# CurvatureFlowFilter

CurvatureFlowFilter[image]

applies a mean curvature flow filter to image.

CurvatureFlowFilter[image,t]

specifies the amount of curvature flow time t to be applied.

CurvatureFlowFilter[image,t,k]

applies the curvature flow with a modified conductance term parametrized by k.

# Details

• Curvature flow filtering is an anisotropic diffusion method used for smoothing images while preserving edges. It effectively spreads the curvature along a contour, thereby rounding corners and reducing the Euclidean length of contours.
• CurvatureFlowFilter implements a Euclidean shortening filter.
• CurvatureFlowFilter works on 2D grayscale or multichannel images, operating on each channel separately.
• The diffusion in a curvature flow filter runs parallel to the image contours. Diffusion perpendicular to the contours is omitted in order to preserve edges.
• The effect of CurvatureFlowFilter does not depend on the overall normalization of the image values.
• The conductance parameter k can take any positive value. The default value k= renders the unmodified curvature flow filter.
• CurvatureFlowFilter[image] is equivalent to CurvatureFlowFilter[image,1,].
• CurvatureFlowFilter applies the partial differential equation with the contour curvature to every image channel .
• In CurvatureFlowFilter[image,t], t parametrizes the evolution of the curvature flow and thereby the spatial range of the filter.
• If a parameter k is supplied, the curvature flow with a modified conductance term is used.

# Examples

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## Basic Examples(1)

Diffusing an angiography image:

## Scope(4)

### Data(2)

Filtering of grayscale image:

Filtering of multichannel image:

### Parameters(2)

Specify the amount of diffusion:

Specify the conductance term:

## Applications(6)

Remove salt-and-pepper noise:

Remove Gaussian color noise from an image:

Remove smaller circles from the image:

Use a CurvatureFlowFilter to remove smaller stars from an astronomical image:

Smooth the image before converting it to a vector graphic:

## Properties & Relations(1)

CurvatureFlowFilter returns an image of a real type:

Wolfram Research (2010), CurvatureFlowFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/CurvatureFlowFilter.html.

#### Text

Wolfram Research (2010), CurvatureFlowFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/CurvatureFlowFilter.html.

#### CMS

Wolfram Language. 2010. "CurvatureFlowFilter." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CurvatureFlowFilter.html.

#### APA

Wolfram Language. (2010). CurvatureFlowFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CurvatureFlowFilter.html

#### BibTeX

@misc{reference.wolfram_2023_curvatureflowfilter, author="Wolfram Research", title="{CurvatureFlowFilter}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/CurvatureFlowFilter.html}", note=[Accessed: 29-May-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_curvatureflowfilter, organization={Wolfram Research}, title={CurvatureFlowFilter}, year={2010}, url={https://reference.wolfram.com/language/ref/CurvatureFlowFilter.html}, note=[Accessed: 29-May-2023 ]}