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Siva Subramanian M 
Centre for Land Resource Management
The displacement of an object caused by a change 
in the point of observation is called Parallax 
Stereoscopic parallax is caused by taking 
photograph of the same object but from different 
point of observation
 Adjacent but overlapping aerial photos 
are called stereo-pairs and are needed to 
determine parallax and stereo/3D viewing 
http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/stereosc/chap4/
Overlapping photography 
 End lap - ~60% 
 Side lap - ~20-30%
- Locate the principal point (PP, optical center or nadir) 
of each photo by drawing a line between the corner fiducial 
marks 
-Locate the conjugate principal point (CPP) which is the PP 
of the adjacent photo 
-Draw the line between the PP and CPP - this is the flight line 
- Align the photos so that all 4 points lie on a straight line
 A photo’s central projection leads to image 
displacement where objects are shifted or 
displaced from their correct positions 
 Relief displacement is due to differences in the 
relative elevations of objects. All objects that 
extend above or below a specified ground datum 
plane will have their images displaced. 
 The taller the object, the greater the relief 
displacement
 Even from great flying 
heights, tall objects can 
exhibit image 
displacement. 
 In this example from a 
Quick bird satellite 
image, the Washington 
Monument appears to 
lean outwards 
http://www.mfb-geo.ch/text_d/news_old_d8.html
 Objects will tend to 
lean outward, i.e. be 
radially displaced. 
 The greater the object 
is from the principal 
point, the greater the 
radial displacement. 
 Example: storage 
tanks towards the edge 
of photo show greater 
radial displacement. 
Center of 
photo 
Edge of 
photo
 Maps: Scale is constant 
No relief displacement 
 Photos: Scale varies with elevation 
Relief displacement
Note the displacement between the top and base of 
the storage towers in this photo stereo-pair 
Line of Flight 
top 
bottom
 PP = Principal point = Center of photo 
 CPP = Conjugate principal point = Adjacent photo’s PP 
 Absolute stereoscopic parallax  the average photo base 
length = average distance between PP and CPP 
Photo 
base 
PP CPP 
PP
 Differential parallax - the difference between 
the stereoscopic parallax at the top and base of 
the object. 
15.2 mm 
13.5 mm 
dP = 15.2mm – 13.5mm = 1.7 mm
Photo 1 Photo 2 
dP = 2.06-1.46 = 0.6 in 
1.46 
2.06 
Following example 
taken from: 
T.E. Avery & G.L. 
Berlin. 1992, 
Fundamentals of Remote 
Sensing and Air Photo 
Interpretation, MacMillan P 
Calculating the height of the Washington 
Monument via stereo parallax
 h = (H’) * dP / (P + dP) 
where h = object height 
H’ = flying height 
dP = differential parallax 
P = average photo base length
h = (H’) * d / (r) 
Where, 
h = object height 
H’ = flying height = 4,600ft 
d = relief displacement from base to top = 0.6in same as dP 
r = distance from PP to top of object same as (P + dP)
 Object heights can be determined as follows: 
◦ calculate flight altitude (H’) by multiplying the RF 
denominator by the focal length of the camera 
◦ h = d * H’ / r where: 
h = Object height 
d = length of object from base to top 
r = distance from P.P. to top of object 
r 
d 
r
 Parallax wedge - simplest device for 
determining differential parallax 
 Parallax bar - movable floating mark can 
placed at base and tops of objects to 
measure differential parallax
 Stereoplotters - precision 
instruments designed to 
duplicate the exact 
relative position and 
orientation of the aerial 
camera at the time of 
photo acquisition to 
recreate the stereo-model. 
