Max and Min Values of the Structural Similarity Function S(x,a) on the L2 Sphere SR(a), a ∈ ℝN
Given a reference signal a, we analytically solve for the critical points that maximize/minimize the Structural Similarity function S(x,a) while restricting ourselves to points x that lie on an L 2 sphere centered at a with fixed radius R. To do this, we employ the method of Lagrange multipliers and show that at least four (and as many as six) critical points exist, deriving the conditions that guarantee their existence.
KeywordsMean Square Error Lagrange Multiplier Reference Image Image Patch Image Quality Assessment
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- 1.Glew, D.: Self-similarity of images and non-local image processing, M.Math. Thesis, Department of Applied Mathematics, University of Waterloo (2011)Google Scholar