正文：
Title:A Bayesian Approach to Digital Matting
翻译：
标题：一个用于数字抠图的贝叶斯方法
词汇：
Matting：专业术语，消光
正文：
Abstract
This paper proposes a new Bayesian framework for sovling the matting problem,i.e. extracting a foreground
element from a background image by estimating an opaccity for each pixel of the foreground element. Our
approach models both the foreground and background color distributions with spatially-varying sets of Gaussians,
and assumes a fractional blending of the foreground and background colors to produce the final output.It then
uses a maximum-likelihood criterion to estimate the optimal opacity,foreground and background simultaneously.
In addition to providing a principled approach to the matting problem, our algorithm effectively handles objects
with intricate boundaries,such as hair strands and fur,and provides an improvement over existing techniques for
these difficult cases.
翻译：
摘要
这篇论文推荐用一种新的贝叶斯框架来解决图片的消光问题，即通过估计每个前景元素的不透明度来将图片中的前景从
背景中分离。我们的解决方案通过空间变化高斯模型来同时模拟前景和背景的颜色贡献，并且假设是前景色和背景色的
分数混合产生最终的图像。再用最大概率作为标准来同时估计最合适的不透明度，前景，和背景。我们的算法除了提供了
消光问题的方法准则，还能有效的解决错综复杂的边界对象，比如发丝，毛。并且我们提供了对解决这一难题的
现有技术的改进方案.
词汇：
extract：分离 extract sth from sth
opacity: 不透明度，晦涩的
spatially:空间地 adv.
model: 模仿,模拟(imitate) v.
fractional：部分的，断片的，分数
blend:混合
likelihood:概率 n.
criterion:标准
optiaml:最合适的
simultaneously:同时，同步，并发
intricate:错综复杂的
strands：缕，一串
正文：
1.Introduction
In digital matting,a foreground element is extracted from a background image by estimating a color and opacity
for the foreground element at each pixel.The opacity value at each pixel is typically called its alpha,and the
opacity image,taken as a whole, is referred to as the alpha matte or key. Fractional opacities(between 0 and 1)
are important for transparency and motion blurring of the foreground element ,as well as for partial coverage
of a background pixel around the foreground object's boundary.
翻译：
1.引言
在数字消光中，一个前景元素是通过估计每个像素点上前景元素的颜色和不透明度从背景中被分离出来的。在每个像素中的不
透明元素一般被成为alpha。一张不透明通道图，作为一个整体，被称为alpha遮罩或者键，分数不透明度对前景元素的透明度
和运动模糊，以及前景对象边界周围的背景像素部分覆盖的范围都很重要。
词汇：
typically:一般 in a way that a person or group is generally believed to behave
taken as a whole:作为一个整体
matte:遮罩
be referred to:被称为
transparency:透明度，透明性
motion:移动，进展
coverage:范围覆盖
正文：
Matting is used in order to composite the foreground element into a new scene.Matting and compositing were origi-
nally developed for film and video production,where they have proven invaluable.Nevertheless,"pulling a matte" is
still somewhat of a black art,especially for certain notoriously difficult cases sunch as thin whisps of fur
or hair.The problem is difficult because it is inherently underconstrained:for a foreground element over a single
background image ther are in general an infinite number of interpretations for foreground's color versus opacity.
翻译：
消光被用作将前景元素这和到一个新的场景中。消光和组合本来实在电影和视频工作中发展的，在这个领域里被证明这种方法是
十分有效的。尽管绘制一个遮罩仍然是一个黑色艺术，尤其在解决一些著名的难题上，例如细小的毛发。问题很难，因为它本质
上是不受约束的：对于单个背景图像上的前景元素，通常对前景的颜色与不透明度有无限多种解释。
词汇：
composite：adj.综合，合成的。n.综合
originally:本来，原来
invaluable：无价的
Nevertheless:adv.虽然
notoriously：臭名昭著的。
inherently:固有，本质
underconstrained:不受约束的constrained:强迫
infinite:无限的
interpretations:解释
versus:与（vs的全）
in general :一般来说
正文：
In practice,it is still possible to pull a satisfactory matte in many cases.One common approach is to use a background
image of know color(typically blue or green)and make certain assumptions about the colors in the foreground(such as
the relative proportions of red,green,and blue at each pixel);these assumptions can then be tuned by a human operator.
