最新医学图像分割PPT课件.ppt

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1、讨论内容图像分割概述阈值分割医学图像特点:模糊、不均匀、个体差异、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、图像分割概述局部体效应 (partial volume effects)1、图像分割概述Ideal ImageAcquired Image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2、阈值分割阈值分割是最常

2、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CTCT图像图像中皮肤中皮肤骨骼的骨骼的分割分割2、阈值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、阈值分割多门限法2、阈值分割乳腺钼靶图像乳腺钼靶图像单门限分割单门限分割多门限分割多门限分割 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

3、准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ThresholdingThe simplest and most efficient image segmentation method is thresholding.Thresholding is to segment the image into two regions according to the gray

4、 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.Image ThresholdingOriginal image Segmented image (T=128, 145)Determination of ThresholdIn thresholding method, the most difficult is to determine a proper va

5、lue of the threshold.There are different types of the threshold:Global threshold (constant threshold)Adaptive thresholdDetermination of Global thresholdIf the object and background have different distributions, the value of the global threshold can be determined by calculating the histogram of the i

6、mage.The global threshold can also be determined interactively.The threshold can also be determined by optimization. Determination of the globalthreshold from histogramT=150The Otsu Algorithml If t is chosen as a threshold, and p(i) is the normalized histogram0001111( )( )( |, )( )( )( )( )( |, )( )

7、( )tiKi tp ip iP i Htw tp ip ip iP i H tw tp i -1010( )( )1, since ( )1Kiw tw tp i0K-1( )p iiN bits means K = 2NtThe Otsu Algorithm0001111( )( )( )( )( )( )tiKi tp itiw tp itiw t 2200001221111( )( )( )( )( )( )( )( )tiKi tp ititw tp ititw t meansvariances0011( )( )( )( )TOTALw ttw ttMeans and varian

8、ce for each class-10since ( )1Kip iThe Otsu AlgorithmlStatistical discrimination measure based on variance between classes:2argmax*( )0,1,.1BETWEENTttK2220011( )BETWEENTOTALTOTALtwwlRun through all possible values of t, and pick the one that maximizes the discrimination measure:Chosen Threshold The

9、Otsu AlgorithmFor each potential threshold T,1. Separate the pixels into two clusters according to the threshold.2. Find the mean of each cluster.3. Square the difference between the means.4. Calculate the object function of .5. Find the optimal threshold T* that maximizes the value of .2( )BETWEENt

10、2( )BETWEENtDetermination of Otsus thresholdAutomatic Threshold based on mean and standard deviationAutomatic 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 th

11、e weight and can be a real number. ( , )( , )( , )T i jf i jki j( , ), ( , ), ( , )T i jf i ji jDetermination of threshold by maximum entropylWhat is an entropy?lEntropy is the measurement of the information content in a probability distributionlMaximum entropy segmentation is to select such a thres

12、hold that the entropies in both object and background areas have maximum distributions.10lgNiiiHpp obHHH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Determination of threshold by 2-D HistogramlDefinition of 2D histogram: Suppose f(x,y) to be an image of NxN pixels. It

13、s gray level is from 0 to L-1. Segment the image by using the following equation: where lFor the 2D thresholding method, it considers the average gray level of the point (x,y) simultaneously as follows. 01( , )( , )( , )Tbf x yTfx ybf x yT010, ,1b T bLDetermination of threshold by 2-D HistogramlThe

14、average gray level at the point (x,y) of its nxn neighbors is: where lFor 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): 222221( , )(,)nnnnijg x

15、 yf xi yjn nNDetermination of threshold by 2-D Histogram where lFor 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: lP is called the 2D histogram of the image f(x,y) 0,1( , )& ( , )( , )( , )& ( , )S Tbf x ySg x yTf

16、x ybf x ySg x yT010, , ,1b S T bL,2iji jrPN0,1i jLDetermination of threshold 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, th

17、e difference between the gray level and the average is big, which is corresponding to the boundary points. nN2D histogram of imageDetermination of threshold by 2-D HistogramlThe maximum entropy for the 2D histogram is to determine a threshold vector (S,T) such that we can divide the image into objec

18、t (A) and background (B) with the probability of where 0,00,1,(1),0(1),1(1),(1): ,.,: ,.,111s tstststssLLstststPPPAPPPPPPBPPP,00ststi jijPPDetermination of threshold by 2-D HistogramlThe goal of segmentation is to let the entropies in the object and background areas as big as possible, lThe maximum

