Operators

# diff_of_gauss (Operator)

## Name

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

## Signature

diff_of_gauss(Image : DiffOfGauss : Sigma, SigFactor : )

## Description

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.

## Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Automatically parallelized on tuple level.
• Automatically parallelized on channel level.
• Automatically parallelized on domain level.

## Parameters

Image (input_object)  (multichannel-)image(-array) object (byte / uint2)

Input image

DiffOfGauss (output_object)  (multichannel-)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

Typical 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

Typical range of values: 0.1 ≤ SigFactor ≤ 10.0

Minimum increment: 0.01

Recommended increment: 0.1

Restriction: SigFactor > 0.0

## Example (HDevelop)

```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_gauss 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>). If necessary, an exception is raised.

## 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

 Operators