I can explain CV_TM_CORR, but am myself still looking for a good explanation of CV_TM_CCOEFF.
CV_TM_CORR is a cross-correlation, an image/signal processing technique that relies on multiplication. The inputs to a cross-correlation are a smaller sample (with image processing, that's your template image) and a larger target dataset (image). Typically, a cross-correlation is used to find at what position (overlay) does the template/sample most closely match the data in the target image.
Put simply, cross-correlation of a template and an image involves three steps:
- Overlay the sample/template onto the target image.
- For each pixel position in the overlay, multiply the template image pixel value by the target image pixel value. Sum all the products together to get a "score" for the overlay.
- Repeat Step #2 for every possible overlay.
Typically, the overlay position with the highest score is the "winner", especially when using the normalized version of cross-correlation (CV_TM_CCORR_NORMED) - when the positive values line up with positive values and the negative values line up with negative values (which multiply to a positive) and all those positives are summed up, the score peaks, signifying a good alignment. Wikipedia probably does a better job explaining it than I do: Cross Correlation
Looking closer at the OpenCV CV_TM_CCORR equation:
R(x,y) is the cross-correlation score for a single overlay position (x, y).
T(x',y') is the image pixel value for a pixel (x',y') in the template/sample image.
I(x+x',y+y') is the image pixel value for the corresponding (based on the overlay) pixel position in the target image.
We sum up the product of T(x',y') and I(x+x',y+y') for each overlay pixel position - every possible (x', y') in the overlay - to get our score. Then we move to a new overlay (x,y) and repeat to get the other overlay scores.
(Also, please note the typos in the formula contained in the first edition of the O'Reilly book - there are some extraneous powers of two floating around, among other issues. I believe the formulas on the website are correct.)
Now, for CV_TM_CCOEFF.
It's the same basic framework, but with a different underlying calculation for each overlay. I don't understand the CV_TM_CCOEFF calculation. O'Reilly explains that "These methods match a template relative to its mean against the image relative to its mean, so a perfect match will be 1 and a perfect mismatch will be -1; a value of 0 simply means that there is no correlation". However, the equation given for CV_TM_CCOEFF doesn't subtract the mean from each pixel value but instead subtracts the reciprocal of the pixel value sum TIMES the number of pixels (shouldn't it be a division?). Plus, all the simple examples I work out on paper (with small, one dimensional signals) usually don't give me 1, 0, or -1. I also Googled Correlation Coefficient and found variations of this: Pearson Correlation Coefficient, which has all kinds of ... (more)
