1 Introduction

Seamless image editing has been an active research field in recent years.It is widely applied in panorama mosaicing[1],photo composition[2,3],manipulating large collections of photos[4],and so on.Seamless image editing involves combining source regions with target images in a visually natural way. Since input images often contain multiple objects with differently textured backgrounds,a natural-looking editing result should meet the expectations of human visual perception[5]and preserve not only local structure continuity within boundaries but also consistent color and texture transitions between source and target images.

图钉反过来代表点，吸管代表直线，卡纸代表平面。请用最少的图钉或吸管，让彩色的卡纸不接触桌面，有几种不同的方法？（1）只用图钉（2）既用吸管又用图钉（3）只用吸管，小组合作先摆模型，再写实验报告，引导所有学生参与，分析各种方案。学生兴趣盎然，在实验中得出平面的基本性质及其推论，归纳出确定一个平面的四种条件。通过实验、猜想、验证与交流活动，使学生在有趣的游戏中体验和理解数学。

In general,when combining images with very different structures and textures,a successful image editing algorithm should preserve the following properties,to produce results in agreement with our visual perception:

1)Localstructure continuity. When the input images include multiple objects or different structures,the composition should not break the local salient structures in the overlap region,to avoid structure collision or discontinuity.

现阶段，原料方面总体高位运行，氯化铵、一铵、二铵和钾肥继续维持高位盘整，仅尿素方面没有持续坚挺，主产区尿素厂家的报价呈稳中下调的趋势。但有消息称，后期天然气供应可能会受到限制，届时是否会对气头尿素企业的开工率造成影响，再次引起尿素价格的上扬，目前还是个未知数。

2)Smooth color transitions.The composition should blend the colors between input images to avoid blurring due to differences along the boundary.

3)Global texture consistency.When the input images have very different textures,the process should take into account not only gradients but also colors to preserve texture consistency.

（1）聚焦应用能力培养。由于“茶产品分析与检验”的实务性和技术性，教学目的主要使学生能够应用检验分析的方法。所以，教学过程中要以应用能力培养为导向，以此为目的组织教学内容、选择适合的教学方法。

Much research has been conducted to solve these issues.

3)a patch-based approach to encoding texture consistency which requires neither search nor voting.

1)an iterative optimization algorithm to compute optimal boundaries for regions containing multiple objects,which can be used to preserve local structure continuity;

2)a mixed-domain measure to address smooth color transitions and global texture consistency,allowing us to formulate editing as a unified minimization problem;

In this paper,we propose a general approach which we call object-aware image editing(OAIE),based on optimal editing region selection and mixed-domain composition.Our main contributions include:

Based on these contributions, OAIE can simultaneously eliminate local structure artifacts,providesmooth colortransitions,and preserve global texture consistency.

范式概念的出现对现代科学哲学的研究是个巨大的冲击。文献[6]率先提出“范式”这一术语，并阐述了范式是一种有关价值、信念和方法论的共识,即可将一种科学范式的实质看成是一种世界观或方法论；并且提出了科学革命源自于范式变化和概念转换的观点，突破了传统科学和哲学的认知，为其它科学的研究提供了一种全新的研究方法与研究视角，引发了各个领域广泛而深远的讨论。文献[7]最先提出了“技术范式”的概念，认为“技术范式就是解决那些主要技术问题的模型和模式”。

2 Related work

In the image editing literature,many methods have been proposed to address inconsistency in structures,colors,and textures.

2.1 Optimal seam methods

Optimal seam methods are often applied for seamlessly compositing images and textures;they achieve good local structure continuity.They seek a partition curve(an optimal seam)in the overlap region to minimize the difference between the two input images,in order to make the seam as invisible as possible.Generally,objects are visually salient in images[6],so an optimal seam should pass around objects to avoid structure collisions.Dynamic programming[7]or graph cut[8]methods are usually applied to find the optimal seam.Optimal seam methods can handle image composition well when there are only small structure and color differences between input images in the overlap region.However,if the differences are large,it is hard to find a pleasing optimal seam.To combine inconsistent images,Darabi et al.[9]proposed a novel method,image melding(IM),which uses a Poisson equation solver to find suitable colors by minimizing an energy function based on mixed L2/L0norms for colors and gradients.This method can produce a gradual transition between source images without sacrificing texture sharpness.However,when there are too many edges or complex textures around the boundary,the editing result can look unnatural.Tao et al.[10]proposed error-tolerant image composition(ETIC),which minimizes the curl of the target gradients on the foreground–background boundary.However,the editing result may have a very sharp boundary and color leakage may occur.

