2016年Poisson图像编辑：方法回顾与进展

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本文档《Poisson Image Editing》是一篇发表于2016年11月18日的Image Processing Online期刊上的研究文章，由J.Matías Di Martino、Gabriele Facciolo和Enric Meinhardt-Llopis共同撰写。该论文在2016年1月23日提交，并于同年9月12日被接受。论文的国际标准连续出版物编号（ISSN）是2105-1232，遵循Creative Commons BY-NC-SA许可协议。标题“Poisson Image Editing”聚焦于一种利用图像梯度进行操作的技术，也称为基于梯度的图像处理或泊松编辑。这种方法允许用户执行诸如无缝克隆、对比度增强、纹理平滑以及无缝拼接等操作，这些通常通过简单而高效地结合或修改图像的梯度来实现。2003年首次提出这一概念后，该领域已有了许多发展和贡献，作者在文中详细阐述了这种方法的基本原理和后续的研究进展。文章的核心内容包括对原始泊松编辑技术的介绍，它如何利用泊松方程将图像的局部梯度信息扩展到整个图像，从而实现精确和自然的编辑效果。此外，论文还探讨了该方法在实际应用中的优化策略，如处理高分辨率图像、处理复杂边界条件下的问题，以及与其他图像处理技术的融合。论文中还涉及到了一些关键算法和技术改进，比如如何通过迭代求解泊松方程来解决编辑操作中的模糊和失真问题，以及如何利用并行计算加速处理速度。同时，文章可能还会介绍一些评估指标，用于衡量编辑结果的质量和效率。为了方便读者进一步研究和应用，论文提供了在线附加材料、相关软件、数据集以及在线演示链接，链接地址为<https://doi.org/10.5201/ipol.2016.163>。2015年6月16日的版本更新至v0.5.1，标注为IPOL文章类别。《Poisson Image Editing》是一篇深入探讨了泊松图像编辑技术基础及其发展的重要学术文献，对于那些在计算机视觉、图像处理和图形编辑等领域工作的研究人员和专业人士具有很高的参考价值。

J. Mat

ıas Di Martino, Gabriele Facciolo, Enric Meinhardt-Llopis

to similarity crite ri a and they used both L

and L

norms between patches or their gradients to

synthesize the inpainted image. More recently Sadek et al. [

27] also proposed a variationa l model

for gradient-based video editing. In this work optical ﬂow was used to gu i d e the propagation of the

information in the gradient dom a i n . The authors showed that this method was tempora l l y consistent

and able to handle fast and abrupt illumination changes in tim e as well as smooth illuminatio n

changes in space. Their experimental results showed that the proposed model was able to handle a

large number of frames and relatively complex sequences.

Bhat et al. stud i ed a wide variety of applications of Poisson Equation and proposed a set of

techniques and ﬁlters using modiﬁed versions of i t . In 2008 [7] they proposed a varia t i on a l formulation

that combines a data term with a gradient term, the combination of these two kinds of terms allowed

them to derive several kinds of ﬁlters such as Sharpening, Flattening and de-blocking. For example, a

sharpening ﬁlter is proposed as a minimization problem where the objective function trades oﬀ two

terms: a ﬁdelity term to the original image against a ﬁdel i ty term to the ampli ﬁ e d gr a d i ents. The

image that mi n i m i zes this objective function presents boosted high frequencies while its intensity

values keeps close to the input image. In this work the authors a l so present an analy si s of the

proposed functionals in the Fourier domain, and show that the minimization can be performed in a

direct, exa ct and eﬃcient way in this domain. The work previ o u sl y described was extend ed by th e

same authors in [

8, 9]. In th ese works the authors d escr i bed in a more general way their proposed

framework which combines zero order and ﬁrst order (i.e. ﬁrst derivative) ﬁd el i ty terms. In addition

they introduced spatially varying weights over the constraints to approximate the L

norm and

extend some of their previous ideas to video se qu e n ces by addi n g temporal constraints.

More recently Morel et al. [

22] proposed a Fourier i m pl em entation of Poisson ima ge editing

method, which all ows an exact and fast solution of the Poisson equation even when the region of

interest has a complex shape. In addi t i on th e aut h o r s presented a n au t o m at i c meth od for selecting

the region of interest and applied it t o a classic l ocal contrast enhancement principl e . The main

idea behind this work is to solve the Poisson equation over the entire domain using the modiﬁed

gradient map i n si d e the region o f interest, an d the gradient of the background i m age outside it. In

addition Dirichlet boundary conditions are replaced by Neumann conditions (at the edges o f the entire

image). Even though the p r o posed (Fourier) implementation solves the Poisson e qu a t i on over the

entire domain of the image (instead of the selected su b -d o m ai n ) , Morel et al. empirically showed that

the solutions of both (the exact and the Fourier based) i m p l em e ntations are perceptually equivalent

outside the sub-domain for a varied set of im ages. In a similar direction, Limare et al. [

18] proposed

an implementation in the Fourier domain of the Retinex

algorithm as a Poisson Equation with

Neumann boundary conditions. The method Limare et al. p r oposed consists in sett i n g to zero those

gradients whose modu l u s is below certain thr esh o l d , and then compute th e image that correspon d s

to the modiﬁed gradient map by solving the Poisson equation. Thus, in the new image the small

details and shades have been removed, which, according to Retinex t h eo ry models t h e property of

our perception of constant col o r s regardless of their shading. This m et h od is very similar to one of

the ap p l i ca t i on s presented in P´erez et al. work [24] as Texture ﬂattening, i n which only the gradients

at edg e locations are kept before integrating with the Poisson solver. Finally, in a related work by

Morel et a l . [21] a functional containing a ﬁrst order term and a zero order term was u s ed with the

aim of removing the eﬀect of nonuniform i l l u m i n at i o n whi l e pre ser v i n g the ﬁn e deta i l s of the image .

The proposed appr o ach is similar to the one presented by Bhat et al. in [

7], the main diﬀerence lies

in the data (zero order) term, while Bhat et al. adjust the solution to an input image, Morel et al.

adjust the solution to be close to it’s own mean value.

Retinex theory was formulated in 1964 by Edwin H. Land, and was the ﬁrst quantitative attempt to simulate how

the human visual system perceives color.

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2016年Poisson图像编辑：方法回顾与进展

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