Geometric Correction

When satellite or aerial images are captured, they often contain distortions (errors in shape, scale, or position) caused by many factors — like Earth's curvature, satellite motion, terrain height (relief), or the Earth's rotation.
These distortions make the image not properly aligned with real-world coordinates (latitude and longitude).

👉 Geometric correction is the process of removing these distortions so that every pixel in the image correctly represents its location on the Earth's surface.

After geometric correction, the image becomes geographically referenced and can be used with maps and GIS data.

Types 

1. Systematic Correction

Systematic errors are predictable and can be modeled mathematically.
They occur due to the geometry and movement of the satellite sensor or the Earth.

Common systematic distortions:

• Scan skew – due to the motion of the sensor as it scans the Earth.

• Mirror velocity variation – scanning mirror moves at a variable speed.

• Cross-track distortion – image stretching across the scan direction.

• Earth rotation skew – Earth rotates while the sensor scans, shifting positions.

• Platform altitude variation – changes in satellite height.

• Platform velocity variation – changes in satellite speed.

Correction method:
Systematic errors are corrected using mathematical models or formulas derived from satellite geometry and sensor parameters.
This process is often automated and is part of orthorectification, which adjusts images for terrain relief using a Digital Elevation Model (DEM).

2. Non-Systematic Correction

Non-systematic (random) errors are unpredictable — caused by sensor drift, attitude changes, or human error.
They cannot be fixed mathematically and require ground reference points.

It involves aligning image coordinates with real-world coordinates or another image.

Two main approaches:

(a) Image-to-Ground Correction (Georeferencing)

• The image is aligned to real-world ground coordinates (latitude/longitude).

• Requires Ground Control Points (GCPs)—known locations visible on both the image and a map.

(b) Image-to-Image Correction (Registration)

• Used when two or more images of the same area (different times/sensors) must match perfectly.

• One image acts as the reference, and the other is adjusted to match it.

Coordinate Transformation

This step mathematically links image coordinates (rows and columns) to map coordinates (X, Y).

A polynomial transformation is used, where the order of the polynomial defines the complexity of the correction.

👉 Examples:

• 1st order (affine): needs 3 GCPs → corrects translation, rotation, scaling, and skew.

• 2nd order: needs 6 GCPs → can correct moderate curvilinear distortions.

• 3rd order: needs 10 GCPs → handles more complex distortions.

Accuracy Assessment:

Accuracy of geometric correction can be measured by Root Mean Square Error (RMSE):

[
RMSE = \sqrt{\frac{(D_1^2 + D_2^2 + D_3^2 + ... + D_n^2)}{n}}
]

Where D = distance between the corrected pixel and its true location.
A smaller RMSE means higher geometric accuracy.

Resampling

When an image is geometrically corrected or transformed, the pixel grid changes.
Resampling determines what new pixel values to assign in the corrected image.

In simple words:
It's the process of fitting old pixels into a new coordinate grid after correction.

Because the input and output grids rarely match exactly, resampling decides which value each new pixel should take.

Common Resampling Methods:

1. Nearest Neighbour (NN):

   • Takes the value of the closest original pixel.

   • Simple and fast.

   • Best for categorical data (like land use classes).

   • May look blocky.

2. Bilinear Interpolation:

   • Uses the average of 4 nearest pixels.

   • Produces smoother images.

   • Suitable for continuous data (like temperature, elevation).

3. Cubic Convolution:

   • Uses 16 nearest pixels with weighted averages.

   • Produces very smooth and visually appealing images.

   • Best for display and analysis of continuous data.

Miscellaneous Pre-Processing Steps

1. Subsetting

Selecting or cutting out a smaller portion of a large image (based on AOI – Area of Interest).

• Helps reduce file size.

• Makes processing faster.
  Example: Cropping a satellite image to only your study district.

2. Mosaicking

Combining two or more overlapping satellite images to form one continuous image covering a larger area.

• Useful when one scene doesn't cover the full study region.

• Must ensure brightness matching between scenes.

Step	Purpose	Example / Key Point
Geometric Correction	Align image with real-world coordinates	Corrects distortions
Systematic Correction	Fix predictable errors	Uses sensor models, orthorectification
Non-Systematic Correction	Fix random errors	Uses GCPs for georeferencing
Coordinate Transformation	Converts pixel to map coordinates	Uses polynomial equations
Resampling	Assigns pixel values in new grid	NN, Bilinear, Cubic methods
Subsetting	Extracts part of an image	Focus on study area
Mosaicking	Combines multiple scenes	Creates larger continuous image