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1、 中國地質(zhì)大學(xué)（北京） 本科畢業(yè)設(shè)計外文資料翻譯 院（系）： 信息工程學(xué)院 專 　　業(yè)： 計算機科學(xué)與技術(shù) 姓 名： 周瑞旋 學(xué) 號： 04106113 外文出處： Massachusetts Institute of Technology, Computer Science l Intelligence Laboratory

2、 附 件： 1.外文資料翻譯譯文；2.外文原文。 完成日期： 2010 年　4月　20日 暫時性不規(guī)則動態(tài)紋理的背景減法 Gerald Dalley, Joshua Migdal,和W.EricL. Grimson 麻省理工學(xué)院計算機科學(xué)和人工智能實驗室 麻薩諸塞州劍橋大街77號，麻薩諸塞州02139 摘 要 在傳統(tǒng)的混合高斯背景模型下，每個象素的生成過程被模式化為一個對顏色的混合高斯模型。不幸地是，當(dāng)背景包括動態(tài)紋理這個模型表現(xiàn)不佳。就像是樹在風(fēng)中飄動，水面蕩起漣漪。來解決這一問題的不足之處，研究人員最近將這種背景過

3、程看的更加復(fù)雜和/或致密。我們提出了廣義的模型MoG處理動態(tài)紋理。我們在背景模型的語境中做到更好，運用在復(fù)雜場景條件下的復(fù)雜的增長模型有比相互抵觸的方法更加精確的分割，而不是需要大部分的時間觀察本質(zhì)的大部分方面。 1.簡介 在現(xiàn)在的場景分析系統(tǒng)中一個典型的方法是為背景影響創(chuàng)建一個適合的統(tǒng)計模型，當(dāng)一個新的框架出現(xiàn), 不可能被這個模制作的像素點被標(biāo)記在最顯著的位置。Stauffer 和Grimson [11]將起描述為混合高斯模型。 在每個像素處，有一個收集高斯發(fā)射值或者是其他色彩空隙。當(dāng)一個像素值在一個新的框架中被發(fā)現(xiàn), 它是匹配的高斯最有可能的排放。The高斯則是更新這些像素值,利用

4、指數(shù)遺忘近似方案在線k均值算法。這允許在線適應(yīng)變化的成像等約束條件，在照明或?qū)ο筠D(zhuǎn)移靜止不動。像素值被列為前景當(dāng)他們與不平常的高斯技術(shù)相關(guān)聯(lián)或者是當(dāng)他們不能很好的符合任何高斯。他的方法可能實時實現(xiàn)而且若照相機不移動會有更好的效果。然而，對于大部分應(yīng)用程序而言，像樹枝樹葉在風(fēng)中搖曳、水面激起漣漪的事情,應(yīng)該被認(rèn)為是背景即使他們包含運動。因為在個別像素水平，這些動態(tài)的問題引起更大的變化，他們通常無法模仿在一個完全獨立的像素的模型。在中間列的數(shù)字五， 我們看到MoG 前景怎樣不僅掩飾包含行人和車輛，還掩飾由于許多其他像素圖像噪聲的動人的樹木。 最近, Mittal 和 Paragios [5]

5、運用最近的 T框架創(chuàng)造一個色彩與光學(xué)流量的非參數(shù)模型，小心的處理測量的不確定性，核密度估計帶寬，不確定性管理在這里特別重要用于當(dāng)?shù)氐墓饬魉逃械钠缌x的估計。雖然他們的方法仍然模型的圖像為相互獨立的像素，他們生產(chǎn)的結(jié)果令人印象深刻的時候相同的動作,多次觀察每一個街區(qū)T幀。當(dāng)罕見的運動出現(xiàn)時變化是可能發(fā)生的,例如由于一陣狂風(fēng)樹木周期性的發(fā)出瑟瑟聲。更好的分類性能結(jié)果在成本為200個框架的線性載窗口,他們的高度優(yōu)化實現(xiàn)一到兩個命令MoG速度比典型的實現(xiàn)。Sheikh和Shah [10]已經(jīng)建立了一個核心基礎(chǔ)的背景模型運用現(xiàn)在的T框架他們是技術(shù)的籽粒像素顏色和位置。通過允許觀察像素匹配仁為中心在相鄰

