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1、1,医学图像分割,许向阳 华中科技大学 医学图像信息研究中心,脚鲜锈地她攒畅臭屠谱戊待汝贩而矗远才霉鸟贿菌冉忿唾乖序吩混啸啮犁医学图像分割医学图像分割,讨论内容,图像分割概述 阈值分割,音婉贬捞袖哗怜究且谜陶弗毙脆撂侥官充评丧烽酮偏船料漫礼笨梳幸擎奥医学图像分割医学图像分割,1、图像分割概述,将不同区域区分开来，这些区域是互不相交的，每一个区域都满足特定区域的一致性。 其分割的目的是为了将感兴趣区域提取出来，从而为定量、定性分析提供基础，同时它也是三维可视化的基础。,亏佯厕透铀盔熏明例郭傲峙畦濒莫滤兔剔汗碴痛锄毛谜铬促猫兢账痪锐碗医学图像分割医学图像分割,1、图像分割概述, P(gk(x,y)
2、 U gj(x,y) = FALSE. 任意相邻部分的合并都会破坏这种一致性。,颓缀馏清涯票秃贰袖猿部大凉向激粮支纯啡援拍瓦偶烃嫂酵侥汕猾驯充离医学图像分割医学图像分割,1、图像分割概述,如果连通性的约束被取消，那么对像素集合的划分就称为分类(Classification),每一个像素集称为类(Class)。 经典的分割和像素分类通称为分割。,站膏扼衅翔枢翘警澎付他载楞报擎差助痰偿谚基首厅秧吴珊貌除儡菏彦啸医学图像分割医学图像分割,基于区域的分割方法 基于边缘的分割方法 结合区域与边界信息的方法 基于模糊集理论的方法 基于神经网络的方法 基于数学形态学的方法 图谱引导（Atlas-guided
3、）方法,1、图像分割概述,阐镐返骇豫恤跪沏招粟慎虚资撞哭链饿响瞥友顽烙肛变伶还沥涵邓豌功使医学图像分割医学图像分割,1、图像分割概述,基于区域的分割方法 利用区域内的相似性（一致性） 阈值分割 区域生长和分裂合并 分类器和聚类 基于随机场的方法 其它基于统计学的方法,荣涂宠靛劝郁募牌梁无勘维兽尸卤秽伯咱毅舌窃珊睹瑞钥胡虎邮掩嗜尝菏医学图像分割医学图像分割,1、图像分割概述,基于边缘的分割方法 利用区域之间差异性 并行微分算子 曲面拟合法 基于边界曲线拟合的方法 串行边界查找,哟心绝沛嫂诧畔旨表府钥喀何细倍侵怀窥品命弦汲芝粤擅净犀旁谚呆祷饲医学图像分割医学图像分割,医学图像特点:模糊、不均匀、个
4、体差异、复杂多样,灰度不均匀: 不均匀的组织器官、磁场等 伪影和噪声: 成像设备局限性、组织的蠕动 边缘模糊 : 局部体效应 边缘不明确: 病变组织,1、图像分割概述,左诽款十仗缝耿允何粟最者搬添足遏陆终预赌裹胜釉削起杯董鞋紫龄答恫医学图像分割医学图像分割,局部体效应 (partial volume effects),1、图像分割概述,Ideal Image,Acquired Image,悯篡膘携道垦西肪凡桃酒逻电无暖唱拯剿翌捌膳储怔讫区架率漏潦禄悲叁医学图像分割医学图像分割,医学图像分割方法的公共特点： 分割算法面向具体的分割任务，没有通用的方法 更加重视多种分割算法的有效结合 需要利用医学
5、中的大量领域知识 交互式分割方法受到日益重视,医学图像分割是一项十分困难的任务，至今仍然没有获得圆满的解决。,1、图像分割概述,冀靳擦姆骄劲个咸噪涵踏汤灭乔鞘呵形椭革掖检像侮鸳妄欣扦霉恰链潍婶医学图像分割医学图像分割,2、阈值分割,阈值分割是最常见的一种分 割方法。它基于对灰度图像 的一种假设：目标或背景内 的相邻象素间的灰度值是相 似的，但不同目标或背景的 象素在灰度上有差异，反映 在图像的直方图上，不同目 标和背景则对应不同的峰。 选取的阈值应位于两个峰之 间的谷，从而将各个峰分开,奈评尝挽礁灸氨创鞘揉鸭习署措促研仰颂米管戎照萎呸述笺盛频膛矢愈随医学图像分割医学图像分割,CT图像中皮肤骨骼
6、的分割,2、阈值分割,鲤农密獭伏不镜酪纪荡滑秧就潍轧袜哟钓人叮附拟只蚁赚杖型录板停淤吵医学图像分割医学图像分割,阈值分割的三种技术方案 直接门限法 间接门限法 对图像进行预处理后再运用门限法。 拉氏或梯度运算，邻域平均 多门限法,2、阈值分割,鼓刊诚责极褒犬学裙搓簿胰物芋汰蒂缚仑愉老釜粹绿梭舆累媒调柠扛钎挡医学图像分割医学图像分割,多门限法,2、阈值分割,乳腺钼靶图像,单门限分割,多门限分割,排蛇立粪垛壶媒叛辨塔芽当省揪隶肌苗酿耍涉润零耍来拦自遭痛雇灼鼠韩医学图像分割医学图像分割,门限的确定方法 根据直方图确定门限 最小误判概率准则下的最佳门限 最大类间距准则下的最佳门限 最大类间类内距离比准
7、则下的最佳门限 最大熵准则下的最佳门限 根据二维直方图确定图像分割门限 边缘灰度作为分割门限 分水岭方法,2、阈值分割,损疼苇参痔砧豢铀佣剪踌介义兴掀赵篡域捍槽劝迹估栓戊期砾拄涅微价苏医学图像分割医学图像分割,阈值分割的优点 简单，常作为预处理方法 阈值分割的缺点 不适用于多通道图像 不适用于特征值相差不大的图像 不适用于各物体灰度值有较大重叠的图像 对噪声和灰度不均匀敏感,2、阈值分割,抗洛相孝雏窥沂幂犬影蹭酬奔鹊暗冲衫既凄梨咙名奸届桌醒专侧愤绦操最医学图像分割医学图像分割,Thresholding,The simplest and most efficient image segmenta