A floating mark can be 
used trace specific 
elevations. Relief 
displacement is removed 
creating a planimetric 
map. Photo from 
http://www.wsdot.wa.gov/mapsdata/Photo 
grammetry/PhotogImages/earlyStation.gif
•Soft-copy 
photogrammetry 
workstations - computer 
software recreates the 
stereomodel and allows 
for digital mapping 
•Soft-copy 
photogrammtery has 
largely replaced optical-mechanical 
systems 
Photos from: 
http://www.wsdot.wa.gov/mapsdata/ 
Photogrammetry/About.htm 
Digital 
scanner 
Soft copy 
workstation
 One view displayed in red; the other 
perspective view in blue spatially shifted 
 The spatial shift is a 
function of the 
differential parallax 
 To visualize, use 
red-blue glasses 
NASA Mars Lander
 Orthophoto - reconstructed airphoto showing 
objects in their true planimetric position 
 Geometric distortions and relief displacements 
are removed 
 Orthophotoquad - orthophotos prepared in a 
standard quadrangle format with same 
positional and scale accuracy as USGS 
topographic maps
 Digital ortho-photography/ortho-imagery is 
increasingly the imagery of choice for many 
applications 
 Sometimes referred to as 
DOQ - digital orthophoto quad 
 NJ has DOQ imagery for 
1995 and 2002 
Digital orthophoto on 
computer screen 
Photo from: http://www.wsdot.wa.gov/mapsdata/Photogrammetry/About.htm

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Stereoscopic Parallax

  • 1. Siva Subramanian M Centre for Land Resource Management
  • 2. The displacement of an object caused by a change in the point of observation is called Parallax Stereoscopic parallax is caused by taking photograph of the same object but from different point of observation
  • 3.  Adjacent but overlapping aerial photos are called stereo-pairs and are needed to determine parallax and stereo/3D viewing http://www.ccrs.nrcan.gc.ca/ccrs/learn/tutorials/stereosc/chap4/
  • 4. Overlapping photography  End lap - ~60%  Side lap - ~20-30%
  • 5. - Locate the principal point (PP, optical center or nadir) of each photo by drawing a line between the corner fiducial marks -Locate the conjugate principal point (CPP) which is the PP of the adjacent photo -Draw the line between the PP and CPP - this is the flight line - Align the photos so that all 4 points lie on a straight line
  • 6.  A photo’s central projection leads to image displacement where objects are shifted or displaced from their correct positions  Relief displacement is due to differences in the relative elevations of objects. All objects that extend above or below a specified ground datum plane will have their images displaced.  The taller the object, the greater the relief displacement
  • 7.  Even from great flying heights, tall objects can exhibit image displacement.  In this example from a Quick bird satellite image, the Washington Monument appears to lean outwards http://www.mfb-geo.ch/text_d/news_old_d8.html
  • 8.  Objects will tend to lean outward, i.e. be radially displaced.  The greater the object is from the principal point, the greater the radial displacement.  Example: storage tanks towards the edge of photo show greater radial displacement. Center of photo Edge of photo
  • 9.  Maps: Scale is constant No relief displacement  Photos: Scale varies with elevation Relief displacement
  • 10. Note the displacement between the top and base of the storage towers in this photo stereo-pair Line of Flight top bottom
  • 11.  PP = Principal point = Center of photo  CPP = Conjugate principal point = Adjacent photo’s PP  Absolute stereoscopic parallax  the average photo base length = average distance between PP and CPP Photo base PP CPP PP
  • 12.  Differential parallax - the difference between the stereoscopic parallax at the top and base of the object. 15.2 mm 13.5 mm dP = 15.2mm – 13.5mm = 1.7 mm
  • 13. Photo 1 Photo 2 dP = 2.06-1.46 = 0.6 in 1.46 2.06 Following example taken from: T.E. Avery & G.L. Berlin. 1992, Fundamentals of Remote Sensing and Air Photo Interpretation, MacMillan P Calculating the height of the Washington Monument via stereo parallax
  • 14.  h = (H’) * dP / (P + dP) where h = object height H’ = flying height dP = differential parallax P = average photo base length
  • 15. h = (H’) * d / (r) Where, h = object height H’ = flying height = 4,600ft d = relief displacement from base to top = 0.6in same as dP r = distance from PP to top of object same as (P + dP)
  • 16.  Object heights can be determined as follows: ◦ calculate flight altitude (H’) by multiplying the RF denominator by the focal length of the camera ◦ h = d * H’ / r where: h = Object height d = length of object from base to top r = distance from P.P. to top of object r d r
  • 17.  Parallax wedge - simplest device for determining differential parallax  Parallax bar - movable floating mark can placed at base and tops of objects to measure differential parallax
  • 18.  Stereoplotters - precision instruments designed to duplicate the exact relative position and orientation of the aerial camera at the time of photo acquisition to recreate the stereo-model. A floating mark can be used trace specific elevations. Relief displacement is removed creating a planimetric map. Photo from http://www.wsdot.wa.gov/mapsdata/Photo grammetry/PhotogImages/earlyStation.gif
  • 19. •Soft-copy photogrammetry workstations - computer software recreates the stereomodel and allows for digital mapping •Soft-copy photogrammtery has largely replaced optical-mechanical systems Photos from: http://www.wsdot.wa.gov/mapsdata/ Photogrammetry/About.htm Digital scanner Soft copy workstation
  • 20.  One view displayed in red; the other perspective view in blue spatially shifted  The spatial shift is a function of the differential parallax  To visualize, use red-blue glasses NASA Mars Lander
  • 21.  Orthophoto - reconstructed airphoto showing objects in their true planimetric position  Geometric distortions and relief displacements are removed  Orthophotoquad - orthophotos prepared in a standard quadrangle format with same positional and scale accuracy as USGS topographic maps
  • 22.  Digital ortho-photography/ortho-imagery is increasingly the imagery of choice for many applications  Sometimes referred to as DOQ - digital orthophoto quad  NJ has DOQ imagery for 1995 and 2002 Digital orthophoto on computer screen Photo from: http://www.wsdot.wa.gov/mapsdata/Photogrammetry/About.htm