6、像素位置, 他們能翻出來小空間的運動,如樹在風(fēng)中飄動作為背景像Mittal 和 Paragios。他們必須維持一個長期的歷史去維持所有背景中的分辨率。幸運的是，對于很多種類的場景，這個里歷史長度將對于阿拉伯酋長和沙特酋長將會變少，從信息可與國王“分享”由仁,附近的像素值。我們將顯示我們的方法能夠達到同樣的共享我們這樣做的好處,并由其中一小部分很容易。 對任何MOG系統(tǒng)進行修改，Nam and Han [6]最近發(fā)布了一種后臺減法的方法，用顆粒過濾的方法來追蹤衍生像素進程的位置。他們用一種勻速運動（包括高斯噪聲）的模型，然后用彩色柱狀圖來表示一些離散的噪聲出現(xiàn)的頻率。為了使系統(tǒng)操作簡便，他們進

7、行了一些簡單的假設(shè)來應(yīng)對一些特殊的情況，進而得出結(jié)論和做一些修改。有相當(dāng)數(shù)量的結(jié)果是現(xiàn)成的。Zhong and Sclaroff [15] 用一種平均自回歸移動模型來處理一些常規(guī)動力學(xué)背景的紋理。為了保持在96幀，他們保持80eigenimages。 Jojic and Frey [3]用了一種完全不同的方法，他們把Wang and Adelson的模型進行了擴展。他們認(rèn)為圖像是在收集層中產(chǎn)生的，這需要每一層都緊緊相連。他們的模型假設(shè)所有的層數(shù)都是顯而易見并且固定不變的。通過圖像每一層都可以自由的轉(zhuǎn)化。擴展包括了Winn and Blake’s [14]的仿射運動模型。因為尋找最優(yōu)解是很困難

8、的，他們在他們的模型中采用了最優(yōu)近似值的辦法。不像其它方法所提及的，他們應(yīng)用了一種分批處理的辦法，所以它不能被用來處理連續(xù)的圖像。 我們的工作與Stauffer和Grimson關(guān)Sheikh and Shah的工作有關(guān)。我們將使用一個空間里背景似然估計與MoG半?yún)?shù)性的表示法。第二部分我們描述普遍性的模型以及怎樣在其上運行推理。第三部分我們更加突出我們已經(jīng)做過的算法的試驗。第四部分進行推理。 2.我們的模型 由于模型部分不能完全理解，只作部分翻譯。 發(fā)現(xiàn)監(jiān)視的可能性 N(ci; μj ,_j)對于每一復(fù)雜的組成 j,，并且更新它的充分統(tǒng)計量假設(shè)一個證明重量(1)為老年人?__統(tǒng)計新數(shù)據(jù)

9、,指出,在μj _N(ci),_j)。對于一些指數(shù)學(xué)習(xí)速率。典型的EMlike實現(xiàn)這種進一步簡化只有更新最可能的高斯使用1?和作為證據(jù)重量。 根據(jù)初始化及在線更新,第二個途徑接近于變形的高斯協(xié)變性高估的分布更少。最近Porikli 和Thornton [8]運用先前更豐富的模型包括一個貪婪的更新方案的更新和減少效應(yīng)的更新. 所有的這三個更新機構(gòu)已經(jīng)被用于可能性模板。本質(zhì)上等于方程. 1,跟隔壁像素相同 限于單純考慮的技術(shù)和觀察相同的像素位置。在我們的模型中，允許像素產(chǎn)生于附近的高斯　這意味著每個高斯的可能性觀察多個獨立的生成，也意味著因此可能需要更新來自多個同步測量。一個完成這個的方法是保

10、持時間加重樣本和j , 方格樣本和校正(t)j , 已經(jīng)總的影響大小e(t)j 作為跟隨: 當(dāng)α遞歸的降低舊樣本的值是Pcontribution像素的觀察[j].我對高斯,和 　　_ij[j]. = 1,我們的模型參數(shù)進行了， 這個問題在這一點上是如何分配的更新αij 的值。 3．試驗 為了檢驗我們的算法，我們當(dāng)下的出版物上選擇了很多視頻文件，這些視頻文件在樹葉隨風(fēng)搖動、水面蕩起漣漪時提供更好的背景減法我們在平穩(wěn)的幀上為所有前景像素坐上標(biāo)簽。有歧義的或者與前景混合的以及背景已經(jīng)做了上“不關(guān)系”標(biāo)記的像素在我們的評估中被忽略。作為例子的幀在fig5中被指出。同很多現(xiàn)代的背

