Regularised Diffusion-Shock Inpainting

Area of Science:

• Image processing
• Partial differential equations
• Computer vision

Background:

• Image inpainting is crucial for reconstructing missing image regions.
• Existing diffusion-shock methods face challenges with parameter reduction and discrete implementation.
• Anisotropic methods often struggle with maintaining edge sharpness and efficiency.

Purpose of the Study:

• To introduce Regularised Diffusion-Shock (RDS) inpainting, an improved technique for image restoration.
• To enhance the efficiency and reduce the parameter complexity of diffusion-shock inpainting.
• To extend RDS inpainting to handle vector-valued image data.

Main Methods:

• Combining homogeneous diffusion and coherence-enhancing shock filtering.
• Developing a second-order equation that inherits a maximum-minimum principle.
• Implementing regularization to reduce model parameters significantly.
• Extending the method for vector-valued data processing.

Main Results:

• RDS inpainting achieves high-quality results with drastically reduced parameters.
• The method preserves edge sharpness and fills large areas efficiently.
• Performance is comparable or superior to existing PDE-based and integrodifferential inpainting models.
• Successful extension to vector-valued data inpainting.

Conclusions:

• RDS inpainting offers a significant advancement in image restoration.
• The regularization technique overcomes previous limitations in parameter efficiency.
• The method provides a robust and versatile solution for various inpainting tasks, including vector-valued data.