Other approach attempt to pull mattes from natural(arbitrary) backgrounds,using statistics of known regions of foregr-
ound and background colors along the boundary.Once these colors are known,the opacity value is uniquely determined.
翻译：
在实际应用中，在许多案例中得到一个满意的遮罩还是可行的。一个常见的方法就是用一个知的背景颜色（一般来说是蓝色和绿色）
）并且对前景中的颜色作某种假设（例如每个像素对红绿蓝的关联度）。这些假设可以通过人们的操作进行调整。其他的从自然背景
中得到遮罩的是通过已知前景和背景区域的数据来估算沿边界的前景色和背景色一旦这些颜色被知晓，不透明度的值也就被确定了。
词汇：
tune:旋律，节奏，调整
regions:区域，地区
arbitrary:随意
正文：
In this paper,we survey the most successful previous approaches to digital matting--all of them fairly ad hoc--and dem-
onstrate cases in which each of them fails.
翻译：
在这篇论文中，我们研究了大部分的成功的以前的数字遮罩方法--这些方法对于ad hoc都失败了，并且展示他们每一个失败的案例
词汇：
demonstrate:展示，演示，详细解释
正文：
2Background
As already mentioned,matting and compositing were originally developed for film and video production.In 1984,Porter and
Duff introduced the digital analog of the matte--the alpha channel--and showed how synthetic images with alpha could be
useful in creating complex digital images.The most common compositing operation is the operation is the over operation,
which is summarized by the compositiong equation.
C = aF+(1-a)B
翻译：
2.背景
之前已经提起过，消光和结合技术起初是发展与电影视频产品中的。在1984年，Porter and Duff 引入了模拟数字遮罩--不透明通道，
并展示了具有alpha的合成图像如何用于创建复杂的数字图像。最普遍的合成方法如下，通过合成方程进行求和。
C = aF+(1-a)B
词汇：
analog:类似物体，
synthetic:adj.合成的，合成物
正文：
where C,F,and B are the pixel's composite,foreground,and background colors,respectively,and alpha is the pixel's op-
acity component used to linearly blend between foreground and background.
翻译：公式中C,F，B分别是合成的像素，前景色，背景色。并且作为像素不透明度的alpha被用来线性组合前景和背景
词汇：
respectively:adv. in the same order as the things you have just mentioned 分别。
composite: 合成材料n.
component:n.组成部分
blend:v.组合
正文：
The matting process starts from a photograph or set of photographs(essentially composite images) and attempts to
extract the foreground and alpha images.Matting techniques differ primarily in the number of images and in what a pri-
mori assumptions they make about the foreground,background,and alpha.
翻译：消光处理从一副图片或这一组图片（合成的图片是必要的）开始，之后尝试分离出前景图和alpha遮罩。消光技术的主要区别在
于图像的数量以及对前景、背景和alpha的先验假设。
词汇：
priori:先验
正文：
Blue screen matting was among the first techniques used for live action matting.The principle is to photograph the sub-
ject against a constant-colored background,and extract foreground and alpha treating each frame in isolation. This sin-
gle image approach is underconstrained since,at each pixel,we have three observations and four unknowns. Vlahos pioner-
red the notion of adding simple constraints to make the problem tractable;this work is nicely summarized by Smith and
Blinn.For example,under the assumption that.5<=a2<=Fb<=a2Fg,Vlahos constrained the set of equations with:
alpha=1-a1(Cb-a2Cg),
where Cb and Cg are the blue and green channels of the input image,respectively,and a1 and a2 are user-controlled tuning
parameters.Additional constraint equations such as this one,however,while easy to implemnet,are ad hoc,require an expert
to tune them,and can fail on fairly simple foregrounds.
