CN103390274A

CN103390274A - Image segmentation quality evaluation method based on region-related information entropies

Info

Publication number: CN103390274A
Application number: CN2013103054757A
Authority: CN
Inventors: 郝家胜; 陈桦
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2013-07-19
Filing date: 2013-07-19
Publication date: 2013-11-13

Abstract

The invention discloses an image segmentation quality evaluation method based on region-related information entropy. Based on the essence of image segmentation, from the perspective of heterogeneity between regions, non-linear region-related information entropy is introduced as an evaluation measure. The segmentation algorithm aims at the image segmentation results obtained from the same target image, that is, each image region, calculates the non-linear correlation information entropy between regions, and evaluates the segmentation quality of these different algorithms according to different region correlation information entropy, the smaller the region correlation information entropy, The better the image segmentation quality of the corresponding image segmentation algorithm is. The present invention can provide quantitative evaluation results on the closed interval [0, 1], and the evaluation results have high precision and effectiveness, and are suitable for more accurate image segmentation quality evaluation scenarios.

Description

A Quality Evaluation Method for Image Segmentation Based on Region Correlation Information Entropy

技术领域technical field

本发明属于图像分割技术领域，更为具体地讲，涉及一种基于区域相关信息熵的图像分割质量评价方法。The invention belongs to the technical field of image segmentation, and more specifically relates to an image segmentation quality evaluation method based on region-related information entropy.

背景技术Background technique

图像分割贯穿于整个图像分析领域，其结果的好坏对后续应用产生重要的影响。尤其是在医学图像应用中，图像分割的结果是组织体积测量、器官三维重建、手术导航等临床应用的先决条件，因此对分割结果进行准确有效地评价是医学图像分割中的一项有意义的任务。另外，图像分割质量评价还可以达到优化分割的目的，而且对研究新的分割技术也具有指导意义。Image segmentation runs through the entire field of image analysis, and the quality of its results has an important impact on subsequent applications. Especially in medical image applications, the results of image segmentation are prerequisites for clinical applications such as tissue volume measurement, organ three-dimensional reconstruction, and surgical navigation. Therefore, accurate and effective evaluation of segmentation results is a meaningful task in medical image segmentation. Task. In addition, image segmentation quality evaluation can also achieve the purpose of optimizing segmentation, and it also has guiding significance for the research of new segmentation techniques.

图像分割质量评价方法主要有主观评价法、分析评价法和实验评价法三类。其中，主观评价法具有较大的局限性。例如不同人的同一组织和器官的解剖结构的形态、体积和空间位置存在较大差异，而且很多组织（例如脑灰质和白质）之间本来就没有清晰的界限。分析评价法通过对分割算法直接从原理上进行评估，可以免除一些实验因素的影响，但并非所有的算法性能都能够通过分析而得到，而且也不能对分割结果做出直接的评价。因此，通过对具体分割结果的分析来评价分割方法的实验评价法是具有实际意义的。Image segmentation quality evaluation methods mainly include subjective evaluation method, analytical evaluation method and experimental evaluation method. Among them, the subjective evaluation method has great limitations. For example, the shape, volume and spatial position of the anatomical structure of the same tissue and organ in different people are quite different, and there is no clear boundary between many tissues (such as brain gray matter and white matter). The analysis and evaluation method can avoid the influence of some experimental factors by directly evaluating the segmentation algorithm in principle, but not all algorithm performance can be obtained through analysis, and the segmentation results cannot be directly evaluated. Therefore, it is of practical significance to evaluate the experimental evaluation method of the segmentation method by analyzing the specific segmentation results.

实验评价法大致可以分为偏差法和优度法两类。偏差法需要首先提供一个理想分割图象作为参考标准，依此来计算实际分割结果与理想分割图像的差别，这种差别可以是基于错误分割的像素数，也可以是基于错误分割像素点的位置，或者是基于分割结果区域数的差别等等。但在医学图像领域，可供比较的图像样本很难统一认定，因此，这类方法在运用上有很大的局限性。优度法一般是直接以分割结果中的某些图像特征为依据来评价分割质量，这些特征可以是区域对比度或区域一致性等。然而，对于复杂的医学图像分割应用，这些传统的评价准则或者难以应用，或者往往不能给出合理的评价。Experimental evaluation methods can be roughly divided into two categories: deviation method and goodness method. The deviation method needs to first provide an ideal segmentation image as a reference standard, and calculate the difference between the actual segmentation result and the ideal segmentation image based on this. This difference can be based on the number of wrongly segmented pixels or the position of the wrongly segmented pixels. , or based on the difference in the number of segmentation result regions, etc. However, in the field of medical images, it is difficult to uniformly identify the image samples available for comparison. Therefore, the application of such methods has great limitations. The goodness method generally evaluates the segmentation quality directly based on some image features in the segmentation results, and these features can be regional contrast or regional consistency. However, for complex medical image segmentation applications, these traditional evaluation criteria are either difficult to apply, or often cannot give a reasonable evaluation.

