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As I know, there is no function, that calculate the invariant version of matchTemplate. There is some article, which introduce it, but you will have implement it. Link:Link to article

But, in OpenCv there is function, which compare histogram of objects and pattern. It is CalcBackProjPath. Histogram are invariant to rotation, so you can call it once. But it can be much slower, because it use normal Sliding Window. MatchTemplate in OpenCv use Fourier Transform, what really speed up finding interesting point.