2.2 Gradient-domain methods

For objects of interest O,the gradient field can be manipulated by modifying▽fsusing linear or nonlinear transformations:

2.3 Patch-based synthesis

In our mixed-domain composition,we adopt patchbased synthesis to preserve texture consistency,so texture similarity is measured at patch-level rather than at pixel-level.Generally,patch-based synthesis can preserve more texture cues,giving less smooth results than pixel-based synthesis.Figure 9 shows an example,where the results provide a close up of part of Fig.2,using different synthesis methods.The results demonstrate that patch-based synthesis provides more rich texture information.

3 Optimal boundary search

3.1 Definition

As illustrated in Fig.1,seamless image editing requires combining a region of interest Ωr(with external region boundary ∂Ωr)from a source image fsinto the target image ft. Generally,Ωrmay include one or more objects of interest Oi,i=1,...,n(e.g.,n = 3). We define a target of interest Ωi(with external target boundary ∂Ωi)as a subregion surrounding the corresponding Oi(with external object boundary∂Oi),and note that Oi⊆ Ωi⊆ Ωr. Then the optimal editing region selection problem requires finding the optimal targets of interest{Ωi},i=1,...,n,which minimize local structure mismatches.The task can be turned into one of optimizing each target boundary ∂Ωi between ∂Oiand ∂Ωrfor each object of interest Oi.Let Ω = ∪Ωi,O= ∪Oi,Bi= ΩiOi,and B= ∪Bi.Then the optimal editing region Ω is separated into two parts including objects of interest O and backgrounds of interest B.The extra regionΩrΩ is neglected in image editing.The cut Ci connects the boundaries between object of interest Oiand Ωr,and the cut Cijconnects the boundaries between Oiand Oj.

We further define various operators,including the gradient operator ▽ =[∂/∂x,∂/∂y],the Laplacian operator ▽2= ∂2/∂x2+ ∂2/∂y2,the divergence operator ▽·= ∂/∂x+ ∂/∂y,the L2norm ‖·‖,and the pixel count|R|in a region R.

3.2 Optimal boundary for single object

Consider the minimization problem for gradientdomain composition as in Ref.[11],which seeks an image f to approximate the target gradient field v=▽fs(from the source image)in a leastsquares sense with the given user-specified Dirichlet boundary condition:

4.皮肤内。猪疥螨、血虱和蠕形螨寄生于皮肤内。最常见的是猪疥螨，种公猪和繁殖母猪多发，主要寄生在耳廓内面，特征是癣痒症，发病猪皮肤发炎、脱毛、奇痒、消瘦，但病变程度差异较大。

Letting f′=f−fs,Eq.(1)can be written as

Note that the variational energyEq.(2)will approach zero if and only if the boundary condition f′|∂Ω =k(where k is a constant).This observation has been utilized in DDP[13]to define the optimal boundary condition when including a single object of interest.

3.3 Optimal boundaries for multiple objects

In this paper,we extend the case to placing multiple objects within Ωr.Then,the resulting optimal boundaries can be computed by minimizing the following boundary energy function:

（102）尖齿羽苔 Plagiochila pseudorenitens Schiffn.熊源新等（2006）；杨志平（2006）

where the constant kiis a vector for a color image or a scalar for a grayscale image.We may consider each target boundary∂Ωiindependently due to their independence of each other.Since ∂Ωimay pass through all pixels in the region ΩrO,it is intractable to simultaneously estimate{∂Ωi}and{ki}.To solve this problem,an iterative optimization algorithm is proposed,which operates in an alternate manner.

无醛认定项目的实施为人造板和人造板制品生产商宣传无醛产品提供了可靠依据，规范了行业内的无醛制品的识别标准，有效的促进了人造板及其制品环保质量的提升，促进企业品牌的创建。

In Step 3,computing the optimal boundary for Oiis equivalent to finding a shortest closed path in a graph Gi.The nodes in Giare pixels within the band ΩrO while the edges represent 4-connectivity relationships between neighboring pixels.For∂Ωi,the cost((ft(p)−fs(p))−ki)2is defined on each node as the color difference with respect to ki.Following Ref.[13],we break the band connectivity with the shortest boundary cut Ciconnecting∂Oi and ∂Ωr,as shown by black solid lines in Fig.1,and remove all edges crossing the cut from the corresponding graph Gi. In addition,to ensure each optimal boundary encloses only one object,we construct the boundary connection set{Cij}between objects of interest{Oi},shown as black dotted lines in Fig.1,and then apply 2D dynamic programming[26]to find the shortest closed path which connects the two sides of Cias well as passing through the associated boundary connections.