11、景減法系統(tǒng)一樣，我第一次計算方格的馬氏距離的地圖， 以及處理它的方法是用馬爾科夫隨機場去分類像素作為前景或者是背景 (看 [2], [4]).我們的馬爾馬爾科夫隨機場最小化標(biāo)準(zhǔn)的 Potts 能量函數(shù) 當(dāng)有如下條件時 3.1. 變動率指標(biāo)分析 如果我們改變馬爾科夫隨機場的參數(shù)，使之超過實驗和收集中的進程的超像素分類速率, 我們在特性接收器(ROC) 曲線處取點。這時候我們在凸多邊形估計所有的ROC系統(tǒng)的特點。在Fig. 3中, 我們顯示收藏的關(guān)于在那個揮舞著樹木視頻剪輯[12].的實驗的ROC曲線 每個曲線用不同的鄰近值。為了做出這樣的修剪，我們的方法在標(biāo)準(zhǔn)MOG系統(tǒng)前

12、臺破案率有著明顯的有點。比較適合使用3*3窗口，因為某些像素并不適合樹形運動。 圖形4. 利用重復(fù)的結(jié)構(gòu)低于最大的結(jié)構(gòu)運動允許更小的窗口?？紤]背景模型的的每一個像素，如同靜止的樹葉飛向藍天。我們將考慮到村輪廓的當(dāng)前像素出現(xiàn)的狀況。假設(shè)突然刮起一陣大風(fēng)樹葉飄落, 如圖所示運動。 　在褐色的輪廓中，我們現(xiàn)在想為每個像素找到更好的機械高斯背景，與普遍的高斯相適應(yīng)，我們需要一個 99 的窗口；然而一個比33更小的窗口 允許與更小的樹葉匹配。 3.2. 多場景中的實驗 在圖5中我們列舉了比較結(jié)果，這些結(jié)果來自從我們實驗影像中選擇出來的部分影像幀。在前兩行中，我們在向數(shù)據(jù)中輸出最為幀和最為熟知的

13、結(jié)果。第三個和第四行，分別的運用moc模型顯示與最近外觀距離相配的馬氏距離。圖像時為了形象化的目的的開端。和形態(tài)學(xué)運作之后，馬氏距離。最后行包含手標(biāo)記的地面真實，其中每個對象提供一個不同的色調(diào)和不關(guān)心像素在顯示較淡。視頻剪輯由左到右排列為簡到繁。第一列是由經(jīng)典的壁花紙、富山等。 [12]。 200幀，場景是空的，關(guān)閉相機的人積極并持續(xù)震動 樹，產(chǎn)生一個半正規(guī)的動態(tài)紋理。一個人 進入現(xiàn)場，一幀是標(biāo)示地面實況。 “最佳發(fā)布”結(jié)果是最好的結(jié)果從原始文件。對于貓和我們的方法，我們使用相同的參數(shù)，除了鄰里設(shè)置（大?。?。當(dāng)您在馬氏距離地圖，我們的方法抑制揮舞著樹木更有效地比傳統(tǒng)的，并且仍然能夠接最多人

14、很好。 第二列和第三列來columns自于Mittal 和Paragios的交通錄像的410到150幀，我們將他們的結(jié)果放在第二列。這些結(jié)果的梯度變化表明了他們曾用更高級別的模塊來檢測汽車并隱藏與汽車檢測結(jié)果不一致的噪聲。并且被檢測的前景區(qū)域明顯的比整個車輛要小。 因為涌動的葉浪，MoG模型無法完全的隱藏偽造的相似性，即使我們允許它的參數(shù)取得獨立的最優(yōu)值。我們的模型能夠藏匿在這兩個幀中所有偽造的相似，甚至能正確的檢測出在幀150中的兩個步行者 第四個陣列來自幀766，一個極有爭議的禮貌接待伊朗酋長次序。我們不清楚任何現(xiàn)存的已公布的關(guān)于次序的結(jié)果，這個場景由漣漪的水波，隨風(fēng)擺動的大葉熱

15、帶植物，兩只與水的顏色很接近的正在游泳的鴨子組成。相比于MoG 最好的結(jié)果，我們的模型能夠產(chǎn)生更加清淺的陰影并減少模糊的小錯誤 最后的陣列來至于幀36（Zhong and Sclaroff dynamic texture clip動態(tài)紋理接線柱 [15]），我們的前景檢測更加清晰并且更加完全的捕獲漂流瓶。在實際應(yīng)用中，我們已經(jīng)證實我們的理論研究與實際的交通監(jiān)視戶內(nèi)監(jiān)視和海上輪船追蹤的結(jié)果一致。在更多的復(fù)雜的擁有動態(tài)紋理的水面場景，我們已經(jīng)發(fā)現(xiàn)了動態(tài)視覺學(xué)和時空衍生物對于建造未來的用途 4．結(jié)論 在本文中，我們引入了新的圖像生成模式，這種模式考慮到動態(tài)背景紋理的空間不確定性。我們的模式（[