翻译：
蓝色背景消光是在第一类技术中用于真人表演的消光。方法是在一个恒定的颜色背景下拍摄主题，并提取前景和alpha,隔离处理每一帧
对于单个图片上的方法是不受约束的，因为在每一个像素点我们有三个观测值和四个未知数。Vlahos 最先提出增加简单的约束来是的
问题变得可控。这项工作被Smith和Blinn很好的总结。举个例子来说，在这样的一个假设下 .5<=a2<=Fb<=a2Fg,Vlahos 给出了一个约束
集合公式
alpha=1-a1(Cb-a2Cg),
在公式中Cb和Cg分别是输入图像的蓝色和绿色通道，以及，a1和a2是可供用户调整的参数。像这个补充的约束公式尽管很容易实行，但是
特别需要一个专家去调整他们，而且相当简单的前景图上会失败。
词汇：
photograph:n.照片，图片 v.摄影，拍照
isolation:隔离隔绝
observation:观察
pionerred:n.先驱v.首先开展
notion:概念，主张
tractable：adj听话的 easy to control or deal with.
tract: n.管道；简短的论述
ad hoc:adj.特别的；临时；专设adv.特别的
implement：v.实施 n.器具，设备
Additional:额外的，补充的。
正文：
More recently,Mishima developed a blue screen matting technique based on representative foreground and background sam-
ples.In particular,the algorithm starts with two identical polyhedral(triangular mesh)approximations of a sphere in rgb
space centered at average value B of the background samples.The vertices of one of the polyhedral(the background polyh-
edron)are then repositioned by moving them along lines radiating from the center until the polyhedron is as small as
possible while still containing all the background samples.The vertices of the other polyhedron(the foreground polyhedron)
are similarly adjusted to give the largest possible polyhedron that contains no foreground pixels from the sample provided.
Given a new composite color C，then, Mishima casts a ray from _B throung C and defines the intersections with the backgrou
-nd and foreground polyhedra to be B and F,respectively.The fractional position of C along the line segment B F is alpha.
翻译：
最近，Mishima 开发了一个基于代表性前景和背景样本的蓝色消光技术。特别地，该算法以rgb空间中的球体的两个相同的多面体（三角
形网格）近似开始，该球体以背景样本的平均值B为中心。其中一个多面体（背景多面体）的极点重新定位通过沿着从中心辐射出来的直线
移动直到多面体已经足够小但仍然包含所有的背景图片为止。类似的调整拎一个多面体（前景多面体）的顶点以给出最大可能的多面体，其
不包含来自所提供样本的前景元素。给了一个新的组合色C,Mishima从B拔到C画了一条射线，同时通过前景和背景交叉的路口定义未B和F,
沿着线段BF的C的分数位置是α。
词汇：
More recently:最近
representative:n.代表，众议院adj.典型 代表性的
In particular:特别是
identical:adj.相同的
polyhedral:多面体
triangular mesh:三角形的网格
approximations:近似值
sphere：球，领域
vertices:顶点，头顶，极点
radiate:v.辐射adj.辐射状
ray：射线
intersections：路口，马路
正文：
Under some circumstances,it might be possible to photograph a foreground object against a know but non-constant background.
One simple approach for handling such a scene is to take a difference between the photograph and the known background and
determine alpha to be 0 or 1 based on an arbitrary threshold.This approach,known as difference matting is error prone and
leads to "jagged" mattes.Smoothing sunch mattes by blurring can help with the jaggedness but does not generally compensate
for gross errors.
