StereoSAR DEM Theory

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To understand the way StereoSAR DEM works to create DEMs, it is first helpful to look at the process from beginning to end. The following figure shows a stylized process for basic operation of the StereoSAR DEM module.

StereoSAR DEM Process Flow

radar_stereosar_dem_process_flow

Input

There are many elements to consider in the Input step. These include beam mode selection, importing files, orbit correction, and ephemeris data.

Beam Mode Selection

Final accuracy and precision of the DEM produced by StereoSAR DEM module is predicated on two separate calculation sequences. These are the automatic image correlation and the sensor position/triangulation calculations. These two calculation sequences are joined in the final step: Height.

The two initial calculation sequences have disparate beam mode demands. Automatic correlation works best with images acquired with as little angular divergence as possible. This is because different imaging angles produce different-looking images, and the automatic correlator is looking for image similarity. The requirement of image similarity is the same reason images acquired at different times can be hard to correlate. For example, images taken of agricultural areas during different seasons can be extremely different and, therefore, difficult or impossible for the automatic correlator to process successfully.

Conversely, the triangulation calculation is most accurate when there is a large intersection angle between the two images (see the figure below). This results in images that are truly different due to geometric distortion. The ERDAS IMAGINE automatic image correlator has proven sufficiently robust to match images with significant distortion if the proper correlator parameters are used.

SAR Image Intersection

radar_sar_image_intersection_diagram

StereoSAR DEM has built-in checks that assure the sensor associated with the Reference image is closer to the imaged area than the sensor associated with the Match image.

A third factor, cost effectiveness, must also often be evaluated. First, select either Fine or Standard Beam modes. Fine Beam images with a pixel size of six meters would seem, at first glance, to offer a much better DEM than Standard Beam with 12.5-meter pixels. However, a Fine Beam image covers only one-fourth the area of a Standard Beam image and produces a DEM only minimally better.

Various Standard Beam combinations, such as an S3/S6 or an S3/S7, cover a larger area per scene, but only for the overlap area which might be only three-quarters of the scene area. Testing at both Hexagon Geospatial and RADARSAT has indicated that a stereo pair consisting of a Wide Beam mode 2 image and a Standard Beam mode 7 image produces the most cost-effective DEM at a resolution consistent with the resolution of the instrument and the technique.

Import

The imagery required for StereoSAR module can be imported using the ERDAS IMAGINE radar-specific importers for either RADARSAT or ESA (ERS-1, ERS-2). These importers automatically extract data from the image header files and store it in an Hfa file attached to the image. In addition, they abstract key parameters necessary for sensor modeling and attach these to the image as a generic SAR Node Hfa file. Other radar imagery (for example, SIR-C) can be imported using Generic Binary Importer. The SAR Metadata Editor can then be used to attach the generic SAR Node Hfa file.

Orbit Correction

Extensive testing of both OrthoRadar and StereoSAR modules has indicated that the ephemeris data from the RADARSAT and the ESA radar satellites is very accurate (see appended accuracy reports). However, the accuracy does vary with each image, and there is no a priori way to determine the accuracy of a particular data set.

Coherence Change Detection, InSAR, StereoSAR, and OrthoRadar allow for correction of the sensor model using GCPs. Since the supplied orbit ephemeris is very accurate, orbit correction should only be attempted if you have very good GCPs. In practice, it has been found that GCPs from 1:24 000 scale maps or a handheld GPS are the minimum acceptable accuracy. In some instances, a single accurate GCP has been found to result in a significant increase in accuracy.

As with image warping, a uniform distribution of GCPs results in a better overall result and a lower RMS error. Again, accurate GCPs are an essential requirement. If your GCPs are questionable, you are probably better off not using them. Similarly, the GCP must be recognizable in the radar imagery to within plus or minus one to two pixels. Road intersections, reservoir dams, airports, or similar man-made features are usually best. Lacking one very accurate and locatable GCP, it would be best to utilize several good GCPs dispersed throughout the image as would be done for a rectification.

Ellipsoid vs. Geoid Heights

The Radar modules are based on World Geodetic System WGS 84 Earth ellipsoid. The sensor model uses this ellipsoid for the sensor geometry. For maximum accuracy, all GCPs used to refine the sensor model for all Radar modules should be converted to this ellipsoid in all three dimensions: latitude, longitude, and elevation.

