applies a mean curvature flow filter to image.

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

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


  • 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 arbitrary 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,Infinity].
  • applies the partial differential equation partial_tf=kappa TemplateBox[{{del , f}}, Abs] with the contour curvature kappa= del . (del f)/(TemplateBox[{{del , f}}, Abs]) 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 partial_tf=TemplateBox[{{del , f}}, Abs]del .c_k(TemplateBox[{{del , f}}, Abs]) (del f)/(TemplateBox[{{del , f}}, Abs]) with a modified conductance term c_k(TemplateBox[{{del , f}}, Abs])=ⅇ^(-|del f|^2/k^2) is used.
Introduced in 2010