Max and Min Values of the Structural Similarity Function S(x,a) on the L2 Sphere SR(a), a ∈ ℝN

  • D. Glew
  • Edward R. Vrscay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7324)


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.


Mean Square Error Lagrange Multiplier Reference Image Image Patch Image Quality Assessment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • D. Glew
    • 1
  • Edward R. Vrscay
    • 1
  1. 1.Department of Applied Mathematics, Faculty of MathematicsUniversity of WaterlooWaterlooCanada

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