Distortion and Displacement in Air Photos: Lens Distortion, Tilt Displacement, Radial and Relief Displacement (Especially for GATE-Geospatial 2022)

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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 because maps use an orthographic projection (i.e.. using parallel lines of the site) and constant scale to represent features.

Distortions Due to Perspective and Projection

Aerial photographs, on the other hand, are created using a central or perspective projection. Therefore, the relative position and geometry of the objects depicted depend upon the location from which the photo was taken. Now because of this, we get certain forms of distortion and displacement in Air Photos.

  • Distortion: Shift in the location of an object that changes the perspective characteristics of the photo.
  • Displacement: Shift in the location of an object in a photo that does not change the perspective characteristics of the photo (The fiducial distance between an object՚s image and its true plan position which is caused by a change in elevation.)

Four Types of Distortions

There are basically four types of distortions and three types of displacement. Types of distortion include:

  • Film and Print Shrinkage
  • Atmospheric refraction of light rays
  • Image motion
  • Lens distortion

Three Types of Displacement

Types of displacement include:

  • The curvature of the Earth
  • Tilt
  • Topographic or relief (including object height)
  • The effects of film shrinkage, atmospheric refraction and the curvature of the Earth are usually negligible in most cases - the exception is precise mapping projects. Of this lens distortion is usually the smallest of these. So displacement is typically the largest problem/effect impacting our analyses.
  • Both distortion and displacement cause changes in the apparent location of objects ′ in photos. The distinction between the types of effects caused lies in the nature of the changes in the photos. These types of phenomena are most evident in terrain with high local relief or significant vertical features.
  • There are several types of distortion in airphotos. Scale changes are primarily due to changes in terrain elevation but there can also be scale changes between successive images along a flight line due to changes in flying height between prints. This can occur due to turbulence that prevents the pilot from maintaining a constant altitude. Further distortion can occur due to the camera not being level to the ground at the time of exposure. This can occur if the nose of the aircraft is slightly up or down (pitch) or if a wing is tilted up or down (roll) .
  • Both conditions can be caused by turbulence or by manoeuvring to stay on course. The result is the introduction of distortion due to obliqueness in the image. Obliqueness is measured by the angle between a vertical plumb line through the centre of the lens and the optical axis of the camera lens.
  • The principal point (P) is always at the intersection of the optical axis of the camera lens and the image plane. The nadir (N) is the intersection of the vertical plumb line through the centre of the lens and the image plane. On a true vertical airphoto, the principal point and the nadir are the same points but on an oblique airphoto, they are at different positions on the image plane.

As stated above we will consider here three main types of problems/effects caused by specific types of distortion and displacement. These are the problems/effects associated with:

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-known 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 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. If the amount and direction of tilt are known then the photo may be rectified. Some landscape feature (a) is being displayed on a photograph (point a) that is displaced radially inward from the appropriate place on the photograph (c) by the amount d.

Displayed on a Photograph

Radial and Relief Displacement

Because photographs are perspective views, all airphotos are subject to radial or relief displacement which causes objects in the image to be displaced outward from the nadir of the image. Displacement increases with the height of the object and distance from the nadir. Below figure illustrates the radial displacement of a series of hydro poles in a true vertical airphoto. The pole that lies directly below the camera lens is seen in plan view. Poles that lie close to the nadir (principal point in a vertical airphoto) are only slightly displaced while poles further from the nadir are displaced greater distances on the image. The bottom of the pole is closer to the nadir than the top of the pole. The same effect can be seen in images of urban areas in which the tops of buildings are displaced outward relative to the base of the buildings.

Airphotos Relief Displacement
  • Radial displacement is a source of distortion and can result in all objects that are close to the nadir hiding objects that are further away from the nadir. Radial displacement can also make 3-d viewing difficult if objects appear too dissimilar in successive images. This is especially a problem if the scene contains tall objects. Nevertheless, radial displacement can be useful. Radial displacement of objects results in the sides as well as the tops of objects being visible in the airphoto.
  • This can facilitate interpretation since objects such as office buildings and apartment buildings that may be difficult to distinguish from a plan view may be distinguished based on the appearance of the sides of the buildings, e. g. whether or not there are balconies which are more likely to be found on an apartment building. Since radial displacement is always outward from the nadir of the image, we can locate the nadir by finding the intersection of lines showing the direction of object displacement, e. g. lines representing the corners of buildings that have vertical walls.
  • Distortion due to scale changes, obliqueness and radial displacement can make it difficult to transfer detail from airphotos to maps. This is most likely to be a problem in mountainous terrain where there is a significant local relief. The effect is to dramatically change the shape of objects as they appear in successive images along a flight line.

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