isotropic_diffusion🔗
Short description🔗
isotropic_diffusion — Perform an isotropic diffusion of an image.
Signature🔗
isotropic_diffusion( image Image, out image SmoothedImage, real Sigma, integer Iterations )
Description🔗
The operator isotropic_diffusion performs an isotropic
diffusion of the input image Image. This corresponds to a
convolution of the image matrix with a Gaussian mask of standard
deviation Sigma. If the parameter Iterations is
set to 0, such a convolution is performed explicitly. For
input images with a full ROI, isotropic_diffusion returns
the same results as the operator derivate_gauss when
choosing 'none' for its parameter Component. If
the gray value matrix is larger than the ROI of Image the
two operators differ since derivate_gauss takes the gray
values outside of the ROI into account, while
isotropic_diffusion mirrors the values at the boundary of
the ROI in any case. The computational complexity increases linearly
with the value of Sigma.
If Iterations has a positive value the smoothing process
is considered as an application of the heat equation
on the gray value function u with the initial value \(u = u_{0}\) defined by the gray values of Image at a time
\(t_{0}\). This equation is then solved up to a time \(t_{0} + \frac12 \textrm{Sigma}^2\), which
is equivalent to the above convolution, using an iterative procedure
for parabolic partial differential equations. The computational
complexity is proportional to the value of Iterations and
independent of Sigma in this case. For small values of
Iterations, the computational accuracy is very low,
however. For this reason, choosing \(\textrm{Iterations} <
\textit{3}\) is not recommended.
For smaller values of Sigma, the convolution implementation
is typically the faster method. Since the runtime of the partial
differential equation solver only depends on the number of
iterations and not on the value of Sigma, it is typically
faster for large values of Sigma if few iterations are
chosen (e.g., \(\textrm{Iterations} = \textit{3}\)).
For an explanation of the concept of smoothing filters see the introduction of chapter Filters / Smoothing.
Attention🔗
Note that filter operators may return unexpected results if an image with a reduced domain is used as input. Please refer to the chapter Filters.
Execution information🔗
Execution information
-
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.
Parameters🔗
Image (input_object) (multichannel-)image(-array) → object (byte / uint2 / real)
Input image.
SmoothedImage (output_object) image(-array) → object (byte / uint2 / real)
Output image.
Sigma (input_control) real → (real)
Standard deviation of the Gauss distribution.
Default: 1.0
Suggested values: 0.1, 0.5, 1.0, 3.0, 10.0, 20.0, 50.0
Restriction: Sigma > 0
Iterations (input_control) integer → (integer)
Number of iterations.
Default: 10
Suggested values: 0, 3, 10, 100, 500
Restriction: Iterations >= 0
Module🔗
Foundation