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RPC Background

RPC Background

RPC Background

Sensor models are mathematical models that define the physical relationship between image coordinates and ground coordinates, and they are different for each sensor. Rational polynomial coefficients (RPCs) are one type of replacement sensor model, which replaces the rigorous sensor model with an approximation of the ground-to-image relationship. The accuracy of RPCs depends on the accuracy of the original sensor model and the quality of the imagery.

Most modern high-resolution sensors such as QuickBird include pre-computed RPCs with the imagery. If your file has RPC information, you can automatically derive RPC-based geolocation information for individual pixels in an image. This method is not as geographically accurate as performing a full orthorectification, but it consumes less memory and disk space.

RPCs are not the same as a map projection; rather, they relate pixel locations in an image to the corresponding latitude, longitude, and elevation, using a third-order rational polynomial of the following form:

(x,y) = f(latitude, longitude, elevation)

To determine the pixel location of a corresponding point on the ground, the ground point must have accurate values for the following:

  • Latitude (degrees)
  • Longitude (degrees)
  • Elevation (meters)

To find the horizontal geographic location of a ground point, you need accurate values for the following:

  • X and Y pixel coordinates
  • Ground point elevation (meters)

If you do not know the ground elevation, then the coordinate transform assumes an elevation of zero (on the surface of the WGS-84 ellipsoid) or it estimates a mean height from the RPC height offset. This positioning is not accurate except near sea level. With two images of the same area (taken from two different viewing angles), parallax effects will be visible, meaning that geographic coordinates of the same feature will not be the same in the two images.

To ensure more accurate ground coordinates, you should orthorectify all images by:

  • Using ground control points (GPCs) to refine the RPCs, and
  • Supplying an accurate digital elevation model (DEM)

The RPC Orthorectification workflow takes you through these steps.


Grodecki, J., and G. Dial. “Block adjustment of high-resolution satellite images described by rational polynomials,” Photogrammetric Engineering and Remote Sensing 69, no. 1 (2003): 59-68.

McGlone, J. C., editor. Manual of Photogrammetry, Fifth Edition, Bethesda, MD: American Society for Photogrammetry and Remote Sensing, 2004.

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