翻译：在有些情况，图片可能是针对的已知的前景对象但是不是连续的背景，一个简单的方法解决这个场景就是再照片和已知背景直接取差
异，并基于任意阈值去的确定alpha为0或1。这种方法被当作是差异消光，很容易出错，并且出现锯齿，平滑这种问题可以通过滤波，但通常
不会弥补严重错误。
词汇：
prone:v prone to do sth.易于，倾向于adv.易于，倾向于adv
jagged:锯齿状的。
gross:adj重大的，n合计，v.总共赚得
正文：
For Knockout,afer user sementation,the next step is to extrapolate the known foreground and background colors into the un-
known region.In particular,given a point in the unknown region,the foreground F is calculated as a weighted sum of the pi-
xels on the perimeter of the known foreground region.The weight for the nearest known pixel is set to 1,and this weight
tapers linearly with distance,reaching 0 for pixels that are twice as distant as the nearest pixel.The same procedure is used
for initially estimating the background B' based on nearby know background pixels.Figure 1(b)shows a set of pixels that cont-
ribute to the calculation of F and B’ of an unknown pixel.
翻译：
对knockout来说，再用户段之后，下一个步骤就是从已知的前景和背景推断出位置区域。尤其是，给定一个再位置区域的点，前景F被计算
为前景区域周边上的像素的加权和。最近的已知像素的权重设置为1，在距离最近的像素点两倍的距离为0，权重像锥形一样线性递减。同样
的步骤用在推测基于周边已知的背景像素的背景B'。图一展示了一个像素集合这些像素用于计算位置像素的F和B'
词汇：
extrapolate:推断
in particular:特别是
perimeter:周长
tapers:n.锥体v.尖细
正文：
The estimated background color B' is then refined to give B using one of several methods that are all similar in character.
One such method establishes a plane through the estimated background color whith normal parallel to the line B’F.The pixel
color in the unknown region is then projected along the direction of the normal onto the plane,and this projection becomes
the refined guess for B. Figure 1(f)illustrates this procedure.
翻译：
然后，使用在性质上相似的几种方法来细化估计的背景色B'以给出B;一种这样的方法通过估计的背景色建立平面，其中法线平行于线B'F。
然后，在未知区域的像素颜色沿着法线到平面的方向做投影。这个投影就作为B的细化预测。图1（F）阐释了这个过程。
词汇：
refine:vt.提炼 be refined to 被提炼为
estimate:估计
plane:水平面，平的
parallel:平行
establish:建立
projected:投射，计划
projection:投影
正文：
Finally,Knockout estimates alpha according to the relation
α =f(C) − f(B)/f(F) − f(B),
where f(.) projects a color onto one of several possible axes through rgb space(e.g.,onto one of the r-,g-,b- axes).Figure 1(f)
illustrates alphas computed with respect to the r- and g- axes.In general,α is computed by projection onto all of the chosen axes,
and the final alpha is taken as a weighted sum over all the projections,where the weights are proportional to the denominator in
equation(3) for each axis.
翻译：
最后，Knockout通过等式α =f(C) − f(B)/f(F) − f(B),来估计alpha的值，其中f(.)通过rgb空间，将颜色投射到某个可能的轴上，例如r轴，
g轴，b轴。图1（f）展示了alpha关于r轴和g轴的而计算.总的来说，alpha的计算是通过投影到所有的可能的轴上，之后最终的alpha值是所有投影的
加权和，其中的权重与每个轴的等式（3）中的分母成比例。
词汇：
proportional:n.比例，adj.按比例
denominator:分母
正文：
Ruzon and Tomasi take a probabilistic view that is somewhat closer to our own.First, they parttion the unknown boundary region into
sub-regions.For each sub-regions，they construct a box that encompasses the sub-region and includes some of the nearby known foreground
and background regions(see Figure 1(C)).The encompassed foreground and background pixels are then treated as samples from distributions
P(F)andP(B),respectively,in color space.The foreground pixels are split into coherent cluster.and unoriented Gaussians(i.e.Gaussians that
are axis-aligned in color space)are fit to each cluster,each with mean ~F and diagonal covariance matrix ΣF.In the end,the foreground
distribution is treated as a mixture(sum) of Gaussians.The same procedure is performed on the background pixels yielding Gaussians, each
with mean B拔 and covariance ΣB,and then every foreground cluster is paired with every background cluster.Many of these pairings are reject
based on various "intersection" and "angle" criteria.Figure 1(g) shows a single pairing for a foreground and background distribution.
