# Undergraduate Colloquium for Midyear 2022

You are all invited to the undergraduate colloquium of Ms. Rachel Noelle D. Carrido on **Tuesday, 9 August 2022, 10:00 AM**.

** Title:** A Total Variation Approach to Image Inpainting

**Rhudaina Z. Mohammad**

*Adviser:***Erika Antonette T. Enriquez**

*Examiner:*** Abstract:** Inpainting is the image processing task of restoring any missing information in a damaged image or an ancient painting in an undetectable manner. This study focuses on local inpainting of digital images, in particular, the total variation (TV) inpainting model developed by T.F. Chan and J. Shen. We begin with an in-depth discussion on the mathematical framework of image inpainting, including the existence of a noise-free TV inpainting. To numerically implement this model, we derive its corresponding Euler-Lagrange equation, which in turn, is solved using the finite difference method. Lastly, we conduct numerical tests on the model’s performance and present computational examples.

**image inpainting, total variation, Euler-Lagrange equation, finite difference method**

*Keywords:*