Local Morse Theory for Gaussian Blurred Functions

  • James Damon
Part of the Computational Imaging and Vision book series (CIVI, volume 8)


When Gaussian blurring is applied to an intensity function f 0 (x), it yields a family f(x,t) of intensity functions parametrised by t, which is a solution to the heat equation
$$ \frac{{\partial f}}{{\partial t}} = \Delta \left( f \right) = \sum\limits_{i = 1}^n {\frac{{{\partial ^2}f}}{{\partial x_i^2}}} \quad on\quad {R^n} \times {R_ + }$$
and satisfying initial conditions f(x,0) = f 0(x) for f 0 : R nR.


Normal Form Compact Subset Heat Equation Transversality Condition Morse Theory 
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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • James Damon
    • 1
  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

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