Skip to content

Blending images using Poisson’s equation and sparse matrices

License

Notifications You must be signed in to change notification settings

Haim-Segal/Poisson-Blending

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 

History

44 Commits
 
 
 
 
 
 

Repository files navigation

Poisson Blending

Blending images using Poisson’s equation and sparse matrices

Poisson Blending is an algorithm used in image processing for achieving a realistic looking composition of two images using Discrete Poisson equation. The key idea is to approach this challenge as Dirichlet problem. In particular, let us treat the overlapping region between the images (a source image being inserted into a destination image) as the potential field caused by a given density distribution of electric charge or mass which in our case will be related to the laplacian of the images, and as the fixed boundary condition we will take the values of the destination image on the boundary curve enclosing the source image patch.

Finally, we deal with a linear system of equations represented by Ax=b, where the size of the coefficient matrix A is NxN, where N is the number of the pixels in the source image. In order to construct and solve this system I use the great library of Algebraic Multigrid (AMG) solvers PyAMG.

Results

naive blending Naive Blended

Poisson blending Poisson Blended

original images links: source image, destination image

Installation and Usage

run Poisson Blending 2D.py and follow the instructions

Enjoy!

References

Patrick Perez, Michel Gangnet, Andrew Blake, "Poisson Image Editing".