310 15313 15314 15314 15313 15312 15309 15302 15296 15289 15285 15277 15242 15246 15251 15254 15259 15263 15267 15271 15273 15276 15279 15286 15297 15306 15310 15313 15314 15314 15313 15311 15309 15302 15296 15289 15285 15277 15244 15247 15251 15253 15258 15262 15266 15272 15275 15278 15279 15290 15301 15306 15310 15312 15313 15313 15312 15310 15307 15302 15297 15289 15284 15277 15245 15247 15250 15252 15256 15260 15265 15273 15277 15279 15282 15293 15303 15307 15311 15313 15313 15313 15311 15308 15304 15300 15296 15289 15283 15278 15244 15246 15249 15251 15254 15259 15265 15272 15277 15282 15288 15297 15304 15308 15312 15313 15314 15313 15310 15306 15301 15296 15291 15284 15280 15277 15242 15244 15247 15250 15253 15259 15265 15272 15278 15285 15291 15299 15306 15309 15312 15314 15314 15313 15310 15306 15300 15291 15286 15281 15278 15275 15241 15243 15246 15249 15253 15259 15264 15272 15278 15286 15292 15300 15307 15310 15313 15314 15314 15313 15310 15305 15299 15289 15283 15279 15276 15273 15241 15243 15246 15248 15252 15258 15264 15271 15278 15286 15293 15300 15307 15310 15313 15315 15315 15314 15310 15305 15298 15287 15281 15278 15274 15272 15240 15242 15245 15248 15252 15258 15263 15271 15278 15285 15294 15301 15307 15311 15314 15315 15315 15314 15311 15305 15298 15287 15279 15275 15271 15270 15240 15241 15244 15247 15251 15257 15262 15271 15277 15285 15294 15301 15308 15311 15314 15316 15316 15314 15311 15304 15296 15285 15277 15271 15267 15266 15239 15241 15243 15246 15250 15256 15262 15270 15277 15285 15293 15300 15308 15312 15315 15316 15316 15315 15311 15304 15295 15283 15274 15267 15263 15262 15239 15240 15243 15246 15250 15256 15262 15269 15276 15284 15293 15300 15308 15312 15315 15317 15317 15315 15312 15303 15293 15282 15272 15265 15261 15260 15239 15241 15244 15247 15251 15256 15261 15268 15275 15282 15292 15299 15307 15312 15315 15317 15317 15315 15312 15302 15293 15281 15271 15265 15260 15260 15240 15241 15244 15249 15252 15257 15261 15267 15273 15281 15291 15298 15307 15312 15315 15317 15317 15315 15311 15302 15292 15280 15270 15265 15261 15260 15240 15242 15245 15250 15253 15257 15260 15266 15273 15280 15290 15298 15307 15312 15315 15317 15317 15315 15311 15302 15292 15280 15271 15265 15262 15261 15242 15244 15246 15250 15253 15257 15260 15265 15272 15280 15290 15297 15306 15312 15316 15318 15318 15315 15310 15301 15292 15281 15272 15267 15263 15263 15243 15245 15247 15251 15253 15257 15260 15265 15273 15280 15289 15297 15306 15312 15316 15319 15319 15315 15310 15302 15292 15283 15273 15268 15265 15265 15244 15246 15248 15251 15254 15257 15260 15265 15273 15279 15289 15297 15305 15312 15316 15319 15319 15316 15311 15303 15293 15285 15275 15270 15267 15267 15245 15247 15249 15252 15254 15257 15261 15266 15273 15279 15289 15296 15305 15312 15316 15319 15319 15317 15312 15304 15295 15287 15277 15272 15269 15269 15245 15247 15249 15252 15255 15258 15262 15266 15273 15279 15288 15296 15304 15311 15316 15319 15320 15318 15314 15307 15297 15289 15280 15275 15271 15270 15246 15248 15250 15253 15256 15259 15263 15267 15274 15279 15288 15295 15303 15311 15315 15319 15320 15319 15316 15309 15301 15293 15283 15277 15273 15272 15247 15249 15251 15253 15256 15260 15264 15268 15274 15280 15287 15295 15302 15310 15315 15319 15321 15320 15317 15312 15304 15296 15286 15279 15274 15273 15248 15250 15251 15254 15257 15261 15266 15270 15275 15280 15287 15295 15302 15310 15315 15319 15321 15321 15319 15315 15307 15300 15290 15282 15276 15274 15249 15251 15253 15256 15259 15263 15268 15271 15276 15281 15287 15295 15302 15310 15315 15320 15322 15322 15320 15317 15310 15304 15294 15286 15280 15276