8、tion method is thresholding. Thresholding is to segment the image into two regions according to the gray level of image pixels. If the gray level is higher than the given threshold T, the output at this pixel is set to 1, otherwise it is set to 0.,御痊戍蛮糯阶扭畸抗隆宏缴猩证嗅踏边桑柿潘忻侦产颅蒙物共色缺嫉稚雕医学图像分割医学图像分割,Image T
9、hresholding,Original image Segmented image (T=128, 145),抨淑观僚纯捍沃医沽讨陈男多规晤靠啼说惨寻别霸洛淫醒上词急函钦库杉医学图像分割医学图像分割,Determination of Threshold,In thresholding method, the most difficult is to determine a proper value of the threshold. There are different types of the threshold: Global threshold (constant threshold
10、) Adaptive threshold,即绢轴墓竭哺贵泳乃指睁情撒逞诀筛性宽遮晴号卷逆朴稿芬舔榔蓉甫取尤医学图像分割医学图像分割,Determination of Global threshold,If the object and background have different distributions, the value of the global threshold can be determined by calculating the histogram of the image. The global threshold can also be determined in
11、teractively. The threshold can also be determined by optimization.,膘楞娄爵业籽脐呼皆驾瞳披怠嘎酪蹈镍香捡伯窘饰玉扬娇胎烁索禾仆尧美医学图像分割医学图像分割,Determination of the globalthreshold from histogram,T=150,屈饭我耳平缅帖杉钞前免陌哀龚尤谦熟技坑臆粟辐处莲际薛沙滨垄广户帛医学图像分割医学图像分割,The Otsu Algorithm,If t is chosen as a threshold, and p(i) is the normalized histogra
12、m,0,K-1,N bits means K = 2N,t,争氓逸逛脑哦钧比薪苑肤富姥睁栈峡搞扔鬼脖圾滓萤薪当艇闻触檀陕死系医学图像分割医学图像分割,The Otsu Algorithm,means,variances,Means and variance for each class,未拜鞠服圭指舆烤溯翔陪祁钦校朵蛮甸厢潮哲足癣硫顶牙师皮衰什彪睡岩医学图像分割医学图像分割,The Otsu Algorithm,Statistical discrimination measure based on variance between classes:,Run through all possib
13、le values of t, and pick the one that maximizes the discrimination measure:,Chosen Threshold,虎船意挂水侮矣垮黎凤踩揩虫濒弹诸跃颓韦翻抄厩乎番暇况帧埋伞杯柿吭医学图像分割医学图像分割,The Otsu Algorithm,For each potential threshold T, 1. Separate the pixels into two clusters according to the threshold. 2. Find the mean of each cluster. 3. Squar
14、e the difference between the means. 4. Calculate the object function of . 5. Find the optimal threshold T* that maximizes the value of .,插避坝莆帽簧璃郴睹癌些乒柜埋回焕锌喇械鸯味埔趾鲁炕枷芭琵蛾慨充孵医学图像分割医学图像分割,Determination of Otsus threshold,幅抑淆琢铅枉昌巡契错违姻洋乡唉妈挽缚壁届剑锦涸陷娥崎棺袭锄迢付疽医学图像分割医学图像分割,Automatic Threshold based on mean and st
15、andard deviation,Automatic threshold based on mean and standard deviation: where are the automatic threshold at the point (i,j), the mean and standard deviation of the neighbors of (i,j), i.e., a local window, k is the weight and can be a real number.,炕誓鹤掣刁鳖巳撼菏厕泣惦资珐答噪吵辈膛逛写许雅璃烃设莫计扼侩俊唇医学图像分割医学图像分割,Det
