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Springer, Berlin, Heidelberg\"\n+---\n+\n+In this work, the author wants to estimate the displacement field from two frames while compensating for the background motion.\n+\n+To achieve this, each pixel's neighborhood is approximated by a polynomial $$f(x) = X^T Ax + b^T x + c$$, where $$A$$ is a symmetric matrix, $$b$$ a vector and $$c$$ a scalar.\n+\n+These coefficients are estimated by a least squares fit. (*Note*: done by a separable convolution in practice.)\n+\n+From the first and second images, we create $$A_1$$ and $$A_2$$ and calculate the mean to get a new matrix $$A$$.\n+\n+We also introduce $$\\delta b = - \\frac{1}{2}(b_2 (x) - b_1 (x))$$.\n+The problem is then to solve $$A(x)d(x) = \\delta b(x)$$ where $$d(x)$$ is the displacement field.\n+\n+The result from this equation is too noisy. 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