Aerial Photogrammetry – Idealized projection model In the context of photogrammetry, an aerial photograph (captured from a finite flying height with a lens of focal length f) is best idealized as which type of geometric projection for mapping and measurement purposes?

Introduction / Context:
Aerial photogrammetry relies on understanding how terrain points are projected onto the photo plane. The geometric model used in computations must reflect how a real camera forms images. Recognizing that aerial photos are created by rays passing through a single perspective center is foundational to scale, relief displacement, and orientation concepts.

Given Data / Assumptions:

• A finite focal length camera captures the scene from a finite height above ground.
• Light rays from ground points pass through a single optical center (perspective center) before reaching the image plane.
• We are considering the idealized geometric model (ignoring lens distortion and tilt for the core concept).

Concept / Approach:
In central (perspective) projection, all image-forming rays converge at one point: the camera's perspective center. This contrasts with parallel or orthogonal projection where projectors are mutually parallel and conceptually originate at infinity. Central projection accurately represents how a real lens maps 3D terrain onto a 2D photo, which is why photogrammetric collinearity equations use the perspective center explicitly.

Step-by-Step Solution:
Identify the imaging geometry of a lens: rays converge at the optical center → perspective mapping.Match this with the projection type → central (perspective) projection.Exclude parallel/orthogonal models because they assume infinite focal distance and do not produce relief displacement or perspective scale changes.

Verification / Alternative check:
Relief displacement formula d = (r * h) / H and photo scale S = f / H derive from central projection assumptions. These relations would not hold under a parallel projection model.

Why Other Options Are Wrong:

• Parallel/orthogonal projections ignore the finite focal length and perspective center, hence they cannot explain radial displacement.
• “None of these” is invalid because central projection precisely describes aerial photos.

Common Pitfalls:
Assuming near-vertical photos behave like maps; maps approximate orthographic views, while photos are central projections that require rectification for planimetric accuracy.

Final Answer:
Central projection