Image Correction Using Mapping Polynomial: Systematic Distortions & Cross Track Distortion (Especially for GATE-Geospatial 2022)

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Polynomial equations are used to convert the source coordinates to rectified coordinate, using 1st and 2nd order transformation. The coefficients of the polynomial are calculated by the least square regression method that helps in relating any point in the map to its corresponding point in the image.

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Initially, few GCPs (Ground Control Points) coefficients are required to calculate the transformation matrix and the inverse transformation that could convert the reference coordinates of the GCPs back to the source coordinate system. This enables determination of RMS (Root Mean Square) error for chosen transformation. The best order of transformation can be obtained using trial and error process while ignoring the highest RMS error from the least squares computation.

Systematic Distortions

Geometric systematic distortions are those effects that are constant and can be predicted in advance. These are of two types:

  • Scan Skew: It is caused by forwarding motion of the spacecraft during the time of each mirror sweep. In this case, the ground swath scanned is not normal to the ground track.
Scan Skew
  • Known Mirror Velocity Variation: The known mirror velocity variation is used to correct the minor distortion due to the velocity of the scan mirror not being constant from start to finish of scan line.
Mirror Velocity Variations

Cross Track Distortion

These generally occur in all the unrestored images acquired by the cross-track scanners. They result from sampling pixels along a scan line at constant time intervals. The width of a pixel is proportional to the tangent of the scan angle and therefore is wider at either margin of the scan line that compresses the pixel. This distortion is restored using trigonometric functions.

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