diff_of_gauss__ ( Image : DiffOfGauss : Sigma, SigFactor : )

Approximate the LoG operator (Laplace of Gaussian).

diff_of_gauss__ approximates the Laplace-of-Gauss operator by a difference of Gaussians. The standard deviations of these Gaussians can be calculated, according to Marr, from the Parameter Sigma of the LoG and the ratio of the two standard deviations (SigFactor) as: sigma1 = Sigma / sqrt(-2.0 * LoG {1.0/SigFactor} / (SigFactor^2 - 1.0)) sigma2 = sigma1 / SigFactor Result = { Object * gauss(sigma1) } - { Object * gauss(sigma2) } For a SigFactor = 1.6, according to Marr, an approximation to the Mexican-Hat-Operator results. The resulting image is stored in DiffOfGauss.


Parameters

Image (input_object)
image(-array) -> object : byte
Input image

DiffOfGauss (output_object)
image(-array) -> object : int2
LoG image.

Sigma (input_control)
real -> real
Smoothing parameter of the Laplace operator to approximate.
Default value: 3.0
Suggested values: 2.0, 3.0, 4.0, 5.0
Range of values: 0.2 <= Sigma <= 50.0
Minimum increment: 0.01
Recommended increment: 0.1
Restriction: Sigma > 0.0

SigFactor (input_control)
real -> real
Ratio of the standard deviations used (Marr recommends 1.6).
Default value: 1.6
Range of values: 0.1 <= SigFactor <= 10.0
Minimum increment: 0.01
Recommended increment: 0.1
Restriction: SigFactor > 0.0


Example
read_image(:Image:'fabrik':) >
diff_of_gauss__(Image:Laplace:2.0,1.6:) >
zero_crossing2(Laplace:ZeroCrossings::).

Complexity

The execution time depends linearly on the number of pixels and the size of sigma.


Result

diff_of_gauss__ returns TRUE if all parameters are correct. If the input is empty the behaviour can be set via set_system(::'no_object_result',<Result>:). If necessary, an exception is raised.


Possible Successors

zero_crossing1, zero_crossing2


Alternatives

laplace__, derivate_gauss


References

D. Marr: ``Vision (A computational investigation into human representation and processing of visual information)''; New York, W.H. Freeman and Company; 1982.



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