Aerial Triangulation

Aerial Triangulation in Photogrammetry is methods of determine and calculate 3-dimensional object coordinates by photogrammetric means, by using photographs exposed from different positions, covering the same object.

With aerial triangulation in aerial photogrammetry we might be able to calculate 3-dimensional coordinates for object elements on almost any object. We need at least some points with known position that are visible in at least some of the photographs. These points we call ground control points, or any control points, the control points have to be a part of the aerial triangulation.

Why we are using aerial trangulation?

Usually it is more expensive to have people working out in the field, and it is also harder work than what it is to do the work is an office. Because of that different method has been developed to be able to reference a model with as few ground control points as possible. Still we need at least five  control points inside each aerial photogrammetry model to be able to do an absolute orientation of the model.

In aerial photogrammetry,to be able to get that many points a method named aerial triangulation is developed. This method is that we measure several unknown point clearly visible in theaerial triangulation in a stereo instrument. These new points together with the ground control points and the exposures positions for the camera are put together in a big computation. The result we get out of this is the coordinates in the reference system for all the new measured points.

What are the inputs for aerial triangulation? 

1.    Scanned Images
2.    Camera Report
3.    Ground Control Data/ Ground Control Point

Photogrammetry Introduction

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.

Aerial photographs are classified in three types, depending on orientation of the picture. The tilt of the camera lens relative to the horizon is called depression angle.

• Vertical airphoto -- View straight down, depression angle 85° to 90°.
• Low-oblique vantage -- Side view, horizon is not visible, depression angle typically 20-85°.
• High-oblique vantage -- Side view, horizon is visible, depression angle typically less than 20°.

	Vertical kite aerial photograph. Lake Kahola, Kansas. Photo date July 1997, © J.S. Aber.
	Low-oblique kite aerial photograph. Lake Kahola, Kansas. Photo date May 1997, © J.S. Aber.
	High-oblique kite aerial photograph. Lake Kahola, Kansas. Photo date Sept. 1997, © J.S. Aber.

 Scale of a Vertical Airphoto

scale = f ÷ H

scale = photo distance ÷ ground distance

Where: f = lens focal length, and
H = flying height above the ground.

The scale of a vertical aerial photograph can be calculated in two ways. 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 variations, so they are rarely utilized for photogrammetry.

Because of the single-point perspective nature of photography, objects toward the edge of a photograph suffer relief displacement. This is most noticable, because tall objects appear to lean away from the photo center. Conversely 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.

Near-vertical kite aerial photograph. Notice different view of trees near scene center in comparison to trees at far right. This is an example of relief displacement. The bright spot on ground to left (red arrow) is an example of the opposition effect--the position in direct alignment with the sun and camera. Next to the opposition point is a dark spot (blue arrow). This is the shadow of the kite that lifted the camera. Cucharas Pass, Colorado; photo date 6/00, © J.S. Aber.

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.

Stereoscopic vision

Parallax is the basis of stereoscopic vision. The human eyes, spaced a few cm apart, each see the world from slightly different vantage points. This slight difference introduces a parallax that facilitates depth perception. In aerial photography, two vertical photographs of the same ground area may be offset by considerable distance. When the two photos are viewed through a stereoscope, an enhanced depth perception is created in which the heights and slopes of objects are greatly exaggerated. Many types of stereoscopes are in use for this kind of work.

Vertical, stereopair, kite aerial photographs taken over cemetery, Emporia, Kansas. Click on the small image to see full-sized version (129 kb). Photo date 12/98, © J.S. Aber.

Oblique, stereopair, kite aerial photographs taken over residential neighborhood, Emporia, Kansas. Click on the small image to see full-sized version (144 kb). Photo date 12/98, © J.S. Aber.

Sokkia mirror stereoscope for SFAP. This stereoscope is the ideal size for viewing 4x6-inch (10x15-cm) prints from 35-mm film. Taken from ASC Scientific.

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.

 Parallax Height Formulas

h = Hp ÷ b

h = H²p ÷ Bf

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 (taken from Topcon stereoscope manual).

h = (3840 x 2) ÷ 65 = 118 m

h = (3840² x 2) ÷ (998 x 250) = 118 m

WHAT IS PHOTOGRAMMETRY ?

            Simply stated, photogrammetry is the art and science of making measurements from imagery. Historically, this meant using photographs, but today, digital images are becoming the medium of choice for many photogrammetric applications. In fact, the distinction between remote sensing and photogrammetry has gradually become blurred as conventional photogrammetrist employ "non-conventional" imagery for mapping purposes. One of the main advantages of photogrammetry is that the photograph/image forms a permanent record of the situation at that instant in time. This is ideal when change detection is important in a project.

         Imagery is generally collected from an airplane. The advantage is that the camera can capture a very wide image from which the mapping can be performed. For example, most aerial photography uses a film size of 9” x 9” (23 cm x 23 cm). If the scale of the photograph was 1” = 500’ then each photograph would image approximately 4,500’ x 4,500’ on the ground. Thus, with one click of the shutter, the image captures approximately 465 acres of land1. Another advantage of photogrammetry there is no line of sight problems that surveyors may encounter on the ground since we are looking at the land from above. There is, though, a need to have an nobstructed view from the camera.

               Increasing the flying height, or distance from the camera to the object being mapped, has two effects. First, it can increase the area imaged on the photograph. In our example, if the scale was decreased to 1” = 1,000’ then about 1,860 acres would be imaged on the photograph (a four times increase in coverage). This will save time in subsequent measurements on the photograph. But, the second effect of increasing the flying height results in a decrease in the resolution of the image. In other words, features that are too small may not be imaged on the photograph. Thus, the photogrammetrist is left with the task of determining the optimal flying height to match the requirements of the project. Close-range photogrammetry (sometimes called non-topographic photogrammetry) is another area that has found widespread applications. Here, the photography is obtained from the ground, or near the ground level. It is used for a myriad of purposes such as medical photogrammetry, accident reconstruction, aircraft and ship construction, architectural studies and construction sites, just to mention a few. This form of mapping is ideal when the object to be

measured is too hot, cold, unsafe, radioactive, inaccessible and delicate or when objects are moving so as to make direct measurement hazardous.

            Satellite photogrammetry is a relatively new area of practice, especially among conventional photogrammetric companies. Historically, photogrammetry had been used to locate satellites in space in order to establish a more global network of control. With the advent of Global Positioning System (GPS) receivers, the use of photogrammetry with satellites has taken on a new role. Added to this is the emergence of very high-resolution imagery, on the  order of one-meter or less. Thus, the future will see more utilization of this high-resolution imagery to both supplement and supplant conventional aerial imagery. 1 acre = 43,560 square feet