| ES 771 Lecture
James S. Aber |

## Introduction to photogrammetry

Aerial photographs are **not maps**. They are **single-point perspective** views of the Earth's surface, whereas maps are orthogonal representations of the surface. Sizes, shapes, and positions of objects are distorted in aerial photographs. However, aerial photographs can be used to construct maps and to accurately measure distances, heights and elevations. The use of photography for accurate measurement is called **photogrammetry**. Modern mapping airphoto cameras are large, sophisticated instruments, including both film and digital types, typically flown in twin-engine planes from moderate (3000-6000 m) to high (>10,000 m) altitude.

Hexagon Geospatial photogrammetry.

The **scale** of a vertical aerial photograph can be calculated in two ways, as given in the table.

scale = f ÷ H | scale = photo distance ÷ ground distance |

In either case, the units of measurement must be the same. The scale depends on the average height above the ground. In rugged terrain, photo scale varies because of large height differences within the photograph. Likewise oblique or non-vertical photos also display scale variation.

Because of the single-point perspective nature of photography, objects toward the edge of a photograph suffer **relief displacement**. Tall objects appear to lean away from the photo center; low objects are displaced toward the center. Relief displacement is minimal near the photo center and becomes extreme at the photo edge. This allows for a "side view" of tall objects near the edge of the photo. The height of a tall object may be calculated from its relief displacement, and the height of tall objects may also be determined from measurements of shadows.

## Air-photo terminology

**Principal point:** Geometric center of photograph. Literally the point on the ground in line with axis of camera lens.

**Fiducial marks:** Marks on the photograph margins used to locate principal point in photo.

**Conjugate principal point:** Point in overlapping photo that is equivalent to principal point of adjacent photograph.

**Photo base:** Distance between principal point and conjugate principal point measured on a single photograph.

**Ground (air) base:** Ground (air) distance between principal points of overlapping photographs.

**Parallax:** Apparent shift in relative positions of objects when viewed (photographed) from different vantage points. The basis of stereoscopic vision.

## Calculating height using parallax

The calculation of approximate heights and elevations using parallax measurements can be done quickly and easily with the formulas given below. These calculations depend upon the assumptions that ground principal points in each photo are at about the same elevation and that the bases of objects being measured are also at about the same elevation. Two formulas may be used.

p = | difference in parallax between two points in mm |

H = | flying height (altitude - ground elevation) in meters |

b = | average of photo bases measured on each photo in mm |

B = | average of ground bases for each photo in meters |

f = | focal length of camera lens in mm |

h = | difference in height (elevation) of two points in meters |

Example of height calculation: p = 2 mm, H = 3840 m, b = 65 mm, B = 998 m, f = 250 mm.

h = (3840 x 2) ÷ 65 = 118 m |

h = (3840² x 2) ÷ (998 x 250) = 118 m |

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**© Notice:** ES 771 is presented for the use and benefit of students enrolled at Emporia State University. Any other use of text, imagery or curriculum materials is prohibited without permission of the instructor. Last update 2016.