harmonic_interpolationharmonic_interpolationHarmonicInterpolationHarmonicInterpolationharmonic_interpolation (算子名称)

名称

harmonic_interpolationharmonic_interpolationHarmonicInterpolationHarmonicInterpolationharmonic_interpolation — Perform a harmonic interpolation on an image region.

参数签名

描述

该算子 harmonic_interpolationharmonic_interpolationHarmonicInterpolationHarmonicInterpolationHarmonicInterpolationharmonic_interpolation reconstructs the destroyed image data of ImageImageImageImageimageimage inside the region 区域区域区域区域区域区域 by solving the discrete Laplace equation for the corresponding gray value function u. The unique solution, which exists under Dirichlet boundary conditions given by ImageImageImageImageimageimage outside of 区域区域区域区域区域区域, is returned in InpaintedImageInpaintedImageInpaintedImageInpaintedImageinpaintedImageinpainted_image.

This technique is called harmonic interpolation since in function theory the solutions of the Laplace equation are referred to as harmonic functions.

If 区域区域区域区域区域区域 touches the border of the gray value matrix of ImageImageImageImageimageimage and thus some Dirichlet boundary values do not exist, von Neumann boundary conditions are used instead. This means that the gray values are mirrored at the border of ImageImageImageImageimageimage. If no Dirichlet boundary values exist at all, a constant image with gray value 0 is returned.

The spatial derivatives are discretized as and . The equation is solved by an iterative conjugate gradient solver, which iteratively improves the computational error until the maximum norm of its update step becomes a smaller fraction than PrecisionPrecisionPrecisionPrecisionprecisionprecision of the norm of the input data or a maximum of 1000 iterations is reached. PrecisionPrecisionPrecisionPrecisionprecisionprecision = 0.01 thus means a relative computational accuracy of 1%.

注意

Note that filter operators may return unexpected results if an image with a reduced domain is used as input. Please refer to the chapter 过滤器.

运行信息

• 多线程类型:可重入(与非独占操作符并行运行)。
• 多线程作用域:全局(可以从任何线程调用)。
• 在元组级别自动并行化。
• 在图像通道级别自动并行化。
• Automatically parallelized on internal data level.

参数表

可替代算子

inpainting_ctinpainting_ctInpaintingCtInpaintingCtInpaintingCtinpainting_ct, inpainting_anisoinpainting_anisoInpaintingAnisoInpaintingAnisoInpaintingAnisoinpainting_aniso, inpainting_mcfinpainting_mcfInpaintingMcfInpaintingMcfInpaintingMcfinpainting_mcf, inpainting_textureinpainting_textureInpaintingTextureInpaintingTextureInpaintingTextureinpainting_texture, inpainting_cedinpainting_cedInpaintingCedInpaintingCedInpaintingCedinpainting_ced

References

L.C. Evans; “Partial Differential Equations”; AMS, Providence; 1998.
W. Hackbusch; “Iterative Lösung großer schwachbesetzter Gleichungssysteme”; Teubner, Stuttgart;1991.

模块

Foundation

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