Geometric Corrections in Remote Sensing Summary

Geometric Corrections in Remote Sensing

Geometric Correction Concept

  • Definition: Geometric correction involves modifying the position of pixels in an image to improve accuracy.
  • Importance: Enables accurate extraction of distance, area, and direction from images.
  • Transformation: Changes coordinate positions (c', l') based on original position (c, l) or map coordinates (x, y).

Types of Geometric Error

  • Internal Geometric Error: Caused by the remote sensing system itself.
  • Sources: Earth rotation, scanning system variations, relief displacement, tangential scale distortion.
    1. Skew: Introduced by Earth rotation effects.
    2. Ground Resolution Cell Size Variation: Affected by system altitude and scan angles.
    • Example: 705 km above ground level for Landsat 7 minimizes distortion.
    1. One-Dimensional Relief Displacement: Affects objects above local terrain, creating displacement in off-nadir views.
    2. Tangential Scale Distortion: Differences in scanning distance at nadir vs. the edge, altering object shape.

External Geometric Error

  • Causes: Random aircraft movements during data collection including altitude and attitude changes (roll, pitch, yaw).
  • Impacts: Variable imagery scale depending on altitude; gyro stabilization equipment can mitigate roll/pitch errors.

Ground Control Points (GCPs)

  • Definition: Known locations on Earth (e.g., intersections) used to calibrate image data.
  • Requirements: Two sets of coordinates for each GCP: image (i, j) and map (x, y).
  • Application: Paired coordinates allow derivation of transformation coefficients for geometric rectification.

Coordinate Transformation and Registration

  • Registration: Aligning spatial data images to an Earth-based coordinate system.
  • Ensures spatial consistency among multiple layers.
  • Misalignment Correction: Uses GCPs; requires accuracy analysis for effectiveness.

RMS Error and GCP Criteria

  • RMS Error: A metric for assessing the accuracy of geometric rectification.
  • Aim: Establish GCPs with high accuracy, widespread distribution, and sufficient quantity for reliable transformation.

Spatial Interpolation Using Coordinate Transformations

  • First-Order Affine Transformation: Deals with moderate distortions.
  • Parameters: Six transformations (translation, scale, skew, rotation).
  • Input-to-Output (Forward) Mapping: Processes pixel values from the input grid to a rectified output image; can sometimes lead to pixel value loss.
  • Output-to-Input (Inverse) Mapping: Preferred for rectification, ensuring every pixel location receives a value.

Spatial Interpolation Logic

  • Objective: Populate a standard map projection with values from a distorted input image.
  • Root Mean Squared Error provides logistical feedback on the coefficients used in the geometric adjustment.

Intensity Interpolation Methods

  • Nearest Neighbor Resampling: Assigns the closest brightness value from the input to the output pixel location.
  • Bilinear Interpolation: Averages brightness from four nearest pixels based on weighted distances to the desired position.
  • Cubic Convolution: Similar to bilinear but incorporates 16 surrounding pixels for increased accuracy.