# Geometric Errors

Internal and external geometric errors is common in remotely sensed imagery. It is critical to identify the source of internal and external error, as well as whether it is predictable or random.

A. Internal geometric errors: Are caused by the sensor system and/or the effects of Earth’s rotation and curvature. These errors are predictable or calculable, and they are frequently referred to as systematic, and they can be identified and corrected using pre-launch or platform ephemeris.

The following are some of the causes of geometric distortions that cause internal geometric errors in remote sensing images:
• skew caused by the rotation of the Earth
• Scanner-induced variation in ground resolution cell size and dimensional relief displacement, as well as
• Scanner-induced tangential scale distortion

B. External geometric errors: are typically introduced by natural phenomena that vary in space and time. The most significant external variables that can cause geometric error in remote sensor data are random movements of the spacecraft at the exact time of data collection, which typically involve:
• Altitude changes

Systematic/ predictable errors are predictable and can be corrected with data from the platform’s orbit and knowledge of Systematic errors are predictable in nature and can be corrected using data from the platform’s orbit and knowledge of internal sensor distortion. Scan skew, mirror-scan velocity, panoramic distortions, platform velocity, and earth rotation are all examples of systematic distortions.

Unsystematic errors are corrected by geometrically registering remote sensing imagery to a known ground coordinate system.

Geometric Correction

Before proceeding, it is important to understand the definitions of the terms used to describe geometric correction of remote sensing images.
Geometric correction is the process of correcting skew, rotation, and perspective errors in raw remotely sensed data.

Rectification : the process of aligning an image with respect to a map (map projection system). In many cases, the image must also be oriented so that the top of the image corresponds to the north direction. Georeferencing is another term for it.

The two most common geometric correction procedures are as follows:

A. image-to-map rectification
B. image-to-image registration

A. image-to-map rectification: the process of making an image’s geometry planimetric.

Image-to-map geometric rectification should be used whenever precise area, direction, and distance measurements are required.

However, it may not remove all distortions caused by highly undulating terrain heights, resulting in what is known as relief displacement in images.

Typically, this process entails matching some image pixel coordinates (both row and column) with their map coordinate counterparts.

B. Image-to-image registration: is the process of aligning one image to be coincident with respect to another image, allowing the user to select a pixel in one image and its positionally exact counterpart from the other image.

Image rectification and image registration use the same general image processing principles. If a previously corrected image to a map reference system is used as the base image, the second image retains all geometric errors present in the base image.

This approach, however, is more appropriate when images from multiple dates are used to observe changes on the ground.

This is due to the fact that if two images are separately rectified to the map reference system, each may have the same overall error but of a different nature, resulting in twice the individual errors when the two rectified images are used together.

Steps in Geometric error correction

1. Collection of Ground Control Points

2. solve polynomial equation using ground control point

3. Transformation of the Image to the Geometry of the Reference
Map/Image

4. Assessment of Error

5. Resampling