In August, we started a discussion on orthorectification in the Geospatial Frequently Asked Question (G-FAQ), and this month we conclude the two-part series. In the first part of the series, the focus was on the basics of orthorectification and how orthorectified data can be differentiated from georeferenced data. In this edition of the G-FAQ, we turn our attention to accuracy testing of orthorectified data. We also investigate RPC files which are often required to orthorectify imagery products.

As a quick reminder, we focus on these core questions in this two-part G-FAQ series:

What is the difference between georeferenced and orthorectified data? How is orthorectification completed and its accuracy tested? What are RPC files and how are they used in orthorectification?

In the August 2014 G-FAQ edition, we learned that georeferenced data has no accuracy guarantee. In order to have this assurance, imagery must be orthorectified; and to orthorectify imagery, you need a minimum of an elevation model and a camera model or rational polynomial coefficients (RPCs). In order to have the highest accuracy possible, you also need ground control points, a topic we will turn our attention to in the next G-FAQ series. For now, we can define ground control points as known locations on the surface of the planet with highly accurate XY (e.g. latitude and longitude) and Z (e.g. meters above sea level) survey coordinates.

Accuracy Testing of Orthorectified Imagery

Now let’s continue the discussion started last month with a look at accuracy testing of orthorectified imagery. In general, there are four factors which control the final accuracy of orthoimage. First, the image itself is a major contributing factor; and specifically, the off-nadir angle of the data and the topography it covers. Off-nadir is the angle the satellite was tilting when the imagery was collected, and for reference, zero degrees off-nadir would be pointing straight down at the ground. Imagery collected with a higher off-nadir (generally over 25 degrees) and/or over areas with lots of relief (such as mountains, hills and valleys) will be less accurate when orthorectified. Second, there is method used to orthorectify the imagery, and as was discussed last month, using a camera model in this process can result in a slightly more accurate final product. Third, the quality of the ground control used in orthorectification can impact accuracy. While we will not discuss control until next month, simply stated, the more accurate the ground control are, the more accurate the final orthoimage will be. Finally, there is the location and distribution of the ground control. If all of the control are clustered in the same small area, it can be accurate there but then far less accurate as you move away from this cluster. In general, the accuracy of orthoimage declines as you move away from the locations of ground control points (GCPs).

In order to test the accuracy of the orthoimagery you created, ground control points are required. Without ground control points, there is no way to assure accuracy in the final product so admittedly this is a bit of circular logic; and it can be rather frustrating when you lack this control. As such, for the next part of this discussion, let’s assume that you used ground control to create an orthoimage.

There are two ways to validate accuracy by using GCPs: the hold-out and the leave-one-out cross validation methods. In the hold-out method, accuracy is validated by taking a portion of the control you have, applying it to the imagery during orthorectification and then leaving out a subset to test the final accuracy once the ortho is complete. While this method has the advantage of being easy to compute, the disadvantage is that it can be unreliable as it depends on a set of control not used in the ortho process; and if there is a low number of GCPs for the project, these test points can be a poor, unrepresentative sample. The leave-one-out cross validation method is more complex to implement but it can have more reliable results. In this method, you test the accuracy of your orthoimage by subsetting out test control and control to be used in the ortho process, and then repeating this process multiple times – each time with a different subset of test control and control used to ortho.

Testing the accuracy of an orthorectified image is pretty straightforward once you determine the method to implement. Using the control you held out, the first step in accuracy testing is locating each test point in the orthoimagery. Once you have found the GCPs in your imagery, you will measure the straight line distance to its actual location on the ground. Each GCP’s actual location on the ground is determined by the XY (e.g. latitude and longitude; or northing and easting) coordinates recorded during the field survey. Repeat this process for each of your test points and record the measured distances in a spreadsheet.