3.4 Obtaining objects of interest

To compute the optimal boundaries,we need to f i rstly obtain the objects of interest{Oi}. Level sets[27]can be used to perform automatic object segmentation.However,as the editing of objects of interest usually needs user interaction(e.g.,to only select certain objects),we rely on obtaining objects of interest by interactive segmentation techniques.To do so,a user simply draws a box surrounding the object of interest,and then GrabCut[28]is applied to extract the object of interest.Note that even if the objects of interest are not obtained very accurately,our computation of optimal boundaries still can avoid structure inconsistency since the optimal boundaries usually pass through smooth regions rather than object edges.

4 Object-aware editing

4.1 Mixed-domain composition

Optimalediting region selection can preserve local structural continuity well. However,if the backgrounds of the input images differ greatly in color and texture(e.g.,pasting a source of interest from a smooth region into a target image with coarse textures),color bleeding or texture artifacts still may occur when reconstructing from a gradient field,even with well-optimized boundary conditions.To address this issue,we must enhance color and texture consistency between images.Therefore,we perform mixed-domain composition by solving the following minimization problem:

where the consistency energy ECprovides a unified consistency metric for measuring gradients and colors.The gradient-domain energy is defined on all targets of interest to obtain smooth color transitions,using Dg(p)=||▽f(p)− v(p)||2,while the color-domain energy is defined on backgrounds of interest to preserve global texture consistency.We adopt a patch-based metric for encoding texture consistency and definewhere f(p)and ft(p)are the background pixel sets in w×w image patches Nw(p)centered at p,and NBw(p)=Nw(p)∩B.Unlike the IM method[9],this patch-based approach neither needs search nor voting. The trade-off parameter λ is used to balance the influence of the two terms.

De fi ning a binary mask M,the minimization problem may be written as

For backgrounds of interest B,the gradient field is manipulated by modifying or mixing source and target gradient fields:

We make use of backward differences to discretely approximate Eq.(7),leading to a large sparse linear system:

Figure 5 presents another example of selective modification which changes the local color of a target of interest. In Fig.5(a),the object and target boundaries are marked in blue and red respectively.The PIE result exhibits color bleeding artifacts around the object,while OAIE avoids this problem effectively.To explain why,let us consider the difference between the minimization problems solved by PIE and OAIE.Compared to PIE,the minimization problem for OAIE includes an extra texture consistency term defined using a patch-based approach. It has been demonstrated in Ref.[9]that patch-based synthesis can produce a gradual transition between images without sacrificing texture sharpness.This allows OAIE to produce a smooth transition across image edges without color bleeding and texture blurring.

4.2 Object-aware gradient manipulation

Unlike traditional composition methods[11,15]which manipulate the guidance gradient field for the target region using a unified operator,OAIE manipulates the guidance gradient fields of O and B separately with independent operators,in an object aware way.

4.2.1 Transformation operators

Gradient-domain methods are usually adopted to obtain smooth color transitions. They make use of known gradient information to produce the final composition by interpolation.The basic idea is to reconstruct the image from gradient fields with specified boundary conditions.Prez et al.[11]proposed an effective image blending approach,Poisson image editing(PIE).By solving a Poisson equation with user-specified Dirichlet boundary conditions,this approach can blend colors seamlessly between input images. However,its effectiveness heavily depends on careful alignment of the structures of the input images along the userdrawn boundary.Agarwala et al.[2]combined graph cut optimization and gradient-domain composition to create photomontages. Zomet et al. [12]proposed an L1-based gradient-domain stitching method to eliminate visible seams in the overlap region by use of gradient fields. Jia et al.[13]proposed an easy blending method,drag-and-drop pasting(DDP),by optimizing boundary conditions for gradient-domain composition.Farbman et al.[14]introduced an alternative,mean-value coordinate based approach,to carry out seamless cloning via a weighted combination of values along the boundary.Bhat et al.[15]proposed a unified variational model,GradientShop,to perform a number of image and video editing tasks. It contains many filters and uniformly uses quadratic optimization,lowering the computation time.Li et al.[16]performed multiscale editing by applying a nonlinear filter bank to adjacent pixels at each level of a Gaussian pyramid,to eliminate visual artifacts.However,visual artifacts still occur when the trade-off parameter is too large or too small.In Ref.[17],the authors presented a gradient-based variational model for video editing,which addresses the problem of propagating gradient-domain information along the optical fl ow of the video.With this method,a user can edit a frame by modifying the texture of an object’s surface and then propagate this edit throughout the video.Bie et al.[18]incorporated the users’intent in outlining the source patch,to tackle structure con fl icts between the source image patch and the target image.Hua et al.[19]added an extra edge-aware constraint term in a general gradient-domain optimization framework,enforcing similar image filtering effects while preserving edges.In Ref.[20],Zhang et al.performed image copy-andpaste with optimized gradients,where they created a gradient transition map in the cloning area and then used an interpolation-based method to calculate the composition results from the reconstructed gradient map.