Determining Photo Scale Using a Map MSR = Map Scale Reciprocal Scale of the Map: 2 in. = 1 mile Say the measured distance of some feature on Map (MD) & Photo (PD) are: MD = 0.58 in. PD = 1.35 in MSR = 1 mile 2 in. PSR photo = 5280 ft. 1 mile GD or D MSR Map Dist. Photo Dist. PD or d 12 in. 1 ft. PSR = = 31, 680 31,680 0.58 in. 1.35 in. GD (D) = 1.35 in 13,611 1 ft. 12 in. 1 ch. 66 ft. = 13,611 = 23.2 chains Distance Correction Factor (DCF) DCF = PSR photo PSR device DCF * Distance = Actual Distance When using a device such as a Dot Grid or a Michigan Photo Interpreters Scale one must account for the fact that the device scale will be different than that on the photo. DCF recognizes that and allows the difference by division of the two PRS s PSR multiplied by the distance.. photo * Distance = Actual Distance PSR device
Variation in Scale on a Single Photo Tilt The farther the object is away from the camera the smaller the photo scale. Scale of a tilted photo changes in a regular manner throughout the photo. Scale changes across photo in direction of tilt ( to axis). Scales are constant along each line parallel to tilt access, while such lines each has a different scale. Larger Scale Smaller PSR # Smaller Scale Bigger PSR # Terrain/Topography (within a single photo) & Slight Altitudinal Variation (between photos) PSR = GD / PD also = H g / f f is fixed, but H (or H g ) varies terrain & aircraft altitude variations Higher ground elevations Larger scale than lower elevations Confusing but PSR decreases with increase in elevation Larger Scale Smaller PSR # Smaller Scale Bigger PSR #
Scale determination using Map Scale Reciprocal (MSR) Problem Solving Pairs: You have a photo of unknown scale and a map of the same area map scale of 1 = 5 miles. If the distance between the two roads is 8 inches on the photo and 0.5 inches on the map, what is the average scale of the photo? Hint: a variation on the formula 1 = d" X D" is possible. PSR MSR = d" map D" photo First: Convert scale of the map to RF 1in 1ft 5mi 12in 1mi = 1 5280ft 316800 MSR = 316800 Next: set up ratios as shown in the formula PSR = 0.5" 316800 8" Finally: Solve for PSR = 0.5"(316800) 8" = 19800
Once scale is known, distances can be determined from aerial photos The slow way with an engineer s scale 1) Measure the distance of interest to the nearest 100 th inch using an engineers scale (50 scale) with the aid of stereoscope magnification. 2) Plug the photo distance (d or PD) into the formula 1 = d" PSR D" and solve for ground distance (D or GD). An example Suppose you are using a photo with a scale or RF of 1:6000 (PSR = 6000) You measure the distance (d or PD) between two buildings and it is 2.13 inches 1 = 2.13" 6000 D" Solving for D gives (2.13 * 6000) / 1 = 12780 or 1065 feet
Michigan Photo Interpreters Scale & Distance Correction Factor A fast way to determine distance using the Michigan Photo Interpreter s Scale 1) There is a device for measuring distances directly using the MPI Along the edge there is a device for measuring distance in chains on photos at a scale of 1:20,000. Simply place the 0 end on one point and read the GD in chains to the next point (1 chain = 66 ft.) 2) If a photo is actually 1:15,840 scale and you measure a distance between two points to be 12 chains using the 1:20000 MPI Scale, then you can compute the correct photo distance (d or PD) using the formula from above ( 1 = d X D correct measurement should be 15840 Correct d = 20000 12 ch. ) to determine what the 15840 20000 12 ch. = Correct d = 9.5 ch. = Correct d 3) When used in this way, PRS Photo PRS Device is referred to as the distance correction factor (DCF) 4) DCF used in situations where both photo and device scales are known...more about this in Lab
A REVIEW: What steps you would use? Suppose you have 45 minutes to determine 20 ground distances between different points on central campus (i.e. dist. Curtiss Hall to Beardshear Hall). You have access to a 100-foot measuring tape, a ruler that contains a 50 scale, a calculator, and aerial photo 25 (showing the central campus area).
