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+ •(Dr. Pierre Elbischger  MIP1/ISAP'SS09
A1) 7 Highboost filtering (2) For the lowpass filter, the Gaussian filter is often used. More robust to noise compared to the sharpening using the Laplacian
Tunable parameters σ (spatial spread) and A (sharpening intensity) A=2 the expression is identical to unsharp masking (a=1, see previous slides) In general an arbitrary highpass filter can be used. If we use the Laplacian for the highpass
filter, then for: A=1 the expression is identical to the (negative) Laplacian of the image
A=2 the expression becomes identical to the sharpening using a Laplacian (see previous slides) 19.05.2009 Dr. Pierre Elbischger  MIP1/ISAP'SS09 8 Probability  Classical definition (Laplace 1812)
A twodimensional representation of the outcomes of two dice, and the subspaces
associated with the events corresponding to the sum of the dice being greater than 8,
or less than or equal to 8. 19.05.2009 Dr. Pierre Elbischger  MIP1/ISAP'SS09 9 Empirical probability (VonMises 1936)
The experiment is repeatable forP ( A) := lim n event occurs nA times.
n times whereby the
n
The probability is defined by the relative frequency nA/n.
Due to the fact that n is always finite, P(A) can only be an estimate.
Law of large numbers → For an increasing number of experiments, the probability
approaches a limit.
A n →∞ Example: Relative frequency (throw a dice n times) 19.05.2009 Dr. Pierre Elbischger  MIP1/ISAP'SS09 10 Distribution function
FX (α ) : P( x ≤ α )
=
Example: Dice 19.05.2009 Properties: d X (+∞)
FX (−∞)
F
= 0 an= 1
FX (α 2 ) − FX (α1 ) P (α1 < x ≤ α 2 ) ≥ 0
=
P(= α ) 0, if FX is continous.
x= Dr. Pierre Elbischger  MIP1/ISAP'SS09 11 Probability density function
The first derivative of the distribution function FX(α) is defined as the probability
density function (PDF) fX(α) of the random variable x. dFX (α )
f X (α ) :=
dα
Properties: f X (α ) ≥ 0
=
FX (α ) α ∫
⇐ monotony of the distribution function
f X (γ ) ⋅ d γ in particular +∞ =
FX (+∞) −∞ ∫ =
f X (γ ) ...
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This note was uploaded on 07/09/2009 for the course MEDIT 1 taught by Professor Pierreelschbinger during the Spring '09 term at Carinthia University of Applied Sciences.
 Spring '09
 PIERREELSCHBINGER

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