Poisson image Editing (Poisson images editing)

Written by Samson Mulder @ samsonlab.com

For more information visit http://www.samsonlab.com

The Open course abroad is very hot recently. Many students like to see a public course at Stanford, Massachusetts. But the biggest tragedy of domestic college students is that they don't want to do homework. Many people take a look at the open class and it's over, and very few people will do their homework. I saw Stanford's machine learning during college and I liked it. Especially inside that auto-navigating vehicle and three-dimensional reconstruction technology. The auto-guided car finally did a real job in the Freescale game during college. and three-dimensional reconstruction technology is really difficult. Until now, I haven't been able to make a demo. Want to feel that they are a step across too high, there is no gradual process. So they looked for a computer vision course at Brown University, which, according to their project, was shallow to hard and might be better.

Interested students can refer to this link: http://www.cs.brown.edu/courses/csci1950-g/

Today we will discuss the next Proj 2, Poisson image blending

Speaking of Poisson, you can mention the students of the Poisson's teacher, Laplace. To learn the image or signal, it must be familiar to the Laplace operator and the Laplace convolution. Before Poisson image fusion occurs, there is also a fusion algorithm called Laplacian pyramid blending. The two effects can be seen in the following diagram:

Unmatched window Drawing Fusion	Poisson Blend	Laplacian

(Image provided by Steve Gomez of Brown University)

The key to Poisson fusion is to get the transformed pixels by solving the Poisson equation. Poisson equation

Poisson's equation is a kind of partial differential equation in mathematics, which is common in electrostatics, mechanical engineering and theoretical physics. The equation form is as follows:

Δf =−ρ

The Δ here represents the Laplace operator,

δ≡∂2∂2x+∂2∂2y

The F and ρ can be the equations of real or complex numbers on the manifold. wherein the ρ can be expressed as ρ=ρ (x, y) in the form. Poisson image editing

Poisson image editing is an important application of Poisson equation, the first point of this application is Poisson image editing. SIGGRAPH 2003, this article on the current image editing technology has a very important impact, followed by a lot of similar image editing methods, such as [Jiaya Jia et al. Drag And-drop pasting] In 2006, the optimal fusion boundary was proposed to improve the effect of the Poisson image editing, [Zeev Farbman et al. coordinates for instant image cloning] was proposed in SIGGRAPH 2009 using Mean-value Coordinates is used to calculate image editing based on gradient domain, the method is simple and fast, thus avoids solving the complex Poisson equation. The following are some typical applications for the powerful function of the Minppasun equation in image editing.

Seamless Integration

The traditional image fusion precisely chooses the Fusion region: the process is tedious and the workload is big, often cannot obtain the good result alpha-matting: The function is powerful, but realizes the complex based on the Poisson equation seamless Fusion chooses the fusion region the process simple and the convenience finally can obtain the seamless fusion result, We choose a seamless fusion of images based on the Poisson equation method. Why the Poisson equation is applied to the image
Easy to apply in the gradient domain of images through local image editing → global fusion effect Seamless fusion application-image synthesis, image editing, image stitching variational method Interpretation Poisson image editing

The Delta i_a represents the gradient of the fused image block, and the meaning of the variational equation above shows that our seamless fusion is guided by the gradient field in the source image block, which smoothly spreads the difference between the target scene and the source image in the fusion boundary to the fusion image block I, so The fused image blocks can be seamlessly fused to the target scene, and their hue and illumination can be consistent with the target scene. An example of image editing based on Poisson equation Image Synthesis

As shown in the following illustration, we use two different methods for image fusion:

　　

The diagram is a simple image copy, as shown on the right, where the result is unnatural and has a distinct boundary.

　　

The graph is based on Poisson image editing effect diagram, as shown on the right, there is no obvious boundary in the result diagram, the source image block seamlessly and naturally fused into the sky. Seamless Image stitching

The following is the result of seamless image-based stitching, which is made up of 25 images, each showing the children of different poses on the beach, with Poisson Fusion, creating a seamless, natural and interesting new image.

　　 Image editing

The picture below is the result of the image editing, by changing the blending boundaries of the flowers, and re-fusing them into the image, so that they can naturally change their tones and present a new visual effect.

　　

This paragraph is excerpted from Zhejiang University, the original Zhang Yoon-jin.

The theory is about here. I am not, theoretical aspects can only do imaginative achievement here, inexpressible of the realm, so can only be some of Daniel's works to integrate, hope to some help for beginners.

Finally, I will be in the recently written Poisson image editing algorithm published in Google Code,license is the GNU Public License, I hope that the students have some help.

Post Address: http://code.google.com/p/imageblending/