Once you have the distances measured from the test GCPs to their actual locations on the ground, it is time to calculate an accuracy for your orthoimage. There are three common ways to report this accuracy: root mean square error (RMSE), circular error 90% (CE90%) and the US National Map Accuracy Standards (NMAS). Here is a brief description of each of these accuracy calculations:

A table showing the relationship between NMAS, CE90% and RMSE accuracy statements. You can see that as the map scale gets larger (e.g. moving from 1:12,000 to 1:4,800), the NMAS requires more accurate imagery.

• RMSE – calculated as the square root of the sum of the straight-line differences of the X and Y coordinates of test control points and their ‘real’ position on the ground. Basically, this is the average distance your orthoimagery is off from its ‘real position’ on the ground.
• CE90% – a distance that defines the radius of a circle whereby 90% of test control points will fall within their ‘real’ ground positions.
• NMAS  – this final way of reporting accuracy is more of a standard then it is a way to calculate this value. Established in 1947 by the USGS, the NMAS assures orthorectified imagery used by the Federal government meets certain accuracy requirements as its scale changes. Take for example an orthoimage with a maximum zoom scale of 1:4,800, according to the NMAS, this data should have a 13.33-foot CE90%. So then, for any given map scale, there is an accuracy standard (often reported in CE90%) that this data must adhere too. For more information about NMAS, please refer to this previous edition of the G-FAQ.

Before we move on from this subtopic, a few words to the wise about accuracy testing. First, while it seems that accuracy is a well-defined topic, it is rather flexible so to speak. And I say this as depending on what control you decide to use for accuracy testing, the results can be radically different. If you select test control points that are all in flat areas, you will find higher accuracies; and the converse is the same for selecting test control on hills and/or mountains (i.e. the accuracy will be lower). Second, as a general rule of thumb, it is often possible to get imagery collected by the newer satellites, WorldView-1/2 and GeoEye-1, within 2 or 3 pixels of their ‘real’ ground positions, assuming good GCPs and an elevation model are used in the process; and for the remaining satellites, a final accuracy within 5 pixels is often achievable.

A Primer on Rational Polynomial Coefficients (RPCs)

In the final section of this two-part series, let’s take a look at RPC files and their importance in orthorectification. Broadly speaking, RPC files are a way to describe the position of satellite imagery on the ground in a standardized and effective manner. A RPC file contains two equations which relates image space (i.e. the line and column position of a pixel) to object space (i.e. its latitude and longitude, northing and easting, etc.). One equation computes line position to X and the other column position to Y, both equations build out XY positions from the upper-left corner of an image. The coefficients for each of these two equations is calculated by the imaging companies and is based on the satellite’s position and orientation when the data was collected as well as the proprietary rigorous camera model.

RPC files then are generic equations for all sensors that are easy for commercial remote sensing software developers to implement. In many cases, these software makers will substitute RPC files for use in orthorectification as opposed to gathering proprietary camera models from each of the imaging companies (which can be a time consuming process). While the goal is to incorporate all of the factors considered in the rigorous camera model into a RPC file, there is a small difference between the two. This can result in a slightly larger residual error in the final orthoimage for the version produced with RPC files. As a final note, each imaging company has a slightly different format for RPC files – for example, DigitalGlobe calls them RPB files while Airbus delivers them in XML format.

In the next G-FAQ series, we will turn our attention to ground control points which are the secret ingredients to making extremely accurate orthoimagery.

Do you have an idea for a future G-FAQ? If so, let me know by email at brock@apollomapping.com.

Find Out More About This Topic Here

• Center of Geotechnologies, Riccardo Slvini – QuickBird Stereophotogrammetry for Geological Mapping
• DIIAR, Maria Antonia Brovelli – Accuracy Assessment of High Resolution Satellite Imagery
• Michigan Tech University – Photogrammetric Control Surveying
• Penn State University – Orthorectification
• Rutgers University – Geometric Correction of Imagery
• University of Oregon – Geometric Rectification

Brock Adam McCarty
Map Wizard
(720) 470-7988
brock@apollomapping.com