Warp Operator
The Warp operator is a component of coregistration. This operator
computes a warp function from the master-slave ground control point (GCP) pairs produced
by GCP Selection operator, and generates the final co-registered image.
Compute Warp Polynomial
Once the valid master-slave GCP pairs are known, a polynomial of a
certain order is computed using a least square method, which
maps the master GCPs onto the slave 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 master-slave 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 master-slave GCP pairs.
- Then the master GCPs are mapped to the slave image with the warp function,
and the residuals between the mapped master GCPs and their corresponding slave GCPs are computed. The
root
mean square (RMS) and the standard deviation for the residuals are also computed.
- Next, the master-slave 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 master-slave GCP pairs from previous
elimination are used.
- Finally the master-slave GCP pairs are filtered with the user
selected RMS threshold and the final warp function is computed with the
remaining master-slave 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 master
image to the slave 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 master and slave 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
- Master GCP coordinates
- Slave 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 slave image
pixel value.
- Show Residuals: Display GCP residual file if selected.
