无缝图像编辑

无缝图像编辑 SeamlessImage Editing Mei Hongzhi 2017152109

My topic will be divided into 3 parts: • 1.What is Seamless Image Editing. • 2.How to implement the technique. • 3.The uses of this technique.

1.What is Seamless Image Editing. We are interested in achieving local changes, ones that are restricted to a region manually(手动地) selected, in a seamless and effortless manner. The extent of the changes ranges from slight distortions(扭曲) to complete replacement by novel content.

2.How to implement the technique. There is an influential SIGGRAPH 2003 paper titled “Poisson Image Editing”, by Patrick Perez, Michel Gangnet, and Andrew Blake. The main method to implement seamless image editing is just “Poisson Image Editing(泊松图像编辑)”

Traditional image fusion: Select the fusion area accurately: the process is tedious and the workload is heavy, and the results are often not good Alpha-matting: powerful, but complex Seamless fusion based on Poisson equation： The process of selecting the fusion region is simple and convenient.Theresult is a seamless fusion. Therefore, we choose Poisson equation-based method for seamless image fusion!

What is Poisson Image Editing The mathematical tool at the heart of the approach is the Poisson partial differential equation with Dirichlet boundary conditions(狄利克雷边界条件) which species the Laplacian(拉普拉斯变换) of an unknown function over the domain(域) of interest, along with the unknown function values over the boundary of the domain.

The motivation is twofold. First, it is well known to psychologists [Land and McCann 1971] that slow gradients(梯度) of intensity, which are suppressed by the Laplacianoperator(拉普拉斯算子), can be superimposed on an image with barely notice-able effect. Conversely, the second-order variations extracted by the Laplacian operator are the most signicant perceptually. Secondly, a scalar function(标量函数) on a bounded domain is uniquely de-ned by its values on the boundary and its Laplacianin the interior(内部的拉普拉斯行列式). The Poisson equation therefore has a unique solution and this leads to a sound algorithm.

What is Laplacian operator First of all, the Laplace operator is the simplest isotropic differential operator(各向同性微分算子), it has rotation invariance(旋转不变性). The Laplace transform of a two-dimensional image function is the second derivative of isotropy(各向同性的二阶导数), which is defined as:

In the figure (a) below, the “leap” of grey-scale map(灰度图)the existence of edge. If we use the first-order derivative, we can see the existence of edge "leap" more clearly (shown here as peak value). What happens if you take the second derivative on the edge? , as shown in figure (c). You'll find that at the extreme of the first derivative, the second derivative is 0. So we can also use this feature as a method to detect image edges. (a) (b) (c)

It's easy to see from the template form that if there's a bright spot in a darker area of the image, then the Laplace transform will make that bright spot even brighter. Because the edges of the image are the ones where the grayscale jumps, the Laplace sharpening template is useful for edge detection. However, this operator can be determined by the zero-crossing between positive and negative peaks of quadratic differentiation, and it is more sensitive to isolated points or endpoints.

We can interpolate each color component independently, so we can only consider a scalar color function. The simplest interpolation function f defined on f* on : minimizes the problem of interpolation (1)

It's a gradient operation. The minimum must satisfy the relevant Lagrange equation. (2) It's the Laplace operator. Equation (2) is the Laplace equation under Dirichlet boundary conditions. For image editing applications, this simple method may have unsatisfactory results, fuzzy interpolation effect, but there are many ways to overcome it. One is to use more complex partial differential equations (the repair technique in [Bertalmio et al. 2000]). Our recommendation here is to introduce more constraints on the boot domain to modify the problem.

(3) A bootstrap domain is the vector domain v used in the extended version of the minimization problem (1) : Its solution is the only solution of poisson's equation under Dirichletboundary conditions: (4) It‘s the divergence(散度) of v= (u,v). The basic mechanism of poisson image editing is: in the selected color space, three color channels correspond to one poisson equation as shown in (4).

For Dirichlet boundary conditions defined on arbitrary shapes, it is better to solve the variational problem (3) directly rather than calculate poisson's equation (4). Its solution satisfies the following linear equations:

Seamless cloning Importing gradients(导入梯度) Concealment(隐藏) Seamless cloning tools thus ensure consistency between the boundaries of the original image and the target image. It can be used to hide unwanted parts of an image or to insert new elements. It's more flexible and easier to use than traditional technologies.

Gradient mixing(梯度混合) In some cases we need to combine the properties of f* and g. For example, sometimes we add an object with a hole in it, or a partially transparent object on a textured or cluttered background. At each point in Ω,we retain the larger variables in f* or g according to the following guidance field.

Insertion(插入)/Feature exchange(特征交换)

Inserting transparent objects(插入透明对象)Inserting one object close to another(将一个对象插入到另一个相近图像中)

3.The uses of this technique.

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DOWNLOADSathttp://vcc.szu.edu.cn Thank You! 梅洪志 2017152109

无缝图像编辑