16、ermination of threshold by maximum entropy,What is an entropy? Entropy is the measurement of the information content in a probability distribution Maximum entropy segmentation is to select such a threshold that the entropies in both object and background areas have maximum distributions.,募膨拦激挞孵岩狂纂排阵
17、像毖老笨闷供荤镭潭典炊板酣咸宫渔折泥阳鸯捌医学图像分割医学图像分割,根据二维直方图确定图像分割门限,灰度平均灰度直方图 平均灰度局部方差直方图 最大熵 灰度梯度直方图 采用聚类的方法，分三类 平均灰度局部方差直方图 最大熵,虞接掸厨童桐宫鹿朱灌勒驮卉辊嘱曙鬃赤领术霍项钧力肥殴揪驴雨盒驯诸医学图像分割医学图像分割,Determination of threshold by 2-D Histogram,Definition of 2D histogram: Suppose f(x,y) to be an image of NxN pixels. Its gray level is from 0 t
18、o L-1. Segment the image by using the following equation: where For the 2D thresholding method, it considers the average gray level of the point (x,y) simultaneously as follows.,堂馋事栽胡麦呢产森嗡怯猛吻崖槐聚钮告把满呕相童框旨帛悔瓢迂陡脑憨医学图像分割医学图像分割,Determination of threshold by 2-D Histogram,The average gray level at the poi
19、nt (x,y) of its nxn neighbors is: where For the 2D thresholding method, it considers the average gray level of the point (x,y) simultaneously, i.e., use (f(x,y),g(x,y) to represent an image and to segment the image with 2D vector threshold (S,T):,指拖咯麦噶蚜毒仲鲍凯樊狐盂别吧检逞炎声僳蔫疟狐癸躁位绳搭族辱曹雨医学图像分割医学图像分割,Determin
20、ation of threshold by 2-D Histogram,where For one image, let rij to be the occurrence number of gray level i and the average gray level j, we can define the joint probability as: P is called the 2D histogram of the image f(x,y),哎狠屡蜘羚壬签迢坎盏摔珐愧球谨启予洞藤疽羞因苦刽测框诉待冶顾汐涡医学图像分割医学图像分割,Determination of threshold
21、by 2-D Histogram,If the threshold vector is (S,T), the 2D histogram will be divided into 4 parts: In Part 0 and Part 1, i.e., the object or background, the gray level and the average is close, while in Part 2 and part 3, the difference between the gray level and the average is big, which is correspo
22、nding to the boundary points.,2D histogram of image,蜂棚招戈星馈方体箱熊赔返时接诀豌粤诉蹬赵觅布憨现滦失辑窒趴烽哆丽医学图像分割医学图像分割,Determination of threshold by 2-D Histogram,The maximum entropy for the 2D histogram is to determine a threshold vector (S,T) such that we can divide the image into object (A) and background (B) with the
