Max and min values of the structural similarity function s(x, a) on the L2 sphere SR(a), a ε R N

  • Authors:

  • D. Glew;Edward R. Vrscay

  • Affiliations:

  • Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada;Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada

  • Venue:
  • ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part I
  • Year:
  • 2012

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Abstract

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 L2 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.