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### Non-Standard Projections Background

Non-Standard Projections Background

## Non-Standard Projections Background

In addition to supporting standard map projections with known tie points and fixed pixel sizes, ENVI also supports non-standard projections such as affine map transformations, RPCs, and RSMs. These are not true map projections, but they give a reliable estimate of geographic locations for each pixel.

### Affine Map Transformations

Projections define the physical relationship between image coordinates (i,j) and ground/map coordinates (x,y). The following figure illustrates the transformation from an image to a standard map projection where the pixel size is fixed:

ENVI performs transformations from images to standard map projections using information that you enter in the Reproject Raster tool.

In some cases, however, a standard map projection may not be available. The simplest type of non-standard projection that ENVI supports involves an affine map transformation. ENVI applies a mathematical transformation to warp the image and to calculate geographic coordinates for each pixel. The pixel size varies in the rectified image. This type of projection contains a high degree of variability and is not geographically accurate; the (x,y) locations in the rectified image are only best guesses.

When you only know the geographic coordinates and map projection of the four corner points of an image, you can enter coordinates in the Geographic Corners field of the ENVI header file. These points are used to calculate an affine map transformation for the image.

Images that are rectified using an affine map transformation are designated by the word “pseudo” under the File Information section of the Data Manager.

### Sensor Models

Sensor models are another type of map information used to define the physical relationship between image coordinates and ground coordinates. A sensor model is a mathematical model that replaces the rigorous (physical) sensor model associated with a specific image by representing the model’s ground-to-image relationship. It is used to map a 3D ground point to a 2D image point. Various commercial spaceborne image providers utilize sensor models, particularly RPCs, which are the most common type in current use (McGlone, 1984).

#### RPCs

Rational polynomial coefficients (RPCs) model the ground-to-image relationship as a third-order, rational, ground-to-image polynomial. See McGlone (1984) for the theory behind the RPC model.

You can compute RPCs prior to single-image orthorectification by building interior and exterior orientation models. ENVI uses an iterative, converging solution to compute RPCs and adds the RPC information to the input file header so that you can use the file with DEM Extraction.

Some sensors such as Quickbird, IKONOS, OrbView-3, and Cartosat-1 provide pre-computed RPCs along with the respective imagery. If your file has associated 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 is less computationally and disk-space intensive than orthorectification.

Tip: If your image file has pre-computed RPC information, ENVI uses the mean elevation value used in the RPC transformation for the entire image. However, you can significantly increase the geolocation accuracy of the image if you associate the image with a DEM. Once initialized, this technique will result in accuracy equivalent to performing a full orthorectification.

For NITF files, RPC information is contained in the RPC00A and RPC00B Tagged Record Extensions (TREs). If either of these TREs exists in a NITF file, ENVI uses the RPC model to emulate a projection by default.

#### RSM

RSM is a type of community sensor model (CSM) that corrects the deficiencies of RPC-based sensor models. An RSM contains a variety of enhancements over the RPC model, including:

• Increased accuracy over images with large number of rows or columns (such as image strips) by breaking the image into tiles with separate models.
• The ability to store varying degrees of complexity in the polynomial representation used.
• The ability to store error estimation information so that the precision of individual solutions can be computed.

ENVI uses the Mensuration Services Program (MSP) and its elevation sources to calculate image-to-ground and ground-to-image coordinates. A separate classified DoD plug-in is required to use CSMs and RSMs in ENVI.

References

Dowman, I., and J. T. Dolloff. (2000). An evaluation of rational functions for photogrammetric restitution. International Archives of Photogrammetry and Remote Sensing 33(B3): pp. 254-266.

McGlone, J. C., editor. (2004). Manual of Photogrammetry, Fifth Edition, American Society for Photogrammetry and Remote Sensing.

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