16、15]，[10]，[5]）比最近引進的來處理這個問題的方法更加緊湊。，在乎混合的高斯模型框架中，我們可以很容易地實施，并且它的性能優(yōu)于競爭對手的方法。 5．鳴謝 這部分工作經(jīng)費由國防部高級研究計劃局提供（DARPA）。 Background Subtraction for Temporally Irregular Dynamic Textures Gerald Dalley, Joshua Migdal, and W. Eric L. Grimson Massachusetts Institute of Technology, Computer Science and Arti

17、ficial Intelligence Laboratory 77 Massachusetts Ave., Cambridge, MA 02139 Abstract In the traditional mixture of Gaussians backgroundmodel, the generating process of each pixel is modeled as a mixture of Gaussians over color. Unfortunately, this model performs poorly when the background consist

18、s of dynamic textures such as trees waving in the wind and rippling water. To address this deficiency, researchers have recently looked to more complex and/or less compact representa tions of the background process. We propose a generalization of the MoG model that handles dynamic textures. In the

19、context of background modeling, we achieve better, more accurate segmentations than the competing methods, using a model whose complexity grows with the underlying complexity of the scene (as any good model should), rather than the amount of time required to observe all aspects of the texture. 1. I

20、ntroduction A typical approach in current scene analysis systems is to build an adaptive statistical model of the background image. When a new frame is presented, pixels that are unlikely to have been generated by this model are labeled as foreground. Stauffer and Grimson [11] represent the backgro

21、und as a mixture of Gaussians (MoG). At each pixel, a collection of Gaussians emits values in RGB (red, green, blue) or some other colorspace. When a pixel value is observed in a new frame, it is matched to the Gaussian most likely to emit it. The Gaussian is then updated with this pixel value using

22、 an exponential forgetting scheme that approximates an online k-means algorithm. This allows online adaptation to changing imaging conditions such as shifts in lighting or objects that stop moving. Pixel values are labeled as foreground when they are associated with uncommon Gaussians or when they d

23、o not match any Gaussian well. This approach lends itself to realtime implementation and works well when the camera does not move and neither does the “background.” However, for most applications, objects such as branches and leaves waving in the wind, and waves in water, should be considered as bac

24、kground even though they involve motion. Because these dynamic textures cause large changes at an individual pixel level, they typically fail to be modeled well under a fully independent pixel model. In the middle column of Fig. 5, we see how the MoG foreground mask not only (correctly) includes bot

25、h pedestrians and the vehicle, but also includes many other pixels due to image noise and moving trees. More recently, Mittal and Paragios [5] used the most recent T frames to build a non-parametric model of color and optical flow, with care taken to handle measurement uncertainty when estimating k

26、ernel density bandwidths. Uncertainty management is especially important here due to the inherent ambiguities in local optical flow estimation. While their approach still models the image as a collection of independent pixels, they produce impressive results when the same motions are observed many t

27、imes in every block of T frames. Challenges are likely to occur when infrequent motions occur, such as trees rustling periodically (but not constantly) due to wind gusts. Better classification performance results in a cost linear in T. For a 200-frame window, their highly optimized implementation is

28、 one to two orders of magnitude slower than typical MoG implementations. Sheikh and Shah [10] have also developed a kernel-based model of the background using the most recent T frames. Their kernels are Gaussians over the pixel color and location. By allowing observed pixels to match kernels centere

29、d at neighboring pixel locations, they are able to interpret small spatial motions such as trees waving in the wind as being part of the background. Like Mittal and Paragios, they must maintain a long enough kernel history to representall modes in the local background distribution. Fortunately, for

30、many types of scenes, this history length will be shorter for Sheikh and Shah since information can be “shared” by kernels spawned by nearby pixels. We will show that our approach is able to achieve similar sharing benefits, and we do so by including a small set of easilyimplemented modifications to

31、 any standard MoG system. Nam and Han [6] recently published a background subtraction method that uses particle filtering to track the positions of the generative model’s pixel processes. They use a constant velocity (plus Gaussian noise) motion model, and they represent the appearance distribution

32、of an individual pixel process as a color histogram. In order to make the problem tractable, they make several simplifying assumptions that allow for independent decisions in the inference and update stages. Limited quantitative results are given. Zhong and Sclaroff [15] use an autoregressive moving

33、 average model for scenes with highly regular dynamic background in 80 eigenimages. Jojic and Frey [3] have taken a radically different approach, extending a model proposed by Wang and Adelson [13]. They consider an image to be generated by a collection of layers, where near layers occlude far ones.

