laplace_of_gauss ( Image : ImageLaplace : Sigma : )

LoG-Operator (Laplace of Gaussian).

laplace_of_gauss calculates the Laplace-of-Gaussian operator, i.e., the Laplace operator on a Gaussian smoothed image, for arbitrary smoothing parameters Sigma. The Laplace operator is given by:

                  2            2
   __            d            d
   \/ g(x,y)) = --- g(x,y) + --- g(x,y)
                  2            2
                dx           dy
The derivatives in laplace_of_gauss are calculated by appropriate derivatives of the Gaussian, resulting in the following formula for the convolution mask:
                       /  2   2     \     /    2   2 \
  __              1    | x + y      |     |   x + y  |
  \/ G (x,y) = ------- | ------ - 1 | exp | - ------ |
      s              4 |     2      |     |       2  |
               2 pi s  \  2 s       /     \    2 s   /


Parameters

Image (input_object)
image(-array) -> object : byte / int1 / int2 / int4 / real
Input image.

ImageLaplace (output_object)
image(-array) -> object : int2
Laplace filtered image.

Sigma (input_control)
number -> real / integer
Smoothing parameter of the Gaussian.
Default value: 2.0
Suggested values: 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0, 7.0
Range of values: 0.2 <= Sigma <= 20.0
Minimum increment: 0.01
Recommended increment: 0.1
Restriction: Sigma > 0.0


Example
read_image(&Image,"mreut");
laplace_of_gauss(Image,&Laplace,2.0);
zero_crossing2(Laplace,&ZeroCrossings);

Possible Successors

zero_crossing1, zero_crossing2


Alternatives

laplace__, diff_of_gauss__, derivate_gauss


See also

derivate_gauss



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