19、entropies of the object and background will correspond to the optimal threshold vector (S,T). ,0011,( , )ln( , )ln( , )( , )( , )sti ji jAijststLLi ji jBi sj tststABPPHs tPPPPHs tPPH s tHs tHs tDetermination of threshold by 2-D Histogram-ExperimentDetermination of threshold by Fuzzy EntropylThe Bloc

20、kB and BlockW are defined in Fig. 1(a) and (b). Four fuzzy sets, BrightX, DarkX, BrightY, DarkY, are defined based on the S-function and the corresponding Z-functions as follows: (Z()=1-s()( )( , , , )( )( , , , )( )( , , , )( )( , , , )BrightXx Xx XDarkXx Xx XBrightYy Yy YDarkYy Yy YxS x a b cBrigh

21、tXxxxZ x a b cDarkXxxyS y a b cBrightYyyyZ y a b cDarkYyyDetermination of Threshold by Fuzzy Entropy,0011,( , )ln( , )ln( , )( , )( , )sti ji jAijststLLi ji jBi sj tststABPPHs tPPPPHs tPPH s tHs tHs tDetermination of threshold by Fuzzy EntropylThe fuzzy relation Bright is a subset of the full Cartes

22、ian product space XY lSimilarly, ( , )( , ) = min(x),(y) BrightBrightXBrightYBrightXBrightYx yx yBrightBrightXBrightYXY( , )( , ) = min(x),(y) DarkDarkX DarkYDarkXDarkYx yx yDarkDarkXDarkYXYDefinition of Fuzzy EntropylLet A be a fuzzy set with membership function , where are the possible outputs fro

23、m source A with the probability . The fuzzy entropy set A is defined as: lThe total image entropy is defined as: 1( )( ) ( )ln( )NfuzzyAiiiiHAx P xP x ( )Aix,1,.,ix iN()()()BWH imageH BlockH BlockDetermination of threshold by Fuzzy EntropylAs shown in Fig. 1(a), the dark block BlockB can be divided

24、into a nonfuzzy region RB and a fuzzy region R1lSimilarly, the bright block BlockW is composed of a nonfuzzy region RW and a fuzzy region R2, as shown in Fig. 1(b) 1,( , )1,( , ),( , )1,( , )BDarkBDarkBBlockx yx yx yBlockRx yx yx yBlock2,( , )1,( , ),( , )1,( , )WBrightWBrightWBlockx yx yx yBlockRx

25、yx yx yBlockDetermination of threshold by Fuzzy EntropylThe 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)lTo find the best set of a,b,and c is an optimization problem which can be solved by differ

26、ent 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: 1) find the 2-D histogram of the image; 2) perform fuzzy partition on the 2-D histogram; 3) compute the fuzzy entropy. lStep 1) nee

27、ds 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). The threshold is selected as the crossover point of the membership function which has membership 0.5 implying the largest fuzzines

28、s.Determination of threshold by Fuzzy EntropyDetermination of threshold by Fuzzy EntropyDetermination of threshold by Fuzzy Entropy-Experiment1Comparison of global and local threshold segmentationDetermination of threshold by Fuzzy Entropy-Experiment2HP DCE/9000K-means clusteringK-means follow a sim

29、ple 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 of different location causes different result. So, the better

30、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 an early groupage is done. At this point we need to re-calculate

31、 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. As a result of this loop we may notice that the k centroids ch

32、ange their location step by step until no more changes are done. In other words centroids do not move any more.K-means clustering Finally, this algorithm aims at minimizing an objective function, in this case a squared error function. The objective function where is a chosen distance measure between

33、 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.11KnjijjiJxcjijxcK-means clustering AlgorithmThe algorithm is composed of the following steps:1. Place K points into the space represented by the objects that ar

34、e 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 been assigned, recalculate the positions of the K centroids.4. Repeat Steps 2 and 3 until the centroids no longer move. This produces a separati

35、on of the objects into groups from which the metric to be minimized can be calculated.Fuzzy K-means clustering 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 o

36、r classes, n is the total number of feature points or vectors and is a weighting exponent. And we have: (2)11KnjijijjiJxc(1,)m1101, 1, 01, local minimum solutions of equation (1) was demonstrated if and only if:1ij2111()1, ()(/)nmjijiijnKmmijijkjikxcdd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：变化阈值法利用像素点空间位置：变化阈值法结合局部灰度结合局部灰度结合连通信息结合连通信息基于最大熵原则的阈值选择方法基于最大熵原则的阈值选择方法55 结束语结束语