Poisson Image Editing Patric Perez Michel Gangnet and

Poisson Image Editing Patric Perez, Michel Gangnet, and Andrew Black (SIGGRAPH 2003) Presentation by : Lingli He 6 , jun 2017 1

Input Images source image target image 2

Editing Results Simple Cloning Result Poisson Seamless Cloning 3

Motivation • Problems : how to remove the seams between the mixed images 4

Goals • importing (cloning) transparent and opaque source image regions into a destination image in a seamless and effortless manner. • Seamless modification of appearance of the image within a selected region. 5

Background • A famous psychologists show that the secondorder variations extracted by the Laplacian operator are the most significant perceptually (Land Mc. Cann 1971) • A scalar function on a bounded domain is uniquely defined by its values on the boundary and its Laplacian in the interior. • The Poisson equation has a unique solution. 6

Related work– poisson equation Fattal et al. 2002 Entire images Lewis 2001 harmonic interpolation Our method Local images Our method Guided Interpolation 7

Related work—multiresolution images blending • Burt and Adelson 1983 long range(larger gradient) mixing • Poisson seamless cloning small gradient 8

Related work– seamless cloning inpainting techniques-PDE. more complex than poisson equation ( Bertalmio et al. 2000 ) Example-based interpolation methods ; handle large holes and textured boundaries ( Barret and Cheney 2002) a guided interpolation framework , with the guidance being selected by the user , and this framework is not limited in seamless cloning 9

Interpolation Problem • • S: a closed subset of R 2 Ω: a closed subset of S, with boundary ∂Ω f*: known scalar function over SΩ f: unknown scalar function over Ω 10

Membrane Interpolation • To find the value of f , Solve the following minimization problem: the gradient operator • subject to Dirichlet boundary conditions: 11

Solution : Euler-Lagrange Equation 12

Laplace Equation • Solution: Laplace Equation with Dirichlet boundary conditions Laplacian operator • this method produces an unsatisfactory due to over-blurring 13

Guided Interpolation • v: guided field • v may be gradient of a function g 14

Guided Interpolation • Solve the following minimization problem: • subject to Dirichlet boundary conditions: 15

Poisson Equation • Solution : This time the Euler-Lagrange equation reduces to the Poisson equation: • written more concisely as: G denotes v 16

if v is conservative • If v is the gradient of an image g • Correction function so that • performs membrane interpolation over Ω: 17

Discrete Poisson Solver • Discretize directly by : Discretized gradient Discretized v: g(p)-g(q) all pairs that are in Ω) • for neighbors p and q with 18

Discrete Poisson Solver • Partial Derivative for neighborhood overlaps boundary(Big yet sparse linear system): • Partial Derivative for interior points: 19

Discrete Poisson Solver: solution • Linear system of equations • sparse (banded) • Symmetric • positive-definite • Irregular shape of boundary requires general solver, such as • Gauss-Seidel iteration with successive overrelaxation • V-cycle Multi-grid • System can be solved at interactive rates 20

Seamless Cloning • Import Gradients from a Source Image g • Discretization ： • Solving Poisson equation: 21

Seamless Cloning Results • Concealment • By importing seamlessly a piece of the background • Multiple strokes input output 22

Seamless Cloning Results • Insertion 23

Seamless Cloning Results • Feature exchange 24

Mixing Gradients • To combine properties of background f* with those of selected resource g • Two Variants of V • v averaged from source and destination gradients (insert transparent images) • Select stronger one from source and destination gradients 25

Mixing Gradients • Variant of V: • Discretization : 26

Mixing Gradients Results • Inserting objects with holes 27

Mixing Gradients Results • Inserting one object close to another 28

Texture Flattening • A sparse sieve ：Preserve only salient gradients × • Discretization : with masking function so that: 29

Texture Flattening results input output 30

Local Illumination Changes • Approximate tone mapping transformation after Fattal et al. 2002: × • Attenuating large gradients 31

Local illumination Changes results input output 32

Local Color Changes • Mix two differently colored version of original image – One provides f * outside – One provides g inside 33

Seamless Tiling • Select original image as g Boundary Bou condition: nda – f *north = f *south = 0. 5 (gnorth + gsouth) – Similarly for the east and west input ry c ond ition cha n ged output 34

Conclusions • Using the generic framework of guided interpolation to develop a variety of tools to edit the contents of an images selection in a seamless and effortless manner. • Seamlessly edit images via poisson solution to guided interpolation under Dirichlet boundary conditions 35

Limitations • Cloning requires either of the images to be smooth • Minimization only adapts low-frequency Content • The backgrounds in resource and destination should be similar 36

Future works • To combine the cloning facilities and the editing ones • Extend the editing facilities to deal with the sharpness of objects of interest • Extend the cloning facilities the editing facilities to 3 D images 37

Thank you! 38

Questions • How to do the Concealment in the 22 page ? • By importing seamlessly a piece of the background, complete objects, parts of objects, and undesirable artifacts can easily be hidden. We need multiple strokes. • How to determine the number of neighbors of p in the 18 page ? • It is a experience point. The number of neighbors of p is two in the 1 D, and four in the 2 D. 39

Questions • Why can the decolorization of background be recolor when changing the local Color of a image ? • Poisson solver can produce three color channel independently by solving three independent poisson equation. 40