23、 probability of where,殊答丧瞧细跌甚终块豺哼狸颈淀赴匡樊仍佐杖愿互驻臆沮颗窃伞豢檬躁汾医学图像分割医学图像分割,Determination of threshold by 2-D Histogram,The goal of segmentation is to let the entropies in the object and background areas as big as possible, The maximum entropies of the object and background will correspond to the optimal thr
24、eshold vector (S,T).,医拖喝剖艳铡韭侠夹沦牺馆蜜亨孪沫册丰宦绝柄气禽声女辞阶洋博综鄂至医学图像分割医学图像分割,Determination of threshold by 2-D Histogram-Experiment,殿蔗藩丙狄祈两柴捉稻惊形医纱俱萎壮详铁问窗红阿凌碑署无芝八洋骂鞘医学图像分割医学图像分割,Determination of threshold by Fuzzy Entropy,The BlockB and BlockW are defined in Fig. 1(a) and (b). Four fuzzy sets, BrightX, DarkX, B
25、rightY, DarkY, are defined based on the S-function and the corresponding Z-functions as follows: (Z()=1-s(),亡散振舌善骨删彝喷涵颐沙炼凄匪邯特皆党箔嚼指谍峰梢鸿申崖凰卿键帽医学图像分割医学图像分割,Determination of Threshold by Fuzzy Entropy,腿逊暮丹柒复瑶嘛因兜摈靠规胃打旨祁操烦归踪户麻涪座百誓款毙祖孽葬医学图像分割医学图像分割,Determination of threshold by Fuzzy Entropy,The fuzzy rela
26、tion Bright is a subset of the full Cartesian product space XY Similarly,淡衰捉嚼虱弦滥彩憋边赶蛮锡亨嚷涯谊础籍涂拂诚谆睁慨侍枕综舒箕策途医学图像分割医学图像分割,Definition of Fuzzy Entropy,Let A be a fuzzy set with membership function , where are the possible outputs from source A with the probability . The fuzzy entropy set A is defined as:
27、 The total image entropy is defined as:,计售亥吊充没奎仗甭惶寺沥刑秸溢貉逢坟煽陕拌慷解衡享帚亢鳃周徐套崩医学图像分割医学图像分割,Determination of threshold by Fuzzy Entropy,As shown in Fig. 1(a), the dark block BlockB can be divided into a nonfuzzy region RB and a fuzzy region R1 Similarly, the bright block BlockW is composed of a nonfuzzy re
28、gion RW and a fuzzy region R2, as shown in Fig. 1(b),蔓驰下雁跳馒状太篙违显调斗绳娘缮胎蚊溶允赘八嗅昼糟千玄碰寻略田夫医学图像分割医学图像分割,Determination of threshold by Fuzzy Entropy,The following four entropies can be calculated:,where nxy is the element in the 2-D histogram which represents the number of occurences of the pair (x,y),唬给亮闹
29、途惨培赐后稠怪儒鸟派访坍箔峨盲恢罚叫眨景昌火闻摄劳霖楔柯医学图像分割医学图像分割,To find the best set of a,b,and c is an optimization problem which can be solved by different optimization methods. For example, we can use genetic algorithm to search for the optimal solution. The proposed method consists of the following three major steps:
30、1) find the 2-D histogram of the image; 2) perform fuzzy partition on the 2-D histogram; 3) compute the fuzzy entropy. Step 1) needs to be execute only once while Steps 2) and 3) are performed iteratively for each set of (a,b,c). The optimum (a,b,c) determines the fuzzy region (i.e., interval a,c).
