Topographic Displacement: Formula & Analysis for Topographic or Height Displacement (Especially for GATE-Geospatial 2022)

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This is typically the most serious type of displacement. This displacement radiates outward from Nadir. Topographic displacement is caused by the perspective geometry of the camera and the terrain at varying elevations.

Principal Point
  • Topographic displacement is not necessarily bad as it allows:
    • Stereo viewing
    • Height measurement and,
    • Topographic mapping.
  • Below figure illustrates an extreme case in which successive images along a flight line have been taken from opposite sides of a mountain ridge. Left-hand image, side A of the mountain occupies most of the image while side B is a narrow sliver. The opposite is true in the right-hand image.
  • The extreme difference between the two images will make it difficult to view this pair of images in three dimensions and will also make it difficult to represent the mountain ridge accurately on a map. This problem can be minimized by flying at higher altitudes to minimize scale variations and radial displacement (relief distortion) ; flying along valleys; using more overlap so that you have more principal points and more images to compare.
Topographic Displacement
Topographic Displacement

Formula for Topographic Displacement

Given,

  • r = distance on the photo from the nadir to the displaced landscape feature. r ′ = actual place on the photo where the landscape feature should be located. d = relief (topographic) displacement.
  • h = height of the landscape feature.
  • A = altitude of the aircraft above sea level.
  • E = elevation of the landscape feature.
  • H = Flying height above the base of the landscape feature at nadir.
  • R = distance from the nadir to the landscape feature.
  • f = focal length

The formula for topographic or height displacement on a single photo is:

Where, d = displacement of landscape feature on the photo h = height of landscape feature

Equation Analysis

A close look at the equations involved in the calculations of relief displacement shows that some important general relationships are involved. These relationships can be stated as follows:

  • There is no topographic displacement at Nadir. If r is zero, then so is d.
  • Assuming datum elevation to be at Nadir, points above the datum are displaced radially away from Nadir while points below datum are displaced radially towards Nadir.

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