Note that, while ERDAS IMAGINE reprojection converts latitude and longitude to UTM WGS 84 for many input projections, it does not modify the elevation values. To do this, it is necessary to determine the elevation offset between WGS 84 and the datum of the input GCPs. For some input datums this can be accomplished using the website: www.ngs.noaa.gov/GEOID. This offset must then be added to, or subtracted from, the input GCP. Many handheld GPS units can be set to output in WGS 84 coordinates.

One elegant feature of StereoSAR DEM module is that orbit refinement using GCPs can be applied at any time in the process flow without losing the processing work to that stage. The stereo pair can even be processed all the way through to a final DEM and then you can go back and refine the orbit. This refined orbit is transferred through all the intermediate files (Subset, Despeckle, and so forth.). Only the final step Height would need to be rerun using the new refined orbit model.

The ephemeris normally received with RADARSAT, or ERS-1 and ERS-2 imagery is based on an extrapolation of the sensor orbit from previous positions. If the satellite received an orbit correction command, this effect might not be reflected in the previous position extrapolation. The receiving stations for both satellites also do ephemeris calculations that include post image acquisition sensor positions. These are generally more accurate. They are not, unfortunately, easy to acquire and attach to the imagery.

Refined Ephemeris

For information, see InSAR Theory.

Subset

Using Subset option is straightforward. It is not necessary that the two subsets define exactly the same area: an approximation is acceptable. This option is normally used in two circumstances.

  • Defining a small subset for testing correlation parameters prior to running a full scene.
  • Constraining the two input images to cover only the overlap area.

Constraining the input images is useful for saving data space, but is not necessary for functioning of StereoSAR DEM — it is purely optional.

Despeckle

Using functions to despeckle the images prior to automatic correlation are optional. The rationale for despeckling at this time is twofold. One, image speckle noise is not correlated between the two images: it is randomly distributed in both. Thus, it only serves to confuse the automatic correlation calculation. Presence of speckle noise could contribute to false positives during the correlation process.

Secondly, as discussed under Beam Mode Selection, the two images the software is trying to match are different due to viewing geometry differences. The slight low-pass character of the despeckle algorithm may actually move both images toward a more uniform appearance, which aids automatic correlation.

Functionally, the despeckling algorithms presented here are identical to those available in Radar module. In practice, a 3 × 3 or 5 × 5 kernel has been found to work acceptably. Note that all ERDAS IMAGINE speckle reduction algorithms allow the kernel to be tuned to the image being processed via the Coefficient of Variation. Calculate this parameter in Speckle Suppression dialog.

Degrade

Degrade option offered at this step in the processing is commonly used for two purposes.

If the input imagery is Single Look Complex (SLC), the pixels are not square (this is shown as the Range and Azimuth pixel spacing sizes). It may be desirable at this time to adjust the Y scale factor to produce pixels that are more square. This is purely an option; the software accurately processes undegraded SLC imagery.

Secondly, if data space or processing time is limited, it may be useful to reduce the overall size of the image file while still processing the full images. Under those circumstances, a reduction of two or three in both X and Y might be appropriate. Note that the processing flow recommended for maximum accuracy processes the full resolution scenes and correlates for every pixel. Degrade is used subsequent to Match to lower DEM variance (LE90) and increase pixel size to approximately the desired output posting.

Rescale

This operation converts the input imagery bit format, commonly unsigned 16-bit, to unsigned 8-bit using a two standard deviations stretch. This is done to reduce the overall data file sizes. Testing has not shown any advantage to retaining the original 16-bit format, and use of this option is routinely recommended.

Coregister

Coregister is the first of the Process Steps (other than Input) that must be done. This operation serves two important functions, and proper user input at this processing level affects the speed of subsequent processing, and may affect the accuracy of the final output DEM.

The coregistration operation uses an affine transformation to rotate the Match image so that it more closely aligns with the Reference image. The purpose is to adjust the images so that the elevation-induced pixel offset (parallax) is mostly in the range (x-axis) direction (that is, the images are nearly epipolar). Doing this greatly reduces the required size of the search window in the Match step.

One output of this step is the minimum and maximum parallax offsets, in pixels, in both the x- and y-axis directions. These values must be recorded by the operator and are used in the Match step to tune StereoSAR DEM correlator parameter file (.ssc). These values are critical to this tuning operation and, therefore, must be correctly extracted from the Coregister step.

Two basic guidelines define the selection process for the tie points used for the coregistration. First, as with any image-to-image coregistration, a better result is obtained if the tie points are uniformly distributed throughout the images. Second, since you want the calculation to output the minimum and maximum parallax offsets in both the x- and y-axis directions, the tie points selected must be those that have the minimum and maximum parallax.

