Combined forward and reverse correlation
Improved correlation techniques employ data from forward (template-to-reference) and reverse (reference-to-template) correlation to identify valid correlation peaks, enforce symmetry in correlation peaks, and/or combine forward and reverse correlation data. In embodiments, these techniques eliminate or reduce rms noise in a recovered signal peak location by enforcing correlation peak symmetry. The forward and reverse correlation methods described herein may be used for validation of correlation peaks, detection of outlier data points and improved interpolation, such as for higher accuracy localization of a peak center with sub-pixel resolution.
1. A method of making a correlation between a first image and a second image in an image processing algorithm, comprising:
computing a first correlation using image data associated with the first image as a template and using image data associated with the second image as a search area;
determining a first correlation peak from the first correlation, the first correlation peak representing an image disparity from the first image to the second image;
computing a second correlation using image data associated the second image as a template and using image data associated with the first image as a search area;
determining a second correlation peak from the second correlation, the second correlation peak representing an image disparity from the second image to the first image; and
validating the first correlation peak by comparing the second correlation peak to a threshold value, the threshold value based upon the first correlation peak.
2. The method of claim 1 further comprising combining the first correlation peak with the second correlation peak to determine a combined peak.
3. The method of claim 2 wherein combining includes element-by-element averaging of data for the respective correlation peaks.
4. The method of claim 2 wherein combining includes element-by-element multiplication of correlation values.
5. The method of claim 2 wherein combining includes combining correlation tables as if the correlation tables were from the same image data source.
6. The method of claim 2 wherein combining includes interpolating the combined peak using an interpolation function.
7. The method of claim 6 wherein the interpolation function is non-separable in the number of dimensions of the image data.
8. The method of claim 6 wherein the interpolation function is based on an Airy function.
9. The method of claim 6 wherein the interpolation function is based on an actual point spread function.
10. The method of claim 6 wherein the interpolation function is based on a spline.
11. The method of claim 6 wherein the interpolation function is based on a Gaussian distribution.
12. The method of claim 1 wherein computing a second correlation includes computing the second correlation relative to the first correlation peak.
13. The method of claim 1 further comprising enforcing correlation symmetry by iteratively introducing a fraction offset to at least one of the first image and the second image until symmetry is achieved in a combined correlation peak of the first correlation and the second correlation.
14. A system comprising:
first computing means for computing a first correlation using image data associated with the first image as a template and using image data associated with the second image as a search area;
second computing means for determining a first correlation peak from the first correlation, the first correlation peak representing an image disparity from the first image to the second image;
third computing means for computing a second correlation using image data associated the second image as a template and using image data associated with the first image as a search area;
fourth computing means for determining a second correlation peak from the second correlation, the second correlation peak representing an image disparity from the second image to the first image; and
fifth computing means for validating the first correlation peak by comparing the second correlation peak to a threshold value, the threshold value based upon the first correlation peak.