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Filling-in by joint interpolation of vector fields and gray levels
C Ballester1, M Bertalmio, V Caselles
1Dept. de Tecnologia, Pompeu-Fabra Univ., Barcelona, Spain. coloma.ballester@tecn.upf.es
Summary
This study introduces a variational method to fill missing image data by interpolating gray levels and gradient directions. This approach automatically extends image structures into missing regions, enabling image restoration and object removal.
Area of Science:
- Computer Vision
- Image Processing
- Computational Mathematics
Background:
- Digital image restoration often requires filling missing data regions.
- Existing methods may struggle with complex hole topologies or simultaneous processing of multiple regions.
Purpose of the Study:
- To introduce a novel variational approach for robustly filling missing data in digital images.
- To develop a method that smoothly extends image features into missing regions automatically.
- To address limitations of existing techniques regarding hole topology and simultaneous processing.
Main Methods:
- A variational approach based on joint interpolation of image gray levels and gradient/isophote directions.
- Solving the variational problem using a gradient descent flow, resulting in coupled second-order partial differential equations.
- Extending isophote lines automatically into missing data regions.
Main Results:
- The proposed method can fill holes of any topology, processing multiple regions simultaneously.
- The approach effectively extends image structures into missing areas, guided by the principle of good continuation.
- Demonstrated applications in restoring old photographs and removing superimposed text (dates, subtitles).
Conclusions:
- The variational approach provides a powerful and flexible method for image inpainting.
- The gradient descent flow offers a stable and effective computational framework for the proposed method.
- Theoretical results support the validity and efficacy of the developed image restoration technique.
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