图像分割的本质是同质性区域的合并和异质性区域的分离，这个过程的目的是对图像中感兴趣区域进行详细、深入的研究，而忽略其他无关的区域。在最优情况下，每个区域被完全的分离，从而精确的提取出感兴趣区域。此时，各区域间的信息相关性最小。也就说，各区域间相关性越小，说明分割质量越高。一般地，这个相关性不会为零，因为这些区域之间总是存在一定的相关性，尤其是医学图像各组织器官之间更是互相关联。这个相关性测度能否成功应用的前提是区域间的信息相关程度的准确度量。The essence of image segmentation is the merging of homogeneous regions and the separation of heterogeneous regions. The purpose of this process is to conduct detailed and in-depth research on regions of interest in the image while ignoring other irrelevant regions. In the optimal case, each region is completely separated, so that the region of interest can be accurately extracted. At this time, the information correlation between regions is the smallest. In other words, the smaller the correlation between regions, the higher the segmentation quality. Generally, this correlation will not be zero, because there is always a certain correlation between these regions, especially among the tissues and organs of medical images. The prerequisite for the successful application of this correlation measure is the accurate measurement of the degree of information correlation between regions.

发明内容Contents of the invention

本发明的目的在于克服现有技术的不足，从图像分割区域之间的异质性角度，引入了非线性相关信息熵作为区域间异质性评价测度，提供一种基于区域相关信息熵的图像分割质量评价方法，为不同图像分割方法生成的不同分割结果的质量提供一种客观定量的评价依据。The purpose of the present invention is to overcome the deficiencies of the prior art. From the perspective of heterogeneity between image segmentation regions, nonlinear correlation information entropy is introduced as the evaluation measure of interregional heterogeneity, and an image based on region correlation information entropy is provided. The segmentation quality evaluation method provides an objective and quantitative evaluation basis for the quality of different segmentation results generated by different image segmentation methods.

为实现上述发明目的，本发明基于区域相关信息熵的图像分割质量评价方法，其特征在于，包括以下步骤：In order to achieve the above-mentioned purpose of the invention, the image segmentation quality evaluation method based on region-related information entropy of the present invention is characterized in that it comprises the following steps:

S1：采用待评价分割算法T₁和参考分割算法T₂分别将目标图像I进行分割，得到不同的分割结果Θ_i,i＝1,2，每个分割结果得到的区域个数记为M_i，分割结果

j＝1,2,…,M_i，Ω⁽ⁱ⁾ _j为分割结果Θ_i的区域；S1: Segment the target image I using the segmentation algorithm T ₁ to be evaluated and the reference segmentation algorithm T ₂ to obtain different segmentation results Θ _i , i=1, 2, and the number of regions obtained by each segmentation result is denoted as M _i , the result of segmentation

j=1,2,...,M _i , Ω ⁽ⁱ⁾ _j is the area of the segmentation result Θ _i ;

S2：对于每个分割结果Θ_i中的M_i个区域

区域中的像素用灰度值保持原值，将目标图像I中区域外的像素灰度值全部记为0，得到

对应的扩展灰度图像；将每个区域

对应的扩展灰度图像以行优先法展开为一维离散随机变量

变量取值个数均为N，N为目标图像I的像素数量；计算两两随机变量和

之间的非线性相关系数j,k＝1,2,…,M_i,j≠k，随机变量

与其自身的非线性相关系数

S2: For each segmentation result Θ _i in M _i regions

area The pixels in the gray value keep the original value, and the area in the target image I The gray values of the pixels outside are all recorded as 0, and the obtained

Corresponding extended grayscale image; each region

The corresponding extended grayscale image is expanded into a one-dimensional discrete random variable by the row-first method

The number of variable values is N, and N is the number of pixels of the target image I; calculate two random variables and

The nonlinear correlation coefficient between j,k=1,2,...,M _i ,j≠k, random variable

The nonlinear correlation coefficient with itself

S3：利用步骤S2中每个分割结果Θ_i的所有非线性相关系数构造分割结果Θ_i的非线性相关矩阵R_i：S3: Utilize all nonlinear correlation coefficients of each segmentation result Θ _i in step S2 to construct the nonlinear correlation matrix R _i of the segmentation result Θ _i :

