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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,讨论内容,图像分割概述阈值分割,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。,1、图像分割概述,P(gk(x,y)U gj(x,y)=FALSE.任意相邻部分的合并都会破坏这种一致性。,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。,基于区域的分割方法 基于边缘的分割
2、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）方法,1、图像分割概述,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,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,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
3、效应(partial volume effects),1、图像分割概述,Ideal Image,Acquired 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
4、，从而将各个峰分开,CT图像中皮肤骨骼的分割,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,单门限分割,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
5、对噪声和灰度不均匀敏感,2、阈值分割,Thresholding,The simplest and most efficient image segmentation 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,othe
6、rwise it is set to 0.,Image Thresholding,Original image Segmented image(T=128,145),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)Adaptive threshold,De
7、termination 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 interactively.The threshold can also be determined by optimization.,Dete
8、rmination of the globalthreshold from histogram,T=150,The Otsu Algorithm,If t is chosen as a threshold,and p(i)is the normalized histogram,0,K-1,N bits means K=2N,t,The Otsu Algorithm,means,variances,Means and variance for each class,The Otsu Algorithm,Statistical discrimination measure based on var
9、iance between classes:,Run through all possible values of t,and pick the one that maximizes the discrimination measure:,Chosen Threshold,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.Square the d
10、ifference between the means.4.Calculate the object function of.5.Find the optimal threshold T*that maximizes the value of.,Determination of Otsus threshold,Automatic Threshold based on mean and standard deviation,Automatic threshold based on mean and standard deviation:where are the automatic thresh
11、old 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.,Determination of threshold by maximum entropy,What is an entropy?Entropy is the measurement of the information content in a probability distributionMaximum ent
12、ropy segmentation is to select such a threshold that the entropies in both object and background areas have maximum distributions.,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 Histogram,Definition of 2D histogram:Suppose f(x,y)to be
13、an image of NxN pixels.Its gray level is from 0 to 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.,Determination of threshold by 2-D Histogram,The average gray level at the poin
14、t(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):,Determination of threshold by 2-D Histogram,where For one image,l
15、et 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),Determination 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
16、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 corresponding to the boundary points.,2D histogram of image,Determination of threshold by 2-D Histogram,The maximum entrop
17、y 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 probability of where,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 possi
18、ble,The maximum entropies of the object and background will correspond to the optimal threshold vector(S,T).,Determination of threshold by 2-D Histogram-Experiment,Determination of threshold by Fuzzy Entropy,The BlockB and BlockW are defined in Fig.1(a)and(b).Four fuzzy sets,BrightX,DarkX,BrightY,Da
19、rkY,are defined based on the S-function and the corresponding Z-functions as follows:(Z()=1-s(),Determination of Threshold by Fuzzy Entropy,Determination of threshold by Fuzzy Entropy,The fuzzy relation Bright is a subset of the full Cartesian product space XY Similarly,Definition of Fuzzy Entropy,L
20、et 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:The total image entropy is defined as:,Determination of threshold by Fuzzy Entropy,As shown in Fig.1(a),the dark block BlockB can be divided into a non
21、fuzzy region RB and a fuzzy region R1Similarly,the bright block BlockW is composed of a nonfuzzy region RW and a fuzzy region R2,as shown in Fig.1(b),Determination of threshold by Fuzzy Entropy,The following four entropies can be calculated:,where nxy is the element in the 2-D histogram which repres
22、ents the number of occurences of the pair(x,y),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 step
23、s: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).The threshold
24、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,Determination of threshold by Fuzzy Entropy,Determination of threshold by Fuzzy Entropy-Experiment1,Comparison of global and local thresh
25、old segmentation,Determination of threshold by Fuzzy Entropy-Experiment2,HP DCE/9000,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.
26、These centroids shoud be placed in a cunning way because 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
27、 point is pending,the first step is completed and an 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
28、nearest new centroid.A loop has been generated.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.,K-means clustering,Finally,this algorithm aims at minimizing an objective functi
29、on,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.,K-means clustering Algorithm,The algorithm is composed o
30、f 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 been assigned,recalculate the positions of the K centroids.
31、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.,Fuzzy K-means clustering,Fuzzy K-means clustering algorithm aims at minimizing the following objective function with respect to the
32、 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),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:,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,