34、 Their model assumes that the number of layers and their depth ordering are known and fixed. Each layer is free to translate across the image. Extensions includeWinn and Blake’s [14] affine motion model. Because finding the optimal solution is intractable, they employ variational approximations to

35、their model. Unlike the other methods mentioned, their approach is batch-mode, so it cannot be used as-is on continuous video feeds. Our work is most closely related to that of Stauffer and Grimson and of Sheikh and Shah. We combine the usage of a spatial neighborhood in background likelihood estima

36、tion with the compactness of a semi-parametric MoG representation In 2, we describe our generative model and how we perform inference on it. In 3, we then highlight experiments we have performed on our algorithm. We conclude in 4. 2. Our model We model the image generation process as arising from

37、a mixture of components that have a Gaussian distribution in color and some spatial distribution: pci __/Xj∈Ni wjN(ci; μj ,_j) , (1) where ci is the observed color at pixel location i, _ ={wj , lj , μj ,_j}j is our model, and Ni is the set of indicesof mixture components that lie in the local spat

38、ial neighborhoodof pixel i. Each component j in our model has anassociated mixture weight wj , a discrete pixel location lj , mean color μj , and color covariance matrix _j . We assumethat each observed pixel value is sampled from our model independently. This same assumption is made with nearl all

39、non-layered approaches, including ones that have a spatial component (e.g. Sheikh and Shah [10]). Note that we are not restricted to the RGB colorspace for observations. As with other models, we are free to use other colorspaces (such as YCrCb) or build an observation space over more exotic features

40、 such as spatio-temporal gradients [7] or optical flow [5]. In our experience we have found that when a proper neighborhood size is chosen, the background-foreground labeling is less sensitive to the choice of colorspace or the inclusion of optical flow features. 2.1. Foreground-background classif

41、ication The primary purpose of most background models is to determine the likelihood that each pixel was generated from the background process. In classic MoG approaches, the model is the same as Eqn. 1, with the constraint that the neighborhood function is degenerate and only selects mixture comp

42、onents at the same location where the colors are sampled, i.e. when Ni =_j lj = i . A collection of mixture components is maintained, where only those with the highest weights are considered part of the model and used in the likelihood evaluation. Under the assumptions that all Gaussians have simila

43、r covariances, all background Gaussians have comparable weights, and that they do not overlap significantly, the squared Mahalanobis distance dij = (ci ? μj)T_?1j (ci ? μj) (2)serves as a good proxy for the negative log likelihood, and it can be computed much more efficiently than the precise likeli

44、hood value. For the experiments presented in this paper, we have followed this tradition and used the squared Mahalanobis feature for foreground-background classification.After the model returns the pixelwise likelihood estimates, a higher-level procedure is responsible for classifying each pixel as

45、 foreground or background. Common choices for the external classifier often include some combination of a simple thresholder, a Markov Random Field optimizer to perform uncertainty-aware label smoothing, morphological operations to remove isolated foreground detections and merge disjoint blobs, and

46、higher-level detection, tracking, or explicit foreground modeling to filter the results. The external classifier choice is outside the scope of the model itself; we will discuss our choice in 3. 2.2. Model update A model consisting of a single Gaussian may be updated online as new observations ar

47、e obtained in an optimal manner by retaining its sufficient statistics. Mixture distributions add the complexity of needing to know which observations were generated from which mixture components. Stauffer and Grimson [11] use an online approximation of expectation maximization. Given a pixel locati

48、on i, theyfind the observation likelihood N(ci; μj ,j) for each mixture component j, and then update its sufficient statistics by assuming an evidentiary weight of (1?) for the old statistics and  for the new data point, where  = N(ci; μj ,j)for some exponential learning rate . Typical hard EMl

49、ike implementations simplify this further by only updating the most likely Gaussian using 1 ? and as evidentiary weights. Depending on initialization and the order of online updates, the second approach tends to yield tighter Gaussian distributions that overestimate the covariance less. More recentl

