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ralab::base::filter::utilities::Mexican_Hat< TReal > Struct Template Reference

Mexican hat wavelet. More...

#include <mexhat.hpp>

Inheritance diagram for ralab::base::filter::utilities::Mexican_Hat< TReal >:

Public Member Functions

 Mexican_Hat (TReal mu, TReal sigma)
 
TReal operator() (TReal x)
 operator More...
 

Protected Attributes

TReal mu_
 
TReal sigma_
 

Detailed Description

template<typename TReal>
struct ralab::base::filter::utilities::Mexican_Hat< TReal >

Mexican hat wavelet.

  \f{eqnarray*}{
   T_1 &= {1 \over {\sqrt {2\pi}\sigma^3}}\\
   T_2 &= \left( 1 - {t^2 \over \sigma^2} \right)\\
   T_3 &= e^{-t^2 \over 2\sigma^2} \\
   \psi(t) &= T_1 \cdot T_2 \cdot T_3
  \f}

is the negative normalized second derivative of a Gaussian function. (Source Wikipedia.) (LoG) Laplace of Gaussian, with Laplace's operator having a (-1,2,-1) Kernel.

Definition at line 43 of file mexhat.hpp.

Constructor & Destructor Documentation

◆ Mexican_Hat()

template<typename TReal >
ralab::base::filter::utilities::Mexican_Hat< TReal >::Mexican_Hat ( TReal  mu,
TReal  sigma 
)
inline
Parameters
mumean
sigmastandard deviation

Definition at line 45 of file mexhat.hpp.

49  :mu_(mu),
50  sigma_(sigma)
51  {}

Member Function Documentation

◆ operator()()

template<typename TReal >
TReal ralab::base::filter::utilities::Mexican_Hat< TReal >::operator() ( TReal  x)
inline

operator

Definition at line 53 of file mexhat.hpp.

54  {
55  TReal two = TReal(2);
56  TReal t1( 1 / (pow(TReal(2. * ralab::constants::PI) , TReal(.5)) * pow(sigma_,TReal(3.))) );
57  TReal t2(1 - pow( x-mu_ , two)/ pow(sigma_, two ) );
58  TReal t3( exp(-pow((x-mu_) , two )/( 2 * pow( sigma_, two ) ) ) );
59  return( t1 * t2 * t3 );
60  }

References ralab::base::filter::utilities::Mexican_Hat< TReal >::mu_, ralab::constants::PI(), ralab::base::filter::utilities::Mexican_Hat< TReal >::sigma_, and x.

Member Data Documentation

◆ mu_

template<typename TReal >
TReal ralab::base::filter::utilities::Mexican_Hat< TReal >::mu_
protected

◆ sigma_

template<typename TReal >
TReal ralab::base::filter::utilities::Mexican_Hat< TReal >::sigma_
protected

The documentation for this struct was generated from the following file:
ralab::base::filter::utilities::Mexican_Hat::sigma_
TReal sigma_
Definition: mexhat.hpp:63
x
KernelTraitsBase< Kernel >::space_type::abscissa_type x
Definition: MatchedFilter.hpp:142
ralab::base::filter::utilities::Mexican_Hat::mu_
TReal mu_
Definition: mexhat.hpp:62
ralab::constants::PI
const double PI(3.14159265358979323846264338327950288)
the ratio of the circumference of a circle to its diameter;