Rectification

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Raw, remotely sensed image data gathered by a satellite or aircraft are representations of the irregular surface of the Earth. Even images of seemingly flat areas are distorted by both the curvature of the Earth and the sensor being used. This chapter covers the processes of geometrically correcting an image so that it can be represented on a planar surface, conform to other images, and have the integrity of a map.

A map projection system is any system designed to represent the surface of a sphere or spheroid (such as the Earth) on a plane. There are a number of different map projection methods. Since flattening a sphere to a plane causes distortions to the surface, each map projection system compromises accuracy between certain properties, such as conservation of distance, angle, or area. For example, in equal area map projections, a circle of a specified diameter drawn at any location on the map represents the same total area. This is useful for comparing land use area, density, and many other applications. However, to maintain equal area, the shapes, angles, and scale in parts of the map may be distorted (Jensen, 1996).

There are a number of map coordinate systems for determining location on an image. These coordinate systems conform to a grid, and are expressed as X,Y (column, row) pairs of numbers. Each map projection system is associated with a map coordinate system.

Rectification is the process of transforming the data from one grid system into another grid system using a geometric transformation. While polynomial transformation and triangle-based methods are described in this chapter, discussion about various rectification techniques can be found in Yang (Yang, 1997). Since the pixels of the new grid may not align with the pixels of the original grid, the pixels must be resampled. Resampling is the process of extrapolating data values for the pixels on the new grid from the values of the source pixels.

Registration

In many cases, images of one area that are collected from different sources must be used together. To be able to compare separate images pixel by pixel, the pixel grids of each image must conform to the other images in the data base. The tools for rectifying image data are used to transform disparate images to the same coordinate system.

Registration is the process of making an image conform to another image. A map coordinate system is not necessarily involved. For example, if image A is not rectified and it is being used with image B, then image B must be registered to image A so that they conform to each other. In this example, image A is not rectified to a particular map projection, so there is no need to rectify image B to a map projection.

Georeferencing

Georeferencing refers to the process of assigning map coordinates to image data. The image data may already be projected onto the desired plane, but not yet referenced to the proper coordinate system. Rectification, by definition, involves georeferencing, since all map projection systems are associated with map coordinates. Image-to-image registration involves georeferencing only if the reference image is already georeferenced. Georeferencing, by itself, involves changing only the map coordinate information in the image file. The grid of the image does not change.

Geocoded data are images that have been rectified to a particular map projection and pixel size, and usually have had radiometric corrections applied. It is possible to purchase image data that is already geocoded. Geocoded data should be rectified only if they must conform to a different projection system or be registered to other rectified data.

Latitude and Longitude

Latitude and Longitude is a spherical coordinate system that is not associated with a map projection. Latitude and Longitude expresses locations in the terms of a spheroid, not a plane. Therefore, an image is not usually rectified to Latitude and Longitude, although it is possible to convert images to Latitude and Longitude, and some tips for doing so are included in this chapter.

SHARED Tip You can view map projection information for a particular file using Image Metadata dialog, as well as modify map information that is incorrect. However, you cannot rectify data using Image Metadata. You must use Rectification tools described in this chapter.

Properties of map projections and of particular map projection systems are discussed in Cartography and Map Projections.

Orthorectification

Orthorectification is a form of rectification that corrects for terrain displacement and can be used if there is a DEM of the study area. It is based on collinearity equations, which can be derived by using 3D GCPs. In relatively flat areas, orthorectification is not necessary, but in mountainous areas (or on aerial photographs of buildings), where a high degree of accuracy is required, orthorectification is recommended.

See Photogrammetric Concepts for more information on orthocorrection.