翻译：
Ruzon 和 Tomasi采取了某些和我相近的概率的观点。首先，他们把位置的边界区域分为几个子区域。对于每个子区域，他们创建一个包括子区域和一些
靠近的前景和背景的盒子。被包含的前景和背景图被作为颜色空间中P（F）和P（B）分布的样本处理。前景像素被分为连贯的簇，用无向高斯去适配每一
个簇，每一个簇都是~F和对角线协方差矩阵ΣF。最后，前景图被看作是一个混合的高斯分布，同样的处理过程在服从于高斯分布的背景像素上，他们分别
为B拔和协方差ΣB，之后每个前景簇和背景簇向配对。基于各种“交叉”和“角度”标准的许多这些配对被拒绝。图1显示了前景和背景分布的单个配对。
词汇：
probabilistic：概率（可能为probability）
encompass:v.包括，环绕围绕。
distribution:n.分布； 分发
coherent:相干，连贯
diagonal：对角线
covariance:协方差
yield:产生，屈服
be paired with:配对
intersection:路口，马路
criteria:标准，准则，规范。
正文:
After building this network of paired Gaussians,Ruzon and tomasi treat the observed color C as coming from an intermediate distribution P(C),somewhere between the foreground and background distributions.The intermediate distribution is also defined to be a sum of Gaussians,where each Gaussian is centered at a distinct mean value C拔 located fractionally(according to a given alpha) along a line between the mean of each foreground and background cluster pair with fractionally interpolated covariance Σc,as depicted in Figure 1(g).The optimal alpha is the one that yields an intermediate distribution for which the observed color has maximum probability;i.e.,the optimal alpha is chosen independently of F and B.As a post-process,the F and B are computed as weighted sums of the foreground and background cluster means using the individual pairwise distribution probabilities as weights.The F and B colors are then perturbed to force them to be endpoints of a line segment passing through the obeserved color and satisfying the compositing equation.
翻译：
在构建完配对的高斯网络之后，Ruzon和tomasi把估计的颜色C作为来自中间分布的P(C),P(c)在前景和背景分布之间。中间分布也被定义为高斯分布之和，其中每个高斯分布都以不同的C拔值作为中心点，坐落在分数线的前景和背景簇之间的插入的协方差，被描述在了图1(g)。最佳的alpha之一是服从从观测颜色最大可能性的中间分布alpha的选择是独立与F和B。后期处理的过程中，F和B被计算为前景和背景簇的加权和，也就是说用独自的配对分布可能性作为权重。然后扰动F和B颜色以迫使成为穿多观察到的颜色，并且满足合成方程的线段的端点。
词汇：
intermediate:中级，中间
interpolated:插
depict:描述，描绘
post-process:后期过程
pairwise:配对
perturbed:担忧的
正文：
Both the Knockout and the Ruzon-Tomasi techniques can be extended to video by hand-segmenting each frame,but more automatic techniques are desirable for video.Mitsunaga et al. developed the AutoKey system for extracting foreground and alpha mattes from video,in which a user seeds a frame with foreground and background contours，which then evolve over time.This approach,however,makes strong smoothness assumptions about the foreground and background(in fact,the extracted foreground layer is assumed to be constant near the silhouette)and is designed for use with fairly hard edges in the transition from foreground to background;it is not well-suit for transparency and hair-like silhouettes.