In practice, the following procedure has been found successful. First, select a fairly uniform grid of about eight tie points that defines the lowest elevation within the image. Coastlines, river flood plains, roads, and agricultural fields commonly meet this criteria. Using Solve Geometric Model tool in StereoSAR Coregistration Tool should yield values in the -5 to +5 range at this time. Next, identify and select three or four of the highest elevations within the image. After selecting each tie point, click Solve Geometric Model tool and note the effect of each tie point on the minimum and maximum parallax values. When you feel you have quantified these values, write them down and apply the resultant transform to the image.

Constrain

This option is intended to allow you to define areas where it is not necessary to search the entire search window area. A region of lakes would be such an area. This reduces processing time and also minimizes the likelihood of finding false positives. This option is not implemented at present.

Match

An essential component, and the major time-saver of StereoSAR DEM software is automatic image correlation.

In automatic image correlation, a small subset (image chip) of the Reference image termed the template (see the "UL Corner of Reference Image" figure below), is compared to various regions of the Match image’s search area (see the "UL Corner of the Match Image" below) to find the best Match point. The center pixel of the template is then said to be correlated with the center pixel of the Match region. The software then proceeds to the next pixel of interest, which becomes the center pixel of the new template.

The following figure shows the upper left (UL) corner of the Reference image. An 11 × 11 pixel template is shown centered on the pixel of interest: X = 8, Y = 8.

UL Corner of the Reference Image

radar_ul_corner_reference_image

The figure below shows the UL corner of the Match image. The 11 × 11 pixel template is shown centered on the initial estimated correlation pixel X = 8, Y = 8. The 15 × 7 pixel search area is shown in a dashed line. Since most of the parallax shift is in the range direction (x-axis), the search area should always be a rectangle to minimize search time.

UL Corner of the Match Image

radar_ul_corner_match_image

The ERDAS IMAGINE automatic image correlator works on the hierarchical pyramid technique. This means that the image is successively reduced in resolution to provide a coregistered set of images of increasing pixel size (see the figure below). The automatic correlation software starts at the top of the resolution pyramid with the lowest resolution image being processed first. The results of this process are filtered and interpolated before being passed to the next highest resolution layer as the initial estimated correlation point. From this estimated point, the search is performed on this higher resolution layer.

Image Pyramid Matching

photog_image_pyramid_matching

Template Size

The size of the template directly affects computation time: a larger image chip takes more time. However, too small of a template could contain insufficient image detail to allow accurate matching. A balance must be struck between these two competing criteria, and is somewhat image-dependent. A suitable template for a suburban area with roads, fields, and other features could be much smaller than the required template for a vast region of uniform ground cover. Because of viewing geometry-induced differences in Reference and Match images, the template from Reference image is never identical to any area of Match image. The template must be large enough to minimize this effect.

StereoSAR DEM correlator parameters shown in STD_LP_HD Correlator Table are for the library file Std_LP_HD.ssc. These parameters are appropriate for a RADARSAT Standard Beam mode (Std) stereo pair with low parallax (LP) and high density of detail (HD). The low parallax parameters are appropriate for images of low to moderate topography. The high density of detail (HD) parameters are appropriate for the suburban area discussed above.

STD_LP_HD Correlator Table

Level

Average

Size X

Size Y

Search -X

Search +X

Search -Y

Search +Y

1

1

20

20

2

2

1

1

2

2

60

60

3

4

1

1

3

3

90

90

8

20

2

3

4

4

120

120

10

30

2

5

5

5

180

180

20

60

2

8

6

6

220

220

25

70

3

10

Level

Step X

Step Y

Threshold

Value

Vector X

Vector Y

Applied

1

2

2

0.30000

0.00000

0.00000

0.00000

0

2

8

8

0.20000

0.00000

0.00000

0.00000

0

3

20

20

0.20000

0.00000

0.00000

0.00000

0

4

50

50

0.20000

0.00000

0.00000

0.00000

0

5

65

65

0.20000

0.00000

0.00000

0.00000

0

6

80

80

0.10000

0.00000

0.00000

0.00000

0

Note that the size of the template (Size X and Size Y) increases as you go up the resolution pyramid. This size is the effective size if it were on the bottom of the pyramid (that is, the full resolution image). Since they are actually on reduced resolution levels of the pyramid, they are functionally smaller. Thus, the 220 × 220 template on Level 6 is actually only 36 × 36 during the actual search. By stating the template size relative to the full resolution image, it is easy to display a box of approximate size on the input image to evaluate the amount of detail available to the correlator, and thus optimize the template sizes.