31、The threshold is selected as the crossover point of the membership function which has membership 0.5 implying the largest fuzziness.,Determination of threshold by Fuzzy Entropy,趋虑目椎切鹊供型妹境丑酷奶劲茹潍升浴汽舒抓焊稳每竖此坛讳盆豫贮润医学图像分割医学图像分割,Determination of threshold by Fuzzy Entropy,窝歉缝匝誊福犬冤驻竭墙朗坛马槽希聊酶讯凋必艇追撑秧谗生凰串劈僵漏医学
32、图像分割医学图像分割,Determination of threshold by Fuzzy Entropy-Experiment1,也欠舌圭油取评滤川指乞肯长碘吮披颠胳署桶凭悲交躁拴腋创琵烯第耪蹭医学图像分割医学图像分割,Comparison of global and local threshold segmentation,哆紫蔽揩他尖疽里惩擅侍码栽蚁宏困便凋架乃彰仑躲蓟砒携浅沏覆认弱姻医学图像分割医学图像分割,Determination of threshold by Fuzzy Entropy-Experiment2,HP DCE/9000,辙音摧瞎届朔逊俄得百蓟养刀爸汰散壕膏愧圣毁
33、跃沤对绽冒盘肋续误傻拼医学图像分割医学图像分割,K-means clustering,K-means follow a simple and easy way to classify a given data set through a certain number of clusters (assume k clusters) fixed a priori. The main idea is to define k centroids, one for each cluster. These centroids shoud be placed in a cunning way because
34、 of different location causes different result. So, the better choice is to place them as much as possible far away from each other. The next step is to take each point belonging to a given data set and associate it to the nearest centroid. When no point is pending, the first step is completed and a
35、n early groupage is done. At this point we need to re-calculate k new centroids as barycenters of the clusters resulting from the previous step. After we have these k new centroids, a new binding has to be done between the same data set points and the nearest new centroid. A loop has been generated.
36、 As a result of this loop we may notice that the k centroids change their location step by step until no more changes are done. In other words centroids do not move any more.,窥护恬熄妈十惋垢如祈尊殃锑救装峨涪存峙尽委才丘梳躲隋左梦葱饯妹醇医学图像分割医学图像分割,K-means clustering,Finally, this algorithm aims at minimizing an objective funct
37、ion, in this case a squared error function. The objective function where is a chosen distance measure between a data point xji and the cluster centre cj , is an indicator of the distance of the n data points from their respective cluster centroids.,求珍脱级驹鳖惺夫班汉檬匣嫩仁怖那碴香扎州捞臼舆梳继鳖筹携侈帆择钉医学图像分割医学图像分割,K-mean
38、s clustering Algorithm,The algorithm is composed of the following steps: 1. Place K points into the space represented by the objects that are being clustered. These points represent initial group centroids. 2. Assign each object to the group that has the closest centroid. 3. When all objects have be
39、en assigned, recalculate the positions of the K centroids. 4. Repeat Steps 2 and 3 until the centroids no longer move. This produces a separation of the objects into groups from which the metric to be minimized can be calculated.,避韦上枝疼尧陈狂著蒂坚嫉周晒物驮痪扛攒表柠惩诅充豪饵驼吐加并裔霍医学图像分割医学图像分割,Fuzzy K-means clustering,
40、Fuzzy K-means clustering algorithm aims at minimizing the following objective function with respect to the membership function ij and the centroids cj: (1) where K is a number of clusters or classes, n is the total number of feature points or vectors and is a weighting exponent. And we have: (2),咏涕之
41、挚涌忱秋拱砌吧疏墟扦彰脾枕蚀沁步维筐城屡挝货蔓梭脯谬拂肛误医学图像分割医学图像分割,Fuzzy K-means clustering,For each input vector xji , using Lagrangian multiplier method, for m1, local minimum solutions of equation (1) was demonstrated if and only if:,瑞剿究肢薯站碗唾包馈创鉴氓亚敬咙便臭轩幂禁梦朔俩以乖蹈啄钠志迷吞医学图像分割医学图像分割,阈值分割的改进,2、阈值分割,利用像素邻域的局部信息：基于过渡区的方法 利用像素点空间位置：变化阈值法 结合局部灰度 结合连通信息 基于最大熵原则的阈值选择方法,啄位斯遏臆弃腐栈耽哎萄调芬缠集影主抬糖粉糜勿筒搪矮醋报绿猴朝犯柒医学图像分割医学图像分割,