翻译：
Knockout和Ruzon-Tomasi的技术都可以被扩展到视频中，通过每一帧进行处理，但是更多的应用于视频自动的技术是被需求的。Mitsunage 发明了一个自动键来分离前景图和alpha遮罩给视屏，在这个技术中，用户播种具有前景和背景轮廓的帧，然后随着时间的推移而演变。这个方法对前景和背景做了很强烈的平滑假设（事实上，被分离出来的前景层是被假设为连续的靠近轮廓），并且在过度前景和背景的时候失败的使用了硬边缘。这种方法不能很好的适应透明和发丝物体的轮廓。
词汇：
seed:种植，种子
coutours:轮廓
envove:发展演变
smoothnes assumptions:平滑假设
silhouette:轮廓
transition:过渡
transparency:胶卷，透明度
正文：
In each of the cases above,a single observaiton of a pixel yields an underconstrained system that is solved by building spatial distributions or maintaining temporal coherence.Wallance provided an alternative solution that was independently(and much later) developed and refined by Smith and Blinn:take an image of the same object in front of multiple know backgrounds.This approach leads to an overconstrained system without building any neighborhood distributions and can be solved in a least-squares framework.While this approach requires even more controlled studio conditions than the single solid background used in blue screen matting and is not immediately suitable for live-action capture,it does provide for real objects.We usse this method to provide ground-truth mattes when making comparisons.
翻译：
在上面的案例中，一个单独的观测的像素服从一个约束的系统。这个系统通过建立的一个空间分布或者是保持了连贯性。
Wallance提供了一个可选择的独立发展的方法，被Smith和Blinn定义为从多个已知的背景图中获取同样的对象。这种方法导致了一种过度约束在没有建立相邻分布的情况下的系统，能够在最小二乘法的框架下求解.尽管这个方法相比较于运用于蓝色消光技术中的单个实体的背景需要跟多的控制的场景条件，也不能够快速的适用于实时播放的捕获。它提供了一个估计分厂准确的前景和背景值对于真实的对象。我们用这种方法在进行比较的时候提供地面真实遮罩。
词汇：
spatial:空间
temporal:分配
coherence:相干性
solid:固体，实体的；固体
capture:捕获
ground-truth:地面实况
comparisons:对照对比
mattes:亚光，遮罩
正文：
Our Bayesian framework
For the development that follows,we will assume that our input image has already been segmented into three regions:"background""foreground",and"unknown",with the background and foreground regions having been delineated conservatively.The goal of our algorithm,then,is to solve for the foreground color F,background color B,and opacity alpha given the observed colorC for each pixel within the unknown region of the image.Since F,B and C have three color channels each,we have a problem with three equations and seven unknows.
翻译：
我们的贝叶斯工作，我们的开发的内容如下，我们假设我们输入的图片已经分为了三个区域：“背景图”，“前景图”，“未知区域”背景和前景被保守的分割开来。我们算法的目标就是在未知区域内对每一个像素，解决其前景Fb背景B和透明度alpha,t通过观测颜色值C,因为F,B，C都有三个颜色通道，我们的问起是三个等式和七个未知数。
词汇：
delineated:描绘，阐述，分界线
conservatively:保守的
正文：
Like Ruzon and Tommasi,we will solve the problem in part by building foreground and background probability distributions from a given neighborhood.Our method,however,uses a continuously sliding window for neighborhood definitions,marches inward from the foreground and background regions,and utilizes nearby computed F,B and α values(in addition to these values from"known" regions) int constructiong oriented Gaussian distributions,as illustrated in Figure 1(d).Further,our approach formulates the problem of computing matte parameters ina wll-defined Bayesian framework and solves it using the maximum a posteriori(MAP) technique.In this section,we describe our Bayesian framework in detail.
