Sub-pixel accuracy and valid correlation signal detection by 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 calculating a correlation peak comprising:
determining a forward correlation peak from a forward correlation between a first image and a second image;
determining a reverse correlation peak from a reverse correlation between the second image and the first image;
validating the forward correlation peak;
validating the reverse correlation peak; and
combining the forward correlation peak and the reverse correlation peak to provide a combined correlation peak,
wherein the determining, the validating, and the combining steps are performed using one or more computing devices.
2. The method of claim 1 wherein combining includes element-by-element averaging of data for the forward and reverse correlation peaks.
3. The method of claim 1 wherein combining includes element-by-element multiplication of a plurality of values from the forward correlation and the reverse correlation.
4. The method of claim 1 wherein combining includes combining correlation tables from the forward and reverse correlations as if the correlation tables were from the same image data source.
5. The method of claim 1 wherein combining includes interpolating the combined correlation peak.
6. A system comprising:
first computing means for determining a forward correlation peak from a forward correlation between a first image and a second image;
second computing means for determining a reverse correlation peak from a reverse correlation between the second image and the first image;
third computing means for validating the forward correlation peak; and
fourth computing means for combining the forward correlation peak and the reverse correlation peak to provide a combined correlation peak.
7. A method of enforcing correlation peak symmetry between a pair of images in an image processing algorithm, comprising:
determining a forward correlation peak from a forward correlation between a first image and a second image;
determining a reverse correlation peak from a reverse correlation between the second image and the first image;
combining the first correlation peak and the second correlation peak to provide a combined correlation peak; and
enforcing symmetry in the combined correlation peak,
wherein the determining, the combining, and the enforcing steps are performed using one or more computing devices.
8. The method of claim 7 further comprising determining a plurality of reverse correlation peaks from a plurality of reverse correlations, and combining the first correlation peak and the second correlation peak to provide a combined correlation peak.
9. The method of claim 7 wherein enforcing symmetry includes element-by-element averaging of data for the forward and reverse correlation peaks.
10. The method of claim 7 wherein enforcing symmetry includes element-by-element multiplication of a plurality of values from the forward correlation and the reverse correlation.
11. The method of claim 7 wherein enforcing symmetry includes combining correlation tables from the forward and reverse correlations as if the correlation tables were from the same image data source.
12. The method of claim 7 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 the combined correlation peak.