Photogrammetry – Geometry of a Vertical Photograph

Photogrammetry is the science of making measurements from photographs, especially for mapping and surveying. When the camera axis is perpendicular (vertical) to the ground, the photo is called a vertical photograph, and its geometry is central to accurate mapping.

Elements of Vertical Photo Geometry

In a vertical aerial photograph, the geometry is governed by the central projection principle. Here's how it works:

1. Principal Point (P)

The point on the photo where the optical axis of the camera intersects the photo plane.
It's the geometric center of the photo.

2. Nadir Point (N)

The point on the ground directly below the camera at the time of exposure.
Ideally, in a perfect vertical photo, the nadir and principal point coincide.

3. Photo Center (C)

Usually coincides with the principal point in a vertical photo.

4. Ground Coordinates (X, Y, Z)

Real-world (map) coordinates of objects photographed.

5. Flying Height (H)

Height of the camera above the ground (datum).
Important for scale calculation.

6. Focal Length (f)

Distance between the camera lens and the film/sensor.
Determines how much of the ground is captured.

Why Geometry Matters

Understanding the geometry allows:

Accurate measurements (distances, heights)
Orthorectification (correcting image distortions)
3D modeling (when combined with overlapping photos in stereo)


Vertical Photo	Camera axis perpendicular to ground
Principal Point	Center of the photo
Focal Length (f)	Lens to image distance
Flying Height (H)	Height above ground
Scale	S=fHS = \frac{f}{H}
Relief Displacement	Radial shift due to elevation

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