翻译：
像Ruzon和Tomasi，我们将通过构建给定的领域的前景和背景概率分布来解决问题。但是我们的方法用一个持续滑动的窗口来定义领域，从前景和背景的区域向内移动，通过建立有向的高斯分布利用附近的元素计算F，B和alpha的值（除了已知区域的这些值外），在图1（d）中已经进行了阐述。之后，我们的方法公式化计算在定义好的贝叶斯框架中的遮罩元素，用最小二乘法进行计算。在这个部分，我们在细节上描述我们的贝叶斯框架。
词汇：
sliding:滑动
march:三月，旅行
inward:
utilizes:利用，采用
formulate:制定，公式化
In this section:在这个部分
正文：
In MAP estimation,we try to find the most likely estimates for F,B and α,given the observation C.We can express this as a maximization over a probability distribution P and then user Bayes's
rule to express the result as the maximization over a sum of log likelihoods:
。。。。。。。
where L(.) is the log likelihood L(.) = logP(.),and we drop the P(C) term because it is a constant with respect to the optimization parameters.(Figure 1(h) illustrates the distributions over which we solve for the optimal F,B and α parameters.)
The problem is now reduced to defining the log likelihoods L(C|F,B,α),L(F),L(B),and L(α)
翻译：
在MAP估计中，我们从给出的观测值C找到可能性最大的F，B,α,作为估计值。我们通过最大化的P概率分布来表达这一公式，用贝叶斯法则表示结果，然后转化为用log函数的可能性之和。在公式中 L（.）的值为logP(.) 我们丢弃了P（C）元素，因为它是一个可调的常熟。图 1（h）阐述了我们处理的最佳的F,B和alpha变量的分布这个问题现在就减少到定义L(C|F,B,α),L(F),L(B),and L(α)
词汇：
express:表达
maximization:最大化
optimal:最佳的
正文：
We can model the first term by measuring the difference between the observed color and the color that would be predicted by the estimated F,B,and α:
...
This log-likelihood models error in the measurement of C and corresponds to a Gaussian probability distribution centered at C拔=αF + (1 − α)B with standard deviation σC .
翻译：第一部分的建模我们可以通过测量观测到的颜色和我们通过估计的F,B和alpha预测出来的颜色的区别。该对数似然模型在C的测量中模型误差对应以C=alphaF+(1-alphaB为中心的高斯概率分布，具有标准差σC。
词汇：
measurement:尺寸，大小
deviation:偏差
正文：
We use the spatial coherence of the image to estimate the foreground termL(F).That is,we build the color probability distribution using the known and previously estimated foreground colors within each pixel's neighborhood N.To more robustly model the foreground color distribution,we weight the contribution of each nearby pixel i in N according to two separate factors.First,we weight the pixel's contribution by alphai2,which gives colors of more opaque pixels higher confidence.Second,we use a spatial Gaussian fall-off gi with σ = 8 to stress the contribution of nearby pixesl over those that are further away.The combined weight is then wi = α2igi
翻译：
我们用图像的空间簇来估计前景元素,我们通过在每个像素领域N内，用一只的先前估计的前景颜色来为这个颜色建立概率分布，为了构建过更加稳健的前景颜色分布，我们根据两个分离的对象衡量在N中每个邻近像素i的贡献度。首先，我们通过ai2来很亮每个像素的贡献，这个给透明像素更多的置信度。第二部，我们用以个空间高斯下降gi,方差为8来约束附近颜色贡献和远离颜色的贡献，这样组合权重就变成了wi = ai2gi;
词汇：
spatial:空间
coherence:附着，凝聚
robustly:稳健地
正文：
Given a set of foreground colors and their corresponding weights,we first partition colors into several clusters using the method of Orchard and Bouman.
For each cluster,we calculate the weighted mean color F and the weighted covariance matrix ΣF :
where W = Σi∈N wi.The log likelihoods for the background L(F) can then be modeled as being derived frome an oriented elloptical Gaussian distribution,using the weighted covariance matrix as follows.
