Photogrammetry – where is scale of a tilted photo equal to a vertical photo? For plane (level) ground, the scale of a true vertical aerial photograph will be the same as the scale of a tilted photograph along the photo-parallel that passes through which key image point?

Introduction / Context:
In aerial photogrammetry, most photographs are not perfectly vertical; a small tilt produces geometric distortions and a scale that varies across the image. Understanding where a tilted photo locally behaves like a vertical photo helps with approximate measurements and planning of control.

Given Data / Assumptions:

• Small to moderate tilt with a well-defined principal point, plumb point, and isocentre on the image.
• Terrain assumed plane (constant elevation) so relief effects are negligible.
• Camera focal length and flying height are constant over the exposure.

Concept / Approach:
For a tilted photograph, the isocentre is defined as the midpoint of the segment joining the principal point and the nadir (or plumb) point. The line through the isocentre parallel to the direction of flight is often called a photo-parallel. Along the photo-parallel passing through the isocentre, the scale of a tilted photograph matches the scale of an equivalent vertical photograph taken from the same flying height over plane ground.

Step-by-Step Solution:
Relate scale on a vertical photo: S_v = f / H for plane terrain.For a tilted photo, local scale depends on distance from the principal line and the tilt angle θ.Along the photo-parallel through the isocentre, the tilt effects balance such that S_t(local) = S_v.Hence the key point that ensures equality of scales is the isocentre.

Verification / Alternative check:
Classical image geometry shows that perspectivity about the isocentre preserves vertical-photo scale along the specific photo-parallel when the terrain is truly plane. Field checks with well-distributed ground control confirm minimal scale bias along this line.

Why Other Options Are Wrong:

• Plumb point and principal point control other constructions (horizon line, principal line) but do not guarantee equal scale.
• Nadir and horizon points define directions/limits, not the equality condition.

Common Pitfalls:
Assuming the entire tilted photo has a single scale; in reality, scale varies across the frame except along special loci like the photo-parallel through the isocentre (for plane ground).

Final Answer:
Isocentre