Three examples of inpainting using the Navier-Stokes based method

from M. Bertalmio, A. Bertozzi, and G. Sapiro, CVPR 2001.


The idea

Image inpainting involves filling in part of an image or video using information from the surrounding area. Applications include the restoration of damaged photographs and movies and the removal of selected objects. In this paper, we introduce a class of automated methods for digital inpainting. The approach uses ideas from classical fluid dynamics to propagate isophote lines continuously from the exterior into the region to be inpainted. The main idea is to think of the image intensity as a `stream function' for a two-dimensional incompressible flow. The Laplacian of the image intensity plays the role of the vorticity of the fluid; it is transported into the region to be inpainted by a vector field defined by the stream function. The resulting algorithm is designed to continue isophotes while matching gradient vectors at the boundary of the inpainting region. The method is directly based on the Navier-Stokes equations for fluid dynamics, which has the immediate advantage of well-developed theoretical and numerical results. This is a new approach for introducing ideas from computational fluid dynamics into problems in computer vision and image analysis.
Move the cursor onto the image to see the NS restoration.

Inpainting of stills


Frame-by-frame video inpainting

Move the cursor onto the video image to see the restored video.

The foreman video overwritten with red lettering.


Super-resolution

Super resolution of one of the eyes from this photograph.

The left shows a section of an image magnified 9 times. The middle image is modified by standard bicubic interpolation. The right image is the result of Navier-Stokes inpainting performed by fixing pivot points in the middle of the cells and evolving all other pixels.


Computations performed by M. Bertalmio. Cool html tricks thanks to Matt Matthews.