翻译：
给一个前景颜色簇和他们的对应簇。我们使用Orchard和Bouman的方法将颜色分为几个簇.对每一个簇，我们计算出平均值F拔，和协方差矩阵 ΣF
对于前景对数概率可以通过被定义的一个无向高斯分布来进行建模，用下面的协方差矩阵。
词汇：
partition:v. n.划分
正文：
The definition of the log likelihood for the background L(B) depends on which matting problem we are solving. For natural image matting problem we are solving.For natural image matting,we use an analogous term to that of the foreground,setting wi to (1 − αi)2gi and substituting B in place of F inevery term of equations,and().For constant-color matting,we calculate the mean and covariance for the set of all pixels that are labelled as background.For difference matting,we have the background color at each pixel;we therefore use the know background color as the mean and a user-defined variance to model the noise of the background;
翻译：
背景L（B）的定义依赖于我们解决的遮罩问题。对于自然消光问题，我们使用前景的类似方法，设置权重wi为(1 − αi)2gi然后用B替换F的位置，在每一个等式中。对于恒色颜色的消光，我们计算出所有的被标记为背景的颜色簇平均值和方差。不同之处在于，我们在每一个像素上都有背景颜色。我们把已知的背景色作为平均值和一个用户定义的值来作为背景的噪音。
词汇：
analogous:类似的，相似的
substituting:替代，替换
正文：
In this work,we assume that the log likelihood for the opacity L（α） is constant(and thus omitted from the maximization in equation).A better definition of L(α) derived from statistics of real alpha mattes is left as future work.
翻译：
在这项工作中，我们假设对数概率L(α)是一个恒定的书（可以冲最大化方程中忽略）一个好的定义L(alpha)来源于正式的alpha遮罩数据留作未来的工作
词汇：
omit:忽略
正文：
Because of the multiplications of α with F and B in the log
likelihood L(C | F, B, α), the function we are maximizing in (4) is not a quadratic equation in its unknowns.To solve the equation efficiently,we break the problem into two quadratic sub-problems,we assume that alpha is a constant.Under this assumption,taking the partial derivatives of (4) with respect to F and B and setting them equal to 0 gives:
翻译：
因为α和F,B在对数概率L(C|F,B,alpha)中相乘，我们在（4）最大化不是一个二次未知方程。为了高效的解决方程，我们吧问题非为了连个二次子问题,我们假设alpha是一个常数。在这个假设下，
取（4）的偏导数相对于F和B,并且设置他们等于0
词汇：
multiplication:乘法
quadratic equation:二次方程
partial:部分的
derivatives:衍生物
partial derivatives：偏导数
with respect to :关于，相对于
正文：where I is a 3*3 identity matrix.Therfore,for a constant alpha,we can find the best parameters F and B by soving the 6*6 linear equation(9).
翻译：I是一个3*3 的单位矩阵。在alpha是一个常数的情况下，我们可以通过一个6*6的线性方程找到一个最好的值F和B
词汇：
identity matrix:单位矩阵
正文：
In the second sub-problem,we assume that F and B are constant,yielding a quadratic equation in alpha.we arrive at the solution to this equation by projecting the observed color C onto the line segment FB in color space:
...
where the numerator contains a dot product between two color difference vector.
To optimize the overall equation we to be much closer to the ground truth.
翻译：
在第二个子问题中，我们假设F和B是常数，在alpha中产生一个二次方程。我们通过将观测到的颜色C投射到颜色空间中的线段FB上来的到问题的答案。
分子上包含一个连个不同颜色向量的点运算。位了最优化我们的总体方程，我们就非常的接近真实值了。
词汇：
yield：产生
numerator:（分数的）分子
overall:总体
正文：
4.2 Natural image matting
Figure 4 provides an artificial example of"natural image matting",one for which we have a ground-truth solution.The input image was produced by taking the ground-truth solution for the previous blue-screen matting example,compositing it over a checkerboard background,displaying the resulting image on a monitor,and then re-photographing the scene
翻译：
自然抠图
土司提供了一这自然抠图的人工案例对这个我们有一个真实的解决方案。输入图片是通过真实的解决方案从之前的蓝色遮罩实例，在（）的背景上组合在显示器其上显示结果图片，然后重新截取画面产生的。