Coincidence of key points on a truly vertical aerial photograph For a truly vertical photograph, which of the following is correct regarding the principal point, isocentre (iso-centre), and plumb point?

Introduction / Context:Three special points are used in photo-geometry: the principal point (intersection of the optical axis with the photo), the plumb point (nadir projection), and the isocentre. Understanding when they coincide simplifies interpretation and computations.

Given Data / Assumptions:

• Truly vertical exposure (zero tilt).
• Calibrated camera with central projection.

Concept / Approach:

When tilt is zero, the optical axis is vertical; the nadir projects at the same point as the principal point. The isocentre, defined via the intersection of the bisector of the angle between vertical and optical axis with the photo plane, also falls at this same point. Hence all three coincide.

Step-by-Step Solution:

Verification / Alternative check:

Photogrammetry references explicitly state coincidence of these three points for true verticals; with tilt, they separate along the tilt direction by amounts depending on f and θ.

Why Other Options Are Wrong:

• Options (a)–(c) list pairwise coincidences but omit the full equivalence which is true in this case.

Common Pitfalls:

• Assuming coincidence on slightly tilted photos; even small tilts create measurable offsets on large-scale imagery.

Final Answer:

Principal point, isocentre, and plumb point all coincide.