Relief (height) displacement on vertical aerial photos – sign and special case For truly vertical aerial photographs, which set of statements about height displacement is correct regarding points above/below the datum and the point directly under the camera?

Introduction / Context:
Relief (height) displacement is a hallmark of central projection. It appears as a radial shift of image points away from the photo’s principal point due to elevation differences. Correctly interpreting its sign and special cases is essential for height extraction and planimetric corrections.

Given Data / Assumptions:

• Vertical aerial photograph (no tilt).
• Datum is mean terrain or a reference plane.
• Principal point and nadir are practically coincident for a truly vertical photo.

Concept / Approach:
For vertical photos, relief displacement magnitude follows d = (r * h) / H, directed radially outward from the principal point for positive height h above datum. Points below the datum show inward displacement (negative with adopted sign). A point on the ray directly beneath the perspective center (nadir) has r = 0, leading to zero displacement.

Step-by-Step Solution:
Above datum (h > 0): vectors point outward → positive sign by convention.Below datum (h < 0): inward shift → negative sign.At nadir: r = 0 → d = 0 regardless of h.Hence, all three statements are simultaneously true.

Verification / Alternative check:
Radial-line methods and parallax bar measurements are based on this sign convention; test models confirm outward growth with positive relief.

Why Other Options Are Wrong:
Any single statement alone omits the complete picture; “None” is wrong because each listed statement is correct.

Common Pitfalls:
Confusing principal point with nadir on tilted photos; for non-vertical photos, these differ and displacement interpretation requires tilt corrections.

Final Answer:
All of the above