# Geometry of Aerial Photography

Volume I, Module 6

## I. Classification of Photographs

In his book on aerial photo interpretation, Paine presents a dichotomous key for classifying aerial photography. The key is listed as follows:

Photographs

Terrestrial Aerial

Vertical Oblique

True Tilted High Low

## Oblique Photos

There are two basic types of oblique aerial photography. These two types are:

1. High angle oblique; and

2. Low angle oblique.

In a high angle oblique, the apparent horizon is shown; while in a low angle oblique the apparent horizon is not shown. Often because of atmosphere haze or other types of obscuration the true horizon of a photo cannot really be seen. However we often can see a horizon in an oblique air photo. This is the apparent horizon.

## Vertical Air Photos

The basic advantages of vertical air photos are:

1. The scale is essentially constant;

2. Measurements of directions are easier than on oblique photograph. Directions can also be measured more accurately;

3. Within limits a vertical aerial photograph can be used as a map (if grids and marginal data are added); and,

4. Vertical aerial photographs are often easier to interpret than oblique and are better for stereo (there is no masking).

The advantages of an oblique aerial photograph include:

## II. Perspective and Projection

Now lets talk about perspective and projection.

First lets consider the viewing perspective of a map. On a map objects and features are both planimetrically and geometrically accurate. That is objects are located on the map in exactly the same position relative to each other as they are on the surface of the Earth, except with a change in scale. This is due to the fact that maps use an orthographic projection (i.e. using parallel lines of site) and constant scale to represent features.

## III. Distortion and Displacement

There are basically four types of distortions and three types of displacement.

Types of distortion include:

1. Film and Print Shrinkage;
2. Atmospheric refraction of light rays;
3. Image motion; and,
4. Lens distortion.

Types of displacement include:

1. Curvature of the Earth;
2. Tilt; and,
3. Topographic or relief (including object height).

## Lens distortion

Small effects due to the flaws in the optical components (i.e. lens) of camera systems leading to distortions (which are typically more serious at the edges of photos). Car windows/windshields, carnival mirrors are probably the best know examples of this type of effect. These effects are radial from the principal point (making objects appear either closer to, or farther from the principal point than they actually are); and may be corrected using calibration curves.

## Tilt Displacement

A tilted photograph presents a slightly oblique view rather than a true vertical record. All photos have some tilt. The perfect gyro stabilization unit, like the perfect lens, has yet to be built. Tilt is caused by the rotation of the platform away from the vertical. This type of displacement typically occurs along the axis of the wings or the flight line. Tilt displacement radiates from the isocenter of the photo and causes objects to be displaced radially towards the isocenter on the upper side of the tilted photo and radially outward on the lower side.

## General Characteristics of Relief Displacement

A close look at the equations involved in the calculations of relief displacement show that some important general relationships are involved. These relationships can be stated as follows:

1. There is no topographic displacement at Nadir. If r is zero, then so is d.

## IV. Orthophotography

Briefly, here there is a growing use of orthophotography today. If you remember back to our discussion of maps at the beginning of the lecture you will remember that orthographic projection depict thing in their true plan position.