Warp Operator

The Warp operator is a component of coregistration . This operator computes a warp function from the reference-secondary ground control point (GCP) pairs produced by GCP Selection operator , and generates the final co-registered image.

Compute Warp Polynomial

Once the valid reference-secondary GCP pairs are known, a polynomial of a certain order is computed using a least square method, which maps the reference GCPs onto the secondary GCPs. This function is known as the warp function and is used to perform the co-registration. Generally the warp function computed with the initial reference-secondary GCPs is not the final warp function used in co-registration because it normally introduces large errors for GCPs. These GCPs must be removed. Therefore the warp function is determined in an iterative manner.

First a warp function is computed using the initial reference-secondary GCP pairs.
Then the reference GCPs are mapped to the secondary image with the warp function, and the residuals between the mapped reference GCPs and their corresponding secondary GCPs are computed. The root mean square (RMS) and the standard deviation for the residuals are also computed.
Next, the reference-secondary GCP pairs are filtered with the mean RMS. GCP pairs with RMS greater than the mean RMS are eliminated.
The same procedure (step 1 to 3) is repeated up to 2 times if needed and each time the remaining reference-secondary GCP pairs from previous elimination are used.
Finally the reference-secondary GCP pairs are filtered with the user selected RMS threshold and the final warp function is computed with the remaining reference-secondary GCP pairs.

The WARP polynomial order is specified by user in the dialog box.

The valid values for the polynomial order are 1, 2 and 3.
For most cases where the input images do not suffer from a high level of distortion, linear warp is generally enough and is recommended as default.
Higher order warp should be used only when image suffers from a high level distortion and a very good co-registration accuracy is required.
Higher order warp requires more GCPs and can introduce large distortions in image regions containing only a few GCPs.

Generate Co-Registered Image

With the determination of warp function which maps pixels in the reference image to the secondary image, the co-registered image can be obtained with interpolation. Currently the following interpolation methods are supported:

Nearest-neighbour interpolation
Bilinear interpolation
Bicubic interpolation
Cubic interpolation (4 and 6 points)
Truncated sinc interpolation (6, 8 and 16 points)

Interpolation for InSAR

For interferometric applications Cubic or Truncated sinc kernels are recommended. These kernels assure the optimal interpolation in terms of Signal-to-Noise ratio.

Residual File

The residual file is a text file containing information about reference and secondary GCPs before and after each elimination. The residual for a GCP pair is the errors introduced by the warping function and can be used as a good indicator of the quality of the warp function. It is often very useful to check the information contained within the residual file to see if the co-registration process can be considered to have been successful. For example, the "RMS mean" value can be used as an approximate figure of merit for the co-registration. User can view the residual file by checkmarking the "Show Residuals" box in the dialog box. Detailed information contained in the residual file are listed below:

Band name
Warp coefficients
Reference GCP coordinates
Secondary GCP coordinates
Row and column residuals
Root mean square errors (RMS)
Row residual mean
Row residual standard deviation
Column residual mean
Column residual standard deviation
RMS mean
RMS standard deviation

Parameters Used

The following parameters are used by the operator:

RMS Threshold: The criterion for eliminating invalid GCPs. In general, the smaller the threshold, the better the GCP quality, but lower the number of GCPs.
Warp Polynomial Order: The degree of the warp polynomial.
Interpolation Method: The interpolation method used computing co-registered secondary image pixel value.
Show Residuals: Display GCP residual file if selected.