Relief (height) displacement on a vertical aerial photograph: identify how it varies with position, terrain elevation, and flying height.

Introduction / Context:
Relief displacement is the apparent radial shift of image points on vertical aerial photographs caused by object height above the reference datum. Understanding its dependencies is crucial for accurate planimetry and for deriving elevations photogrammetrically.

Given Data / Assumptions:

• Vertical photograph with principal point well defined.
• Object point at elevation h above datum, flying height above datum H, focal length f.
• Radial distance r from the principal point to image point.

Concept / Approach:
The first-order relation for relief displacement d on a vertical photo is d ≈ (r * h) / H. Thus, displacement grows with radial distance r and object height h, and diminishes with larger flying height H. The direction of displacement is radially outward for elevated points.

Step-by-Step Solution:
Start with d ≈ (r * h) / H.As r increases (farther from principal point), d increases linearly.As h increases (higher terrain/objects), d increases linearly.As H increases (higher flight), d decreases inversely.

Verification / Alternative check:
At the principal point (r = 0), d = 0, consistent with zero displacement there. Doubling flying height halves displacement, confirming inverse dependence.

Why Other Options Are Wrong:
Each individual statement (a), (b), and (c) is correct; therefore, “All the above” is the correct aggregate choice.

Common Pitfalls:
Confusing relief displacement with lens distortion; ignoring sign convention (outward for elevated points, inward for depressions).

Final Answer:
All the above