1) Find a familiar feature(s) 2) Find ground dist. 3) Measure photo dist. 4) Convert to same units 5) Divide GD by PD PSR Using road by Science II GD = 41 ft. wide PD = 0.4/5 th of inch = 0.4 * 0.2 = 0.08 PSR = 41 ft 0.08 in 12 in 1 ft = 492 0.08 = 6150 Sidewalk to Sidewalk GD = 74 m PD = 2.3 using 50-scale PD = 2.3 * 0.2 = 0.46 PSR = 73.914 m 0.46 in PSR = 2910.0 0.46 12 in 1 ft PSR = 6326 or RF 1:6326 3.28084 ft 1 m Something a Mile Long PRS = 63360" 10.16" = 6236
Impacts of Scale on Accuracy A) Using a engineer s scale, we can measure photo distances to the nearest 100 th of an inch (0.01 inches). B) Using a magnifying comparator, we can achieve accuracy to the nearest 0.005 inches. C) Hence, it is obvious that differences in photo scale will impact the accuracy of any ground measurements we derive from aerial photographs. The smaller the photo scale (small object size) the harder it is to precisely measure the objects seen on the photo.
Impacts of Scale on Accuracy Problem Solving Pairs: A photo is at a known scale of 1:20000. A ground distance between two points is 100 feet. What is the photo distance between the two points? The correct photo measurement should be 0.06 inches. If we measure 0.05, our scale calculation will yield 1:24,000 If we measure 0.07, our scale calculation will yield 1:17,100 Suppose we pick a distance of 500 feet on the ground (GD). The correct photo measurement (PD) should be 0.3 inches. If we measure 0.29, our scale calculation will yield 1:20,690 If we measure 0.31, our scale calculation will yield 1:19,355 500 12 20000 = 6000 20000 = 0.3 6000/0.29 6000/0.31 What s the point here? Because of our inability to measure distances precisely, reporting PSR values in decimal or even less than the nearest 100 gives a false sense of accuracy to potential users of your work. So, only report RF or PSRs to the nearest 100. 1:20,700 or 1:19,400
Impacts of Scale on Accuracy It should be obvious that if we are working with photos that are at a scale larger than 1:20,000 (e.g., 1:15,840), the scale error associated with 0.01 measurement error will be smaller. Conversely, if we work with photos that are at a scale smaller than 1:20,000, (e.g., 1:40,000) the scale error associated with a 0.01" measurement error will be larger. Moral or the story. Important guidelines of scale determination: 1) Pick ground points that are as far apart as possible to reduce the impact of an error in photo measurement. 2) For aerial photos, it doesn't make much sense to report scales of 1:20145 or 1:23,473.682. The best you can hope for is a scale to the nearest 100 PSR, so don't report any more accuracy than that.
Impacts of Scale on Accuracy Again, we assume a scale of 1:20,000. But this time, the problem is to determine a ground distance from the photo. At this scale, a photo distance of 0.01 inches translates to a ground distance of 16.67 feet. PSR * PD = GD 20,000 * 0.01 = 200 200 /12 = 16.67 ft. Consequently, a mismeasurement of 0.01 at this scale will result in an error of nearly 17 feet assuming the scale is exactly correct. For very small distances, we can use a magnifying comparator which can measure to the nearest 0.005, but an error of 0.005" still results in a ground distance error of just over 8 feet. Now assume that we are working with photos at a scale of 1:6000 At this scale, a photo distance of 0.01 translates to a ground distance of 5 feet. Consequently, a mismeasurement of 0.01 at this scale will result in an error of 5 feet. A magnifying comparator capable of measuring to the nearest 0.005 inches will give an error of 2.5 feet for every 0.005 inches mismeasurement. Another important rule for using aerial photos is that in order to obtain more accuracy from any measurements that are taken, you need to work with larger scale photos. Finally, an overall rule would be to work with the largest scale photos that your project and budget will permit.
Michigan Photo Interpreter s Scale (MPI)
7.5 minute Topo Quads Public Land Survey (PLS) 1 Township = 6 x 6 miles 36 Sections = each 1 x 1 mile