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where the transformation operator τ is used to change the appearance of targets of interest(e.g.,their texture,illumination,contrast,color,etc.)and can be chosen from the transformation set Λ={clone,illuminate,smooth,recolor,...}.Here,clone provides seamless cloning,illuminate provides local illumination change,smooth provides texture smoothing(e.g.,cartoonization),recolor provides object recoloring,and so on. Note that different operators can be used for each object.

4.2.2 Mixture operators

where M(p)is 1 if p∈B,and 0 otherwise.Based on the Euler–Lagrange equation,we obtain:

where the mixture operator φ is chosen from the set Θ={src,max,min,avg,...}where src stands for using the source gradient,max/min/avg stand for picking the larger/smaller/average gradient from▽fsand▽ft,etc.

4.2.3 Combination

Finally,the gradient fields from Eqs.(9)and(10)are combined to form the new guidance gradient field in editing region Ω.This new guidance gradient field is substituted into Eqs.(5)–(8).

4.3 Algorithm comparison

OAIE performs composition with gradient fields in an optimized target region Ω with boundary conditions on ∂Ω,as well as colors in B. By contrast,PIE reconstructs images from gradient fields in Ωrwith non-optimized boundary conditions on ∂Ωrwhile DDP performs this process with gradient fields in an optimized target region Ω with boundary conditions on{∂Ωi}.ETIC optimizes the boundary conditions by minimizing the curl of the gradients on ∂Ωr. IM carries out image composition with patch-based synthesis using the textures in ΩrΩ.

5 Experimental results

To demonstrate the effectiveness of our OAIE approach,we have implemented several seamless image editing applications and compare the results with those from four state-of-the-art methods:PIE[11],DDP[13],ETIC[10],and IM[9].Various such results are given below.

5.1 Seamless cloning

Seamless cloning aims to copy a region of interest from a source image and seamlessly insert it into a target image.In this process,the guidance gradient fields of the editing region Ω and backgrounds of interest B are manipulated with Eqs.(9)and(10)respectively.

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Figure 2 shows a seamless cloning example which combines a region of interest containing multiple objects with a target image.The result of direct cloning is shown in Fig.2(c),with object boundaries and optimal boundaries marked in blue and red respectively.Results generated by the four methods PIE,DDP,ETIC,and IM all have artifacts in the background region,e.g.,around the object boundaries.However,OAIE obtains a more natural result since it considers a unified constraint on both object appearance and background texture simultaneously.

Figure 3 provides a further seamless cloning example which inserts a source region with a smooth background into a target image with rich textures.None of the other four methods preserve texture consistency well(leading to unnatural colors or textures),while OAIE obtains consistency of both local structures and global textures.

5.2 Selective modification

Selective modification aims to adjust local or global appearance(e.g.,texture,color,illumination,etc.),so image cloning methods such as DDP,ETIC,and IM are not applicable. We compared our results from OAIE with those from the PIE method.During selective modification,optimal editing region selection is neglected,so fs=ft,while the gradient fields of O and B can be obtained using the same or different operators.

Figure 4 demonstrates examples of global and local selective modification. Figure 4(a)demonstrates global recoloring of Fig.3(h)with the recolor operator.This operator multiplies the RGB channels of the original image by different values respectively to form the source image,and then performs seamless composition.Figure 4(b)shows the result of using operator illuminate to reduce local specular reflections(shown in blue in Fig.4(a)).The operator illuminate modifies the gradient field using v=αβ|▽f|−β▽f where α = β =0.2,following Ref.[11].We see that when either global or local operators are applied to the cloned composition,the resulting textures still remain natural,verifying the robustness of OAIE.

where|A(p)|represents the number of available pixels in a 4-neighborhood A(p)centered at p;it satisfies|A(p)|≤4.vpqis the projection of v((p+q)/2)on the edge[p,q]in the direction ofgiven by vpq=v((p+q)/2)·The computational complexity for constructing the sparse linear system is O(|Ω|); the space complexity for storing the coefficient matrix is O(|Ω|).Many efficient technologies such as Ref.[29]can be adopted for solving the sparse linear system.We set w=9 and λ=1 in this paper.

