Simultaneous Structure and Texture Image Inpainting by: Bertalmio, Sapiro, Vese, Osher Presented by: Shane Brennan June 7, 2007 EE 264 – Spring 2007

What Is Inpainting?

Inpainting can also be used for other purposes including: Humor Entertainment Improving aesthetic quality of images And for less playful purposes…

How To Inpaint (yes you can do it too!) Identify the regions you want to fill/remove Continue any lines arriving at those regions Fill in the regions with texture/color from the surrounding areas Enjoy!

Image Inpainting by: Marcelo Bertalmio and Guillermo Sapiro Proceedings of SIGGRAPH 2000

The (very) Basic Idea Form an iterative algorithm Each update gets you closer to the desired result

The Update Image Want to propagate “information” (aka lines) into the region being inpainted Need information, and direction it is heading Project information on that direction Rate of Change of Information Direction of Information

What Is Information? Since want result to be smooth, use laplacian of the image to represent information. L = I * 2 The rate of change of the information entering a pixel is the derivative of the laplacian = [L i,j+1 - L i,j-1, L i+1,j – L i-1,j ]

Propagation Direction Tangent to the isophate line (which is the information) arriving at the boundary Tangent easily computed as: N = [-I Y, I x ] note: I use the (x,y) coordinate notation

Anisotropic Diffusion Areas where N = [0, 0] will never get updated! These are smooth regions “Bleed” smooth regions into the region being inpainted Also ensures lines stay smooth and curved BUT! Very problematic! My form of diffusion: The authors form: ???

Bad Result Due to My Diffusion

How About Texture?

Texture Synthesis by Non- Parametric Sampling by: Alexei Efros and Thomas Leung IEEE International Conference on Computer Vision, Corfu, Greece, September 1999

How It Works Take a pixel to be synthesized. Find which pixels near it have already been synthesized (or pre-existed). Define this to be the mask For every pixel in the image (the candidates), compare the WxW neighborhood to the neighborhood around the pixel to be synthesized using a distance metric, but only on pixels defined by the mask Keep either the K most similar neighborhoods, or the neighborhoods whose distance is less than T (W, K, and T are user-defined values) Of the remaining regions, select one at random Assign the intensity of the center pixel of the selected region to the pixel being synthesized

A Visualization…

How About Structure?

The Problem Image inpainting works well on regions with structure, but not on regions with texture Texture synthesis works well on regions with texture, but not on regions with structure Early papers: for each pixel decide if structure or texture, and perform the appropriate filling method But there is a better way…

Simultaneous Structure and Texture Image Inpainting by: Bertalmio, Sapiro, Vese, Osher IEEE Transactions On Image Processing, Vol. 12, No. 8, August 2003

How It Works Decompose image into two parts: structure image and texture image Perform inpainting on the structure image Perform texture synthesis on the texture image Recombine the two images to get final result But how to decompose? no, not like that

Modeling Textures With Total Variation Minimization and Oscillating Patterns in Image Processing by: Stanley Osher and Luminita Vese Journal of Scientific Computing, Vol. 19, Nos. 1–3, December 2003

The Initial Version Considered an image to be some underlying “real image” and then noise added. Want to remove the noise (Rudin, Ohser, and Fatemi. 1992) Find structure image, u, that minimizes: Smoothness Term Data Fidelity

Incorporating the Texture No texture in there! But lets consider image to be f = u + v, where u is structure and v is texture. Note v = f – u Solutions to this are known! (refer to report for some references on the solution)

Cutting to the Chase Model texture as x and y components, call them g 1 and g 2 Some magic... (refer to the paper for more) Smoothness on uReconstruction Error Smoothness on v (remove noise)

An Iterative Solution Break the optimization down into an iterative solution. Although more iterations aren’t always better, in practice need to play with # of iterations Also need to play with tuning parameters. Though there are default values which work well in a broad array of images

Original Image (f) Structure Image (u) Texture Image (v)

Original Image (f)Structure Image (u) Texture Image (v)

Back to Inpainting!

The Algorithm Decompose I in into sub-images u and v Perform inpainting on u to obtain U Perform texture synthesis on v to obtain V I out = U + V And now for some results…

Original Image Structure Image Texture Image Completed Image Inpainted Structure Image Synthesized Texture Image

Original Image Structure Image Texture Image Completed Image Inpainted Structure Image Synthesized Texture Image

Original Image Structure Image Texture Image Completed Image Inpainted Structure Image Synthesized Texture Image

References M. Bertalmio, G. Sapiro, V. Caselles, and C. Ballester. Image inpainting A. A. Efros and T. K. Leung. Texture synthesis by non-parametric sampling. In ICCV (2), pages1033–1038, M. Bertalmio, L. Vese, G. Sapiro, and S. Osher. Simultaneous structure and texture image inpainting, L. Vese and S. Osher. Modeling textures with total variation minimization and oscillating patterns in image processing, 2002.