harmonic_interpolationharmonic_interpolationHarmonicInterpolationHarmonicInterpolationharmonic_interpolation (算子)

名称

harmonic_interpolationharmonic_interpolationHarmonicInterpolationHarmonicInterpolationharmonic_interpolation — 对图像区域执行谐波插值。

签名

描述

算子 harmonic_interpolationharmonic_interpolationHarmonicInterpolationHarmonicInterpolationHarmonicInterpolationharmonic_interpolation reconstructs the destroyed image data of ImageImageImageImageimageimage inside the region RegionRegionRegionRegionregionregion 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 RegionRegionRegionRegionregionregion, 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 RegionRegionRegionRegionregionregion 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

请注意，若使用域缩减后的图像作为输入，滤波器算子可能会返回意外结果。请参阅 滤波器 一章

执行信息

• 多线程类型：可重入（与非独占算子并行运行）。
• 多线程作用域：全局（可从任何线程调用）。
• 在元组级别上自动并行化。
• 在通道级别上自动并行化。
• 在内部数据级别上自动并行化。

参数

替代

inpainting_ctinpainting_ctInpaintingCtInpaintingCtInpaintingCtinpainting_ct, inpainting_anisoinpainting_anisoInpaintingAnisoInpaintingAnisoInpaintingAnisoinpainting_aniso, inpainting_mcfinpainting_mcfInpaintingMcfInpaintingMcfInpaintingMcfinpainting_mcf, inpainting_textureinpainting_textureInpaintingTextureInpaintingTextureInpaintingTextureinpainting_texture, inpainting_cedinpainting_cedInpaintingCedInpaintingCedInpaintingCedinpainting_ced

参考文献

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

模块

基础