In photogrammetry and perspective geometry, the “perspective centre” corresponds to which type of projection used to form an image from a point source?

Introduction / Context:
Understanding the perspective centre is crucial in photogrammetry, camera modeling, and engineering surveying. The perspective centre (also called the projection centre) is the notional point from which straight lines are drawn to the object and then intersect the image plane to form an image.

Given Data / Assumptions:

• Camera behaves as a pinhole (idealized model).
• Image plane is finite and fixed relative to the pinhole.
• Object points are projected along straight lines.

Concept / Approach:
In the pinhole model, each object point connects to the image plane via a straight line through a single point (the perspective centre). This is the definition of central projection, as opposed to parallel/orthogonal projection where projecting rays are mutually parallel and do not pass through a single point.

Step-by-Step Solution:
1) Define perspective centre: unique point source for rays.2) For each object point P, draw line PC (C = perspective centre).3) Intersection of PC with the image plane gives the image of P.

Verification / Alternative check:
Camera calibration equations use central perspective: x = f*(X/Z), y = f*(Y/Z) in a camera-fixed system, showing the dependence on a single projection centre and focal length f.

Why Other Options Are Wrong:
Parallel and orthogonal projections use parallel rays, not a single centre.Cylindrical projection maps onto a cylinder via different construction, not a single point source.

Common Pitfalls:
Confusing “central” with “cylindrical” or assuming orthogonal projection is used in cameras. Real cameras approximate central projection.

Final Answer:
Central projection