An Image Inpainting Algorithm Based On A Modified TV-Stokes Equation

Image inpainting is one of the important contents in the field of image restoration,and also one of research hotspots in many fields such as computer vision, computergraphics and digital image processing, etc. The so-called image inpainting is to fill theregion in an image where information is missing so as for observers not to perceive thatthe damaged areas have been repaired.The image inpainting technology has very high application value in many fields. Forexample, it may be used in film and television special effects, conservation of culturalrelics, restoration of old photos, removal of obstacles and texts in an image, anderror concealment in the videos, etc.In2006, Xue-Cheng Tai et al. proposed a TV-Stokes equation-based model for imageinpainting. First, they applied energy minimization model and zero divergence conditionto get a nonlinear Stokes equation. Then, they transmitted the isophote directions into theareas waiting for the repair through this equation. Once the isophote directions areconstructed, the image inpainting may be implemented according to the isophote directions.In this dissertation, after improving the above model simply, we present a new imageinpainting algorithm. The chapters in this dissertation are arranged as follows:In the first chapter, we mainly introduce the research background, research situationat home and abroad, and application prospect about the image inpainting technology. Atthe same time, we briefly introduce the work of this dissertation and give the relevantpreliminary knowledge.In the second chapter, we introduce several kinds of common image inpaintingmodels based on the variational PDEs, mainly including BSCB model, CDD model and theTV-Stokes equatom-based image inpainting model.The third chapter is the main work of this dissertation. We first use the p-harmonicmodel to modify the energy minimization functional in the TV-Stokes model, thentogether with zero divergence condition to get a nonlinear Stokes equation. Then, wetransmitted the isophote directions into the areas waiting for the repair through thisequation. After the isophote directions are constructed, we use the augmented Lagrangianmethod to restore the image. In the fourth chapter, we give the relevant numerical experimental results. Finally, wesummarize the whole dissertation.