50、y, Porikli and Thornton [8] used a richer prior model with a greedy update scheme to improve the updates and reduce the effects of the order of updates. All three of these update mechanisms have been used on likelihood models essentially equivalent to Eqn. 1, with the neighborhood size restricted to

51、 only consider Gaussians and observations at the same pixel location. In our model, we allow pixels to be generated from nearby Gaussians. This means each Gaussian has the possibility of independently generating multiple observations and thus potentially needs to be updated from multiple simultaneou

52、s measurements. One way of accomplishing this is to retain the time-weighted sample sum s(t)j , squared samplesum corr(t)j , and total effective sample size e(t)j as follows: where ecursively downweighs old samples, ij is thePcontribution of the observation at pixel i to Gaussian j, andj ij =

53、1, and our model parameters are derived as The question at this point is how to assign the update weights ij . There are several logical possibilities, including: ? Pure Soft: For each observation, ci, we update all mixture components that could have generated it, weighting by the likelihood of be

54、ing generated by that Gaussian, i.e. where _ is some threshold that allows us to avoid updating poor matches. If no mixture components pass the _ test, we assume some previously-unseen mixture component generated the pixel and we instantiate a new component j′ at lj′ = i instead of performing an upd

55、ate. ? Pure Hard: We choose the single mixture componentwhich was most likely to have generated the sampleand update it alone, i.e. While the pure soft scheme is appealing from a Bayesian perspective, it (and soft local) also requires that weactually evaluate the likelihoods, N(ci; μj ,j). The

56、hard approaches only require evaluating the much more computationally-efficient squared Mahalanobis distances.In Fig. 1, we have plotted the relative computational costs of the various update methods, relative to the baseline standard MoG approach (hard local with W = 1).These plots aggregate the re

57、sults from running with a variety of parameter settings on several different machines while processing the traffic sequence from Mittal and Paragios [5]. The local approaches are relatively unaffected by the neighborhood size,W, since they do not iterate over the whole neighborhood during the update

58、 phase. It is clear that the pure soft approach incurs a significant additional performance penalty due to its requirements of full likelihood evaluation and that potentially all mixture components in the local neighborhood about a pixel must be updated. For the same set of experiments, we show in F

59、ig. 2 the costs of producing the Mahalanobis distance maps required by the foreground/background classifier. Given an update scheme, we expect the the computational cost to rise linearly with the neighborhood size. The update schemes are independent of this step, so it is interesting to note that by

60、 either choosing hard updates and/or local updates, the Mahalanobis calculations become faster. When we do hard updates, we force each sampled pixel to effect exactly one mixture component. Similarly, local updates can only affect a smaller pool of components. The net affect is that a slightly more

61、compact model can be learned. This more compact model is more computationally efficient as well because fewer Mahalanobis distance calculations are necessary. 3. Experiments To test our algorithm, we selected several videos from recent publications which attempt to provide better background subtra

62、ction in the face of waving trees and/or rippling water. We then hand-labeled all foreground pixels in an evenly-spaced set of frames. Pixels that are ambiguous or are alpha blends of foreground and background are marked as “don’t-care” in our labeling and are ignored in our evaluation. Sample frame

63、s from the videos are given in Fig. 5. Like many modern background subtraction systems, we first compute the background squared Mahalanobis distance map and process it with a Markov Random Field (MRF) to classify pixels as foreground or background (see [2], [4]). Our MRF minimizes a standard Potts

64、 energy function: Where 3.1. ROC Analysis If we vary the MRF parameters over the course of a collection of experiments and record the per-pixel classification rates, we are sampling points in the receiver-operator characteristics (ROC) curve. We then may estimate the overall ROC characteristi

65、cs of the system by taking the convex hull of these points [9]. In Fig. 3, we show the ROC curve for a collection of experiments on theWallflower waving trees video clip [12]. Each curve uses a different neighborhood size. For this clip, our method shows a clear advantage over the standard MoG in fo

66、reground detection rates. Using a 3 3 window is sufficient in this case because the tree motion is limited to a few pixels. Figure 4. Exploiting repetitive texture under large inter-frame motion to allow smaller windows: Consider a background model with one Gaussian per pixel learned from a stationary pair of leaves against the blue sky (leftmost image). We will be concentrating on what happens at the pixel location with the bold outline. Suppose a sudden gust of wind moves the top