# Local Morse Theory for Gaussian Blurred Functions

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

## Abstract

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
$$\frac{{\partial f}}{{\partial t}} = \Delta \left( f \right) = \sum\limits_{i = 1}^n {\frac{{{\partial ^2}f}}{{\partial x_i^2}}} \quad on\quad {R^n} \times {R_ + }$$
(11.1)
and satisfying initial conditions f(x,0) = f 0(x) for f 0 : R nR.

## Keywords

Normal Form Compact Subset Heat Equation Transversality Condition Morse Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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