inpainting_mcfinpainting_mcfInpaintingMcfInpaintingMcfinpainting_mcf (Operator)


inpainting_mcfinpainting_mcfInpaintingMcfInpaintingMcfinpainting_mcf — Perform an inpainting by smoothing of level lines.


inpainting_mcf(Image, Region : InpaintedImage : Sigma, Theta, Iterations : )

Herror inpainting_mcf(const Hobject Image, const Hobject Region, Hobject* InpaintedImage, double Sigma, double Theta, const Hlong Iterations)

Herror T_inpainting_mcf(const Hobject Image, const Hobject Region, Hobject* InpaintedImage, const Htuple Sigma, const Htuple Theta, const Htuple Iterations)

void InpaintingMcf(const HObject& Image, const HObject& Region, HObject* InpaintedImage, const HTuple& Sigma, const HTuple& Theta, const HTuple& Iterations)

HImage HImage::InpaintingMcf(const HRegion& Region, double Sigma, double Theta, Hlong Iterations) const

static void HOperatorSet.InpaintingMcf(HObject image, HObject region, out HObject inpaintedImage, HTuple sigma, HTuple theta, HTuple iterations)

HImage HImage.InpaintingMcf(HRegion region, double sigma, double theta, int iterations)

def inpainting_mcf(image: HObject, region: HObject, sigma: float, theta: float, iterations: int) -> HObject


The operator inpainting_mcfinpainting_mcfInpaintingMcfInpaintingMcfInpaintingMcfinpainting_mcf extends the image edges that adjoin the region RegionRegionRegionRegionregionregion of the input image ImageImageImageImageimageimage into the interior of RegionRegionRegionRegionregionregion and connects their ends by smoothing the level lines of the gray value function of ImageImageImageImageimageimage.

This happens through the application of the mean curvature flow or intrinsic heat equation on the gray value function u defined in the region RegionRegionRegionRegionregionregion by the input image ImageImageImageImageimageimage at a time . The discretized equation is solved in IterationsIterationsIterationsIterationsiterationsiterations time steps of length ThetaThetaThetaThetathetatheta, so that the output image InpaintedImageInpaintedImageInpaintedImageInpaintedImageinpaintedImageinpainted_image contains the gray value function at the time IterationsIterationsIterationsIterationsiterationsiterations * ThetaThetaThetaThetathetatheta .

A stationary state of the mean curvature flow equation, which is also the basis of the operator mean_curvature_flowmean_curvature_flowMeanCurvatureFlowMeanCurvatureFlowMeanCurvatureFlowmean_curvature_flow, has the special property that the level lines of u all have the curvature 0. This means that after sufficiently many iterations there are only straight edges left inside the computation area of the output image InpaintedImageInpaintedImageInpaintedImageInpaintedImageinpaintedImageinpainted_image. By this, the structure of objects inside of RegionRegionRegionRegionregionregion can be simplified, while the remaining edges are continuously connected to those of the surrounding image matrix. This allows for a removal of image errors and unwanted objects in the input image, a so called image inpainting, which is only weakly visible to a human beholder since there remain no obvious artifacts or smudges.

To detect the image direction more robustly, in particular on noisy input data, an additional isotropic smoothing step can precede the computation of the gray value gradients. The parameter SigmaSigmaSigmaSigmasigmasigma determines the magnitude of the smoothing by means of the standard deviation of a corresponding Gaussian convolution kernel, as used in the operator isotropic_diffusionisotropic_diffusionIsotropicDiffusionIsotropicDiffusionIsotropicDiffusionisotropic_diffusion for isotropic image smoothing.


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


ImageImageImageImageimageimage (input_object)  (multichannel-)image(-array) objectHImageHObjectHImageHobject (byte / uint2 / real)

Input image.

RegionRegionRegionRegionregionregion (input_object)  region objectHRegionHObjectHRegionHobject

Inpainting region.

InpaintedImageInpaintedImageInpaintedImageInpaintedImageinpaintedImageinpainted_image (output_object)  image(-array) objectHImageHObjectHImageHobject * (byte / uint2 / real)

Output image.

SigmaSigmaSigmaSigmasigmasigma (input_control)  real HTuplefloatHTupleHtuple (real) (double) (double) (double)

Smoothing for derivative operator.

Default value: 0.5

Suggested values: 0.0, 0.1, 0.5, 1.0

Restriction: Sigma >= 0

ThetaThetaThetaThetathetatheta (input_control)  real HTuplefloatHTupleHtuple (real) (double) (double) (double)

Time step.

Default value: 0.5

Suggested values: 0.1, 0.2, 0.3, 0.4, 0.5

Restriction: 0 < Theta <= 0.5

IterationsIterationsIterationsIterationsiterationsiterations (input_control)  integer HTupleintHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Number of iterations.

Default value: 10

Suggested values: 1, 5, 10, 20, 50, 100, 500

Restriction: Iterations >= 1


harmonic_interpolationharmonic_interpolationHarmonicInterpolationHarmonicInterpolationHarmonicInterpolationharmonic_interpolation, inpainting_ctinpainting_ctInpaintingCtInpaintingCtInpaintingCtinpainting_ct, inpainting_anisoinpainting_anisoInpaintingAnisoInpaintingAnisoInpaintingAnisoinpainting_aniso, inpainting_cedinpainting_cedInpaintingCedInpaintingCedInpaintingCedinpainting_ced, inpainting_textureinpainting_textureInpaintingTextureInpaintingTextureInpaintingTextureinpainting_texture


M. G. Crandall, P. Lions; “Convergent Difference Schemes for Nonlinear Parabolic Equations and Mean Curvature Motion”; Numer. Math. 75 pp. 17-41; 1996.
G. Aubert, P. Kornprobst; “Mathematical Problems in Image Processing”; Applied Mathematical Sciences 147; Springer, New York; 2002.