Rectification

This article is about correcting perspective distortions in image data. For further meanings see rectification .

Under a rectification (lat .: correction ) or equalization is meant the elimination of geometrical distortions in image data caused by z. B. uneven terrain, central perspective recording or incorrect orientation of the recording system. The rectification is primarily used to convert a single image as if it had been taken perpendicular to the object plane (e.g. a house wall). The perspective distortion is thereby compensated again and the image is quasi "rectified", whereby a uniform reproduction scale is obtained for the entire image. This makes it possible to calculate the real size of routes measured in the image, just like with a map. It is a special form of georeferencing images. Photos edited in this way are called digital orthophotos (DOP). This method is often used in photogrammetry and cartography for evaluating satellite and aerial images .

execution

In order to be able to geocode an image, a transformation equation has to be found with which each pixel of the input image can be transferred into the matrix of the output image. There are basically two approaches to finding this equation:

Interpolation method

In the case of interpolation methods, it is not necessary to model the imaging geometry. The transformation is based only on an interpolation between selected control points (so-called ground control points). All distinctive, punctual, position-invariable places, such as road crossings, are suitable as control points. Their coordinates are usually taken from a larger-scale topographic map . Based on the relationship between at least three control points, the position of all other image points can be interpolated, but it is advisable to include as many control points as possible.

Such an interpolation method has the disadvantage that differences in elevation of the terrain are hardly taken into account. It is only possible to include the relief indirectly by choosing the control points so that it is also described. Are the control points z. B. placed along the foot of a slope, on the edge and in the bed of a ditch and on protruding mountain tops, it is possible to describe the shape of the terrain to a limited extent. However, the exact coordinates of such terrain points must be known.

Parametric method

The more complex methods are the parametric methods, in which the recording geometry is modeled and thus a far greater accuracy is achieved. Two prerequisites have to be met: (i) the orientation (position and movement) of the sensor is known and (ii) a digital terrain model of the recorded area is available. Control points are also used to establish the relationship to the reference system.

transformation

The data of the input image can now be rearranged into the matrix of the output image by means of the specific transformation equation. Such a transformation, also called resampling , is usually done indirectly. It is calculated back from the output image to the input image, there the gray value is “fetched” and this is written into the output image.

The gray values ​​can be assigned according to various rules:

1. Nearest Neighbor : the gray value of the pixel is assigned which is closest to the calculated coordinates
2. Bilinear interpolation : the gray value is calculated by linear interpolation between the gray values ​​of the four closest pixels
3. Cubic convolution : the gray value is calculated by a higher order interpolation between the gray values ​​of the 16 closest pixels.

Which rule you choose depends on what you want and what computing effort you want to accept. The cubic convolution is the most computationally expensive, lossless transformation is practically not possible. The advantage of the nearest neighbor method is that radiometric information is retained , as there is no interpolation. This can be beneficial if you want to carry out a classification after georeferencing .

literature

• Karl Kraus : Photogrammetry (Volume 1, Fundamentals and Standard Methods) . With contributions by P. Waldhäusl. 6th edition. Dümmler, Bonn 1997, ISBN 3-42778-646-3 .
• Karl Kraus : Photogrammetry (Volume 2, Refined Methods and Applications). With contributions by Josef Jansa and Helmut Kager. 3rd, completely new and advanced Edition. Dümmler, Bonn 1996, ISBN 3-427-78653-6 .
• Thomas Luhmann: Close-range photogrammetry basics, methods and applications. 3. Edition. Wichmann, Berlin / Offenbach 2010, ISBN 978-3-87907-479-2 .