3.5 Photogrammetry, UAS, and Image Processing

Photo Scale, Flying Height, and Relief Displacement

Photogrammetry extracts measurements from overlapping imagery using camera geometry and control. For a near-vertical aerial photo the scale is:

S = f / (H - h)

where f is the camera focal length, H is the flying height above the datum, and h is the ground elevation. Because h varies, photo scale is not constant — higher ground sits closer to the camera and images at a larger scale than low ground. (Equivalently, scale = photo distance / ground distance.)

Relief displacement is the radial shift of an object's image caused by its height above the datum:

d = r * h / H

where d is the displacement on the photo, r is the radial distance from the principal point (photo center) to the top of the object, h is the object's height, and H is the flying height above its base. Key consequences tested on the FS exam:

• Displacement is radial outward from the principal point; the top of a building leans away from center.
• It is zero at the principal point and greatest at the photo edges and for tall objects.
• It is the basis for measuring object heights from a single photo, but it also distorts a raw photo so it cannot be used as a map.

Stereo Geometry, Overlap, and Ground Sample Distance

Three-dimensional measurement requires stereo coverage: each ground point must appear on at least two overlapping photos so the viewing geometry can be intersected. Standard aerial blocks fly with about 60% forward overlap (endlap) along a flight line and about 30% sidelap between adjacent lines. The apparent shift of a point between the two images of a stereo pair is parallax, and parallax differences yield elevation.

For digital and UAS cameras, the practical resolution metric is ground sample distance (GSD) — the ground size of one pixel:

GSD = (sensor pixel size x flying height) / focal length

equivalently GSD = (flying height x sensor width) / (focal length x image width in pixels). Lower altitude yields finer GSD (smaller ground distance per pixel) and more detail; higher altitude covers more ground per image but coarsens GSD. GSD drives both the smallest mappable feature and the achievable positional accuracy.

UAS Flight Planning and Ground Control

Unmanned aircraft systems (UAS / drones) map by capturing many overlapping photos processed with structure-from-motion (SfM) into a point cloud, surface, and orthophoto. A sound UAS survey requires:

• A flight plan: altitude (for target GSD), overlap (often 70-80% for SfM), and pattern.
• Ground control points (GCPs) — surveyed, well-distributed targets that georeference the block to a datum and scale it.
• Independent check points — surveyed points withheld from the solution and used to verify accuracy.
• Adequate overlap, lighting, and texture for the matching algorithm.

GCPs anchor absolute accuracy; without them (or without RTK/PPK direct georeferencing) the model can be internally consistent yet absolutely wrong. Check points, not the processing software's internal report, are how accuracy is verified.

Orthophotos and the Limits of Imagery

A raw aerial or UAS photo contains relief displacement and tilt and cannot be scaled as a map. Orthorectification uses a terrain model and the camera geometry to remove relief and tilt distortion, producing an orthophoto with uniform scale on which true distances and directions can be measured. The orthophoto's quality is bounded by the terrain model used to rectify it, the GCPs, and the GSD.

The enduring FS lesson is that imagery maps visible surfaces well but has limits:

• It cannot see hidden or subsurface features (utilities under pavement, monuments under brush).
• It records the top reflective surface, so SfM over dense canopy yields a DSM, not bare earth.
• It does not establish boundaries; corners are legal/record evidence, not image features.

So imagery is excellent for planimetric mapping, volumes, and inspection, but boundary and hidden-feature decisions still require conventional ground survey.

Interior and Exterior Orientation

Reconstructing ground geometry from photos requires two sets of parameters the FS exam names. Interior orientation describes the camera itself: the focal length (principal distance), the location of the principal point, and lens distortion — values fixed by camera calibration. Exterior orientation describes where and how the camera was pointed for each exposure: its three position coordinates and three rotation angles (omega, phi, kappa), six parameters per photo.

Solving exterior orientation for a whole block at once, tying photos together with overlap tie points and a few ground control points, is aerotriangulation (bundle adjustment); it minimizes the control needed.

The collinearity condition — that the ground point, the lens center, and the image point lie on one straight line — links these orientations to ground coordinates. You are not asked to solve it by hand on the FS, but recognize that interior plus exterior orientation, anchored by control, converts pixels to mapped positions.

Direct Georeferencing and Accuracy Expectations

Modern UAS often carry RTK or PPK GNSS, recording each camera position to centimeters. This direct georeferencing can reduce — though rarely eliminate — the number of ground control points, but independent check points are still required to verify accuracy. As a rule of thumb, horizontal accuracy tracks the GSD, while vertical accuracy is looser and more sensitive to control geometry and calibration. Flight planning is therefore a deliberate trade among altitude, overlap, control, and the accuracy the deliverable must meet.