5.3 Seamless stitching

Seamless stitching aims to combine multiple source images into a panorama mosaic.Figure 6 illuminates an example of stitching two remote sensing images with a very large tone difference.Optimal seam methods will lead to obvious artifacts due to the color difference between the source images in the overlap region(shown in blue in Fig.6(b)).Since consistency constraints are imposed for both color and texture,OAIE achieves a more globally natural result than PIE,as shown in Figs.6(c)and 6(d).

In addition,OAIE can stitch multiple target parts,as shown in Fig.7,where several face parts from different face images are stitched into an integrated face portrait.The upper row shows the target image and source parts marked in red in the source images,while the bottom row gives the results generated by cloning,PIE,DDP,and OAIE respectively.Various structure or color artifacts can be seen in the results generated from PIE and DDP.In contrast,the result from OAIE is more natural.A potential application of this editing tool is portrait synthesis for police work.

6 Discussion

6.1 Limitations

Like other methods,our method has some limitations when the background structures between source and target images in the editing region collide.As shown in Fig.8,the result generated by our method suffers from color bleeding around the background structures,while the results from PIE and DDP have serious structure artifacts.

6.2 Computational efficiency

Our method is simple and efficient. Firstly,the user selects and drags the region of interest from the source image to the target image.Then,simple interactive segmentation allows the user to indicate the objects of interest.This usually takes about 1–2 seconds of computation depending on the sizes of the objects.After specifying the type of editing required,the composition is performed automatically by using dynamic programming to find optimal boundaries and solving a large sparse linear system for mixed domain composition.The computational complexity of dynamic programming is O(n),while solving a large sparse linear system takes time O(n)[29]where n is the number of variables.

6.3 Patch-level similarity

Patch-based texture synthesis is usually used to address global texture consistency,and has been successfully applied to various editing tasks on still images,video,and stereo pairs. Darabi et al.[9]proposed a novel method,image melding(IM),which adopts patch-based synthesis to find suitable colors,and minimizes an energy function based on mixed L2/L0normsforcolorsand gradients.This method uses an iterative search-andvoting blending scheme,and can produce a gradual transition between inconsistent source images without sacrificing texture sharpness. However,when there are too many edges or complex textures around the boundary,or limited texture sources for synthesis,the editing result can be unnatural.Ma and Xu[21]proposed an efficient manifold preserving edit propagation method which searches feature space using an adaptive neighborhood size,which reduces time and memory costs without reducing visual fi delity. Barnes et al.[4]proposed a fast patch-based optimization method,PatchTable,for efficient computational photography.In Ref.[22],Luo et al.extended the patch-based synthesis framework from 2D to 3D for stereoscopic image editing.They introduced a depth-dependent patchpair similarity measure and a joint patch-pair search. Chen et al.[23]presented an interactive system called sketch2photo to compose a realistic picture from a simple freehand sketch annotated with text labels. Their system found several photographs in agreement with the sketch and text labels by searching the Internet and automatically selected suitable photographs to generate a high quality composition.In Ref.[24],Zhang et al.extended patch-based synthesis to plenoptic images captured by consumer-level lenslet-based devices for interactive light field editing.They represented the light field as a set of images captured from diあerent viewpoints and performed patch-based image synthesis on all affected layers of the central view,and then propagated the edits to all other views.To address the heavy computational burden of gradient-domain operators,Ref.[25]proposed a patch-based synthesis method using a Laplacian pyramid to improve searching for correspondences with enhanced awareness of edge structures.

6.4 Editing quality estimation

Generally,subjective measures are used to evaluate editing quality.This is usually performed by using the human eyes to check the naturalness of the editing results in terms of structure,color,and texture.To verify the advantages of our method,we used blind image quality evaluation as proposed in Ref.[30],considering the image naturalness in the local editing regions.The experimental results showed that our method can give better quality.

7 Conclusions

In this paper,we have proposed a general approach called OAIE for seamless image editing.It jointly performs optimal editing region selection and mixeddomain composition,allowing it to cope with visual inconsistency in local structures and global textures simultaneously. In particular,OAIE provides a unified mixed-domain consistency measure for gradients and colors,in which texture consistency is encoded with a patch-based approach which does not require search.Compared to four state-of-the-art methods,our unified approach is more powerful in preventing global color and texture inconsistencies,while preserving local structure continuity.

Acknowledgements

This work was supported in part by the National Key Research and DevelopmentPlan (Grant No.2016YFC0801005),the National Natural Science Foundation of China(Grant Nos.61772513 and 61402463),and the Open Foundation Project of Robot Technology Used for Special Environment Key Laboratory of Sichuan Province in China(Grant No.16kftk01).

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