Advanced Topics in Computer Graphics Exercise 1 Poisson Image Editing Due date: Presentation by: Tommer Leyvand

General Description The purpose of this exercise is to understand and implement a Poisson seamless cloning image editing tool. Part 1: Smooth image completion Part 2: Poisson seamless cloning

Input Images source image target image

Simple Cloning Result

Poisson Seamless Cloning Result

Some More Results source images target image

Some More Results source images simple cloning

Some More Results source images Poisson seamless cloning

Part 1 Smooth Completion

Image as a 2D Function

Smooth Image Completion What if there is a missing area ? f* – the known image Scalar 2D function from (x,y) to grayscale value. f - the image in the unknown area Ω – the unknown area (domain of f) Will complete the area as smoothly as possible.

Smooth Image Completion (Cont.) Finding the minimum: Euler-Lagrange Discrete Aprx:

Discrete Derivate in 1D  Given a discrete function f(x i )=f i x f f(x i ) f(x j )

Smooth Image Completion (Solving)  Each f x,y is an unknown variable x i, total of N variables (covering the unknown pixels)  Reduces to the sparse algebraic system: N x N = 00b1b2000b3000b1b2000b Known values of f() contribute to the left side x i-w +x i-1 -4x i +x i+1 =-f(x,y+1) f x,y-1 +f x-1,y -4f x,y +f x+1,y +f x,y+1 =0 => x i-w +x i-1 -4x i +x i+1 +x i+w =0 x1x2…xNx1x2…xN

Program Usage The program generates one output image Ex1 –complete Ex1 –complete R G B <output> Where R,G,B are the RGB values [0..255] of the unknown color (usually best as black 0,0,0) Example: Example: Ex1 –complete in1.bmp out1.bmp Ex1 –complete in1.bmp out1.bmp

Wow result input result ground truth

Part 2 Poisson Cloning

Poisson Cloning: “Guiding” the completion  We can guide the completion from part1 to fill the hole using gradients from another source image  Reverse: Seek a function f whose gradients are closest to the gradients of the source image

Poisson Cloning (forward difference) (backward difference)

Poisson Cloning (Solving)  Each f x,y is a variable x i as before, solving  As before this reduces to a sparse algebraic system f x,y-1 +f x-1,y -4f x,y +f x+1,y +f x,y+1 =divG(x,y) => x i-w +x i-1 -4x i +x i+1 +x i+w =divG(x,y)

Program Usage The program generates one output image Ex1 –clone Ex1 –clone x y x y Where x y are the offset for the paste

General Guidelines

Important Remarks  You should write the programs in C or C++ or Matlab.  Document your program thoroughly.  In this assignment there is no need to open a window or use OpenGL in any way.  Visit the exercise web-page

Important Remarks  The work can be done in pairs.  Submit your work on diskettes (or CD’s). Hardcopy of the documentation. Do not print the source-code Do not print the source-code In the documentation: Answer the questions from exercise website In the documentation: Answer the questions from exercise website  Points will be rewarded for nice and original images.

More Important Remarks  Don't forget to check the number of parameters that your program receives.  Don't forget to check memory allocations, if they succeeded or failed.  Pay attention to the borders of the image.  Visualize the gradients/div to better understand what is going on

A Little Help  IrfanView – An image viewer, editor.  FreeImage/CxImage – Open source libraries (C/C++) for working with images.  TAUCS – Sparse solver  See links on the exercise webpage  Important questions: me tommer -a--t- tau.ac.il me tommer -a--t- tau.ac.il