Image Rectification

Basically, three different types of distortion may be present in an SFAP image: lens distortion, image tilt, and relief displacement (see Chapter 3.2). Two methods of correcting these errors, polynomial rectification by ground control points (GCPs) and orthorectification, have already been introduced in Chapter 3.4.1. Also, the precision and survey methods for GCPs have been discussed in Chapters 3 and 9. The following sections look at some exemplary questions and cases related to geocorrecting small-format aerial photographs.

A highly exact geometric correction requires time, effort, a digital elevation model, and excellent ground control. Many SFAP applications may not really need such efforts, and depending on the image and relief characteristics, simpler solutions might be quite sufficient. So how does one judge how correct is good enough? This is always a question of relating the residual error to the desired spatial information detail. The following concerns may play a role in this decision.

• Maximum location accuracy to be expected with a given GSD.

• Desired accuracy for locating or delineating individual, well-defined features.

• Required accuracy for measuring changes in monitoring projects.

• Achievable precision of object delineation.

Consider a project where the invasion by a non-native plant species in an estuarine wetland reserve is to be assessed by quantifying the percentage of affected vegetation cover from aerial photographs. Here, precise orthorectification with <2 cm error would certainly be a wasted effort for several reasons. The images would be affected little by relief displacement because of the flat terrain; a measurement accuracy in the centimeter range is not required for the purpose; and indeed the delineation precision of something as fuzzy as vegetation patches would be much inferior to 2 cm. Another application might be monitoring the development of sharp-edged ephemeral rills on a hillslope during one season and relating their retreat rates to precipitation and runoff measurements. In this case, the measured changes may be grossly inaccurate if the image time series were rectified using a few GCPs only, with check-point RMS errors in the decimeter range.

The differences in positional accuracy achievable with various rectification techniques for a situation with variable terrain are illustrated with Figure 11-1. This vertical photograph of a long gully cutting into a shallow depression between two agricultural fields was taken from 82 m height above field level with an original image scale on the sensor of 1:4100. The altitudinal differences present in the scene amount to ~ 4.5 m (top of field-bordering ridge to bottom of gully). Forty-one GCPs were measured with a total station; 22 of those were used for georectifying the image with different methods in ERDAS IMAGINE and Leica Programmetry Suite, while 19 were reserved as check points for error assessment.

Results show that the abrupt relief changes (see cross-profile in Fig. 11-2) cause relief displacement that cannot be corrected sufficiently with polynomial transformations. Although a large number of GCPs was used, the third-order transformation shown in Figure 11-1A leaves considerable residuals at both control and check points, with a maximum displacement of 43 cm. Rubbersheeting—a piecewise nonlinear polynomial transformation—results in no errors at the control points, but even larger errors at the check points (Fig. 11-1B). This confirms that the GCPs, in spite of their good distribution and abundance, are not able to represent the variations in terrain height adequately. The image is now geometrically correct at the control points, but still distorted in the areas between, with a total RMS error of nearly 30 cm at the check points.

By far the best results are achieved with orthorectification (Fig. 11-1C), where the image is differentially corrected using a digital elevation model. This was realized by setting up a photogrammetric block file with both interior and exterior orientation information (see Chapter 3) and triangulating several overlapping images. A digital elevation model (DEM) was extracted from the image shown in Figure 11-1 and its stereopartner, and this DEM provided the necessary height information for computing and correcting relief distortion. The residual errors, which amount

GCP position in reference system x used as control point in rectification x used as check point in rectification

RMS errors in reference units

Radius proportional to linear RMS, exaggeration 5 x

• error at control point

• error at check point




3rd order


















Total RMS













Total RMS




FIGURE 11-1 Georectified images of gully Bardenas 1, Bardenas Reales, Province of Navarra, Spain. Kite aerial photograph by JBR, IM, and S. Ple-gniere, February 2009; image processing by IM. (A) Rectified by third-order polynomial transformation. (B) Rectified by non-linear rubbersheeting. (C) Orthorectified using a DEM derived from the same image and overlapping stereopair. Location and RMS errors of 22 control points and 19 check points shown by diagram radius with fivefold exaggeration. GSD of all rectified images is 2.5 cm.

FIGURE 11-2 Cross-profile through the middle part of the gully in Figure 11-1, derived from the DEM used for orthorectification.

to only about 3-4 cm of total RMS, are due to the small remaining errors in triangulation and extraction of the DEM, which was not corrected for vegetation errors.

There is no general solution as to how many GCPs are needed for a good georectification. For flat areas with no relief, a theoretical minimum of three is enough, but not recommended because of the lack of error control. A second-order transformation, which is able to take simple smooth relief undulations into account, requires a minimum of six GCPs. As a rule of thumb, twice the minimum number required is a good measure for reducing residual errors.

Because establishing ground control every time a survey is conducted is costly and time-consuming (see Chapter 9.4), it can be a useful method to supplement or even substitute control points with image-to-image rectification in monitoring projects. Non-referenced images may be warped onto a first, thoroughly rectified image by image-to-image registration, picking homologous points in both the reference and input images. This can be done manually or with software for automatic point matching (e.g. IMAGINE AutoSync).

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