Search Area

Considerable computer time is expended in searching the Match image for the exact Match point. Thus, this search area should be minimized. (In addition, searching too large of an area increases the possibility of a false match.) For this reason, the software first requires that the two images be coregistered. This gives the software a rough idea of where the Match point might be. In stereo DEM generation, you are looking for the offset of a point in the Match image from its corresponding point in the Reference image (parallax). The minimum and maximum displacement is quantified in the Coregister step and is used to restrain the search area.

In the "UL Corner of the Match Image" above the search area is defined by four parameters: -X, +X, -Y, and +Y. Most of the displacement in radar imagery is a function of the look angle (see the "SAR Image Intersection" figure above) and is in the range or x-axis direction. Thus, the search area is always a rectangle emphasizing the x-axis. Because the total search area (and, therefore, the total time) is X times Y, it is important to keep these values to a minimum. Careful use at the Coregister step easily achieves this.

Step Size

Because a radar stereopair typically contains millions of pixels, it is not desirable to correlate every pixel at every level of the hierarchal pyramid, nor is this even necessary to achieve an accurate result. The density at which the automatic correlator is to operate at each level in the resolution pyramid is determined by the step size (posting). The approach used is to keep posting tighter (smaller step size) as the correlator works down the resolution pyramid. For maximum accuracy, it is recommended to correlate every pixel at the full resolution level. This result is then compressed by Degrade step to the desired DEM cell size.

Threshold

The degree of similarity between the Reference template and each possible Match region within the search area must be quantified by a mathematical metric. StereoSAR DEM uses the widely accepted normalized correlation coefficient. The range of possible values extends from -1 to +1, with +1 being an identical match. The algorithm uses the maximum value within the search area as the correlation point.

The threshold in STD_LP_HD Correlator Table is the minimum numerical value of the normalized correlation coefficient that is accepted as a correlation point. If no value within the entire search area attains this minimum, there is not a Match point for that level of the resolution pyramid. In this case, the initial estimated position, passed from the previous level of the resolution pyramid, is retained as the Match point.

Correlator Library

To aid both the novice and the expert in rapidly selecting and refining an StereoSAR DEM correlator parameter file for a specific image pair, a library of tested parameter files has been assembled and is included with the software. These files are labeled using the following syntax: (RADARSAT Beam mode)_(Magnitude of Parallax)_(Density of Detail).

RADARSAT Beam Mode

Correlator parameter files are available for both Standard (Std) and Fine (Fine) Beam modes. An essential difference between these two categories is that, with the Fine Beam mode, more pixels are required (that is, a larger template) to contain the same number of image features than with a Standard Beam image of the same area.

Magnitude of Parallax

The magnitude of the parallax is divided into high parallax (_HP) and low parallax (_LP) options. This determination is based upon the elevation changes and slopes within the images and is somewhat subjective. This parameter determines the size of the search area.

Density of Detail

The level of detail within each template is divided into high density (_HD) and low density (_LD) options. The density of detail for a suburban area with roads, fields, and other features would be much higher than the density of detail for a vast region of uniform ground cover. This parameter, in conjunction with beam mode, determines the required template sizes.

Quick Tests

It is often advantageous to quickly produce a low resolution DEM to verify that the automatic image correlator is optimum before correlating on every pixel to produce the final DEM.

For this purpose, a Quick Test (_QT) correlator parameter file has been provided for each of the full resolution correlator parameter files in the .ssc library. These correlators process the image only through resolution pyramid Level 3. Processing time up to this level has been found to be acceptably fast, and testing has shown that if the image is successfully processed to this level, the correlator parameter file is probably appropriate.

Degrade

The second Degrade step compresses the final parallax image file (Level 1). While not strictly necessary, it is logical and has proven advantageous to reduce the pixel size at this time to approximately the intended posting of the final output DEM. Doing so at this time decreases the variance (LE90) of the final DEM through averaging.

Height

This step combines the information from the above processing steps to derive surface elevations. The sensor models of the two input images are combined to derive the stereo intersection geometry. The parallax values for each pixel are processed through this geometric relationship to derive a DEM in sensor (pixel) coordinates.

Comprehensive testing of StereoSAR DEM module has indicated that, with reasonable data sets and careful work, the output DEM falls between DTED Level I and DTED Level II. This corresponds to between USGS 30-meter and USGS 90-meter DEMs. Thus, an output pixel size of 40 to 50 meters is consistent with this expected precision.

The final step is to resample and reproject this sensor DEM in to the desired final output DEM. The entire ERDAS IMAGINE reprojection package is accessed within StereoSAR DEM module.