Photogrammetry — relief displacement, principal point, and scale variation Which combination of statements about vertical photography and terrain effects is correct?

Introduction / Context:
Vertical photographs suffer relief displacement proportional to object height and radial distance from the principal point, and their scale varies with ground elevation. Understanding these effects is vital for mapping accuracy and interpretation.

Given Data / Assumptions:

• Vertical or near-vertical photography with focal length f and flying height H above datum.
• Relief displacement increases with object height and image radial distance.
• Photo scale at elevation h is approximately S = f / (H − h).

Concept / Approach:

Higher platforms (e.g., satellites) have very large H, reducing d = (r * h) / (H − h). At the principal point (r = 0), displacement is nil. For constant H above datum, higher terrain (larger h) yields larger scale since (H − h) is smaller. A statement claiming “scale depends on the scale of topography” is imprecise; scale depends on H and h (elevation), not a pre-existing “scale of topography.”

Step-by-Step Solution:

Verification / Alternative check:

Relief displacement and scale formulas are standard in photogrammetry texts; simple numerical checks confirm trends with H and h.

Why Other Options Are Wrong:

• (e) is incorrect because it would include an imprecise/incorrect dependency description.

Common Pitfalls:

• Forgetting that “principal point” is the image of the camera center; r = 0 there.
• Confusing “flying height above terrain” with “above datum” when comparing scales.

Final Answer:

Only (a), (b), and (c) are correct.