diff_of_gaussdiff_of_gaussdiff_of_gaussDiffOfGaussDiffOfGauss (Operator)

Name

diff_of_gaussdiff_of_gaussdiff_of_gaussDiffOfGaussDiffOfGauss — Approximate the LoG operator (Laplace of Gaussian).

Signature

Description

diff_of_gaussdiff_of_gaussdiff_of_gaussDiffOfGaussDiffOfGauss 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 SigmaSigmaSigmaSigmasigma of the LoG and the ratio of the two standard deviations (SigFactorSigFactorSigFactorSigFactorsigFactor) 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 DiffOfGaussDiffOfGaussDiffOfGaussDiffOfGaussdiffOfGauss.

Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Automatically parallelized on tuple level.
• Automatically parallelized on channel level.
• Automatically parallelized on domain level.

Parameters

read_image(Image,'fabrik')
diff_of_gauss(Image,Laplace,2.0,1.6)
zero_crossing(Laplace,ZeroCrossings)

read_image(&Image,"mreut");
diff_of_gauss(Image,&Laplace,2.0,1.6);
zero_crossing(Laplace,&ZeroCrossings);

read_image(Image,'fabrik')
diff_of_gauss(Image,Laplace,2.0,1.6)
zero_crossing(Laplace,ZeroCrossings)

read_image(Image,'fabrik')
diff_of_gauss(Image,Laplace,2.0,1.6)
zero_crossing(Laplace,ZeroCrossings)

read_image(Image,'fabrik')
diff_of_gauss(Image,Laplace,2.0,1.6)
zero_crossing(Laplace,ZeroCrossings)

Complexity

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

Result

diff_of_gaussdiff_of_gaussdiff_of_gaussDiffOfGaussDiffOfGauss returns 2 (H_MSG_TRUE) if all parameters are correct. If the input is empty the behaviour can be set via set_system('no_object_result',<Result>)set_system("no_object_result",<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>). If necessary, an exception is raised.

Possible Successors

zero_crossingzero_crossingzero_crossingZeroCrossingZeroCrossing, dual_thresholddual_thresholddual_thresholdDualThresholdDualThreshold

Alternatives

laplacelaplacelaplaceLaplaceLaplace, derivate_gaussderivate_gaussderivate_gaussDerivateGaussDerivateGauss

References

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

Module

Foundation