Connecting image inpainting with denoising in the homogeneous diffusion setting

Area of Science:

• Computer Vision
• Image Processing
• Mathematical Modeling

Background:

• Local methods in image denoising and inpainting share conceptual similarities.
• The relationship between these two image processing tasks remains underexplored.

Purpose of the Study:

• To establish a theoretical link between image denoising and inpainting.
• To investigate the denoising by inpainting (DbI) framework in the homogeneous diffusion setting.

Main Methods:

• Studied a denoising by inpainting (DbI) framework averaging multiple inpainting results.
• Derived equivalence between DbI and homogeneous diffusion filtering in 1D.
• Empirically extended findings to 2D and nonhomogeneous diffusion scenarios.

Main Results:

• Established an explicit relation between density and diffusion time for 1D DbI and homogeneous diffusion.
• Experimental results confirm the theoretical findings.
• Demonstrated potential generalization to nonhomogeneous data and diffusivities.

Conclusions:

• The study bridges denoising and inpainting through a unified diffusion framework.
• Highlights the significance of data adaptivity in image processing models.
• Suggests data adaptivity can rival operator adaptivity in performance.