${R R}_{i i} = = (\begin{matrix} 11 & {ρ ρ}_{1,2 1,2}^{((i i))} & \cdot \cdot \cdot \cdot \cdot \cdot & {ρ ρ}_{11,, {M m}_{i i}}^{((i i))} \\ {ρ ρ}_{2,1 2,1}^{((i i))} & 11 & \cdot \cdot \cdot \cdot \cdot \cdot & {ρ ρ}_{22,, {M m}_{i i}}^{((i i))} \\ \cdot \cdot & \cdot \cdot & \cdot &Center Dot; & \cdot \cdot \\ \cdot &Center Dot; & \cdot \cdot & \cdot &Center Dot; & \cdot \cdot \\ \cdot \cdot & \cdot \cdot & \cdot \cdot & \cdot \cdot \\ {ρ ρ}_{{M m}_{i i},, 11}^{((i i))} & {ρ ρ}_{{M m}_{i i},, 22}^{((i i))} & \cdot \cdot \cdot &Center Dot; \cdot \cdot & 11 \end{matrix})$

S4：计算每个非线性相关矩阵R_i的M_i个特征值λ_p,p＝1,2,…,M_i，根据特征值计算每个分割结果Θ_i的区域相关信息熵：S4: Calculate M _i eigenvalues λ _p , p=1,2,...,M _i of each nonlinear correlation matrix R _i , and calculate the region-related information entropy of each segmentation result Θ _i according to the eigenvalues:

${Λ Λ}_{i i} = = 11 + + {Σ Σ}_{p p = = 11}^{{M m}_{u u}} \frac{{λ λ}_{p p}}{{M m}_{i i}} {log log}_{{M m}_{i i}} \frac{{λ λ}_{p p}}{{M m}_{i i}};;$

S5：比较待评价分割算法T₁和参考分割算法T₂的区域相关信息熵，如果Λ₁＞Λ₂，则参考分割算法T₂得到的图像分割结果优于待评价分割算法T₁得到的图像分割结果的质量；如果Λ₁＜Λ₂，则待评价分割算法T₁得到的图像分割结果优于参考分割算法T₂得到的图像分割结果的质量；如果Λ₁＝Λ₂，则两种分割算法得到图像分割结果质量相同。S5: Comparing the region-related information entropy of the segmentation algorithm _T1 to be evaluated and the reference segmentation algorithm _T2 , if _Λ1 > _Λ2 , the image segmentation result obtained by the reference segmentation algorithm _T2 is better than the image obtained by the segmentation algorithm _T1 to be evaluated The quality of the segmentation result; if Λ ₁ < Λ ₂ , the image segmentation result obtained by the segmentation algorithm T ₁ to be evaluated is better than the quality of the image segmentation result obtained by the reference segmentation algorithm T ₂ ; if Λ ₁ = Λ ₂ , the two segmentation results The quality of the image segmentation results obtained by the algorithm is the same.

其中，步骤S2中非线性相关系数

采用等概率法进行盒子划分的方式计算，包括步骤：Among them, the nonlinear correlation coefficient in step S2

The method of box division is calculated using the equal probability method, including steps:

S2.1：一维离散随机变量

和中的元素个数记为N，

和

分别表示

和

的第w,1≤w≤N个元素，分别将

和

中的元素按从小到大排列；S2.1: One-dimensional discrete random variable

and The number of elements in is denoted as N,

and

Respectively

and

The w, 1≤w≤N elements of the w, 1≤w≤N, respectively

and

The elements in are arranged from small to large;

S2.2：分别将

和

中的元素依次划分为b个盒子，盒子个数b根据需要设定，前b-1个盒子中每个盒子的元素个数均为

个，第b个盒子中元素个数为

表示向下取整；

得到的每个盒子记为α_s,1≤s≤b，得到的每个盒子记为β_t,1≤t≤b，将每个盒子中的最小值和最大值作为该盒子的阈值；S2.2: Respectively

and

The elements in are divided into b boxes in turn, the number of boxes b is set according to the needs, and the number of elements in each box in the first b-1 boxes is

, the number of elements in the bth box is

Indicates rounding down;

Each box obtained is denoted as α _s , 1≤s≤b, Each obtained box is recorded as β _t , 1≤t≤b, and the minimum and maximum values in each box are used as the threshold of the box;

S2.3：将的每个盒子分别和的每个盒子组合，构成b×b的扩展二维盒子阵列，依据每个盒子的阈值，将N个元素对放入扩展二维盒子阵列中；S2.3: Will Each box of Combining each box of b to form a b×b extended two-dimensional box array, according to the threshold of each box, the N elements are paired into the extended 2D box array;

S2.4：元素对

中的两个元素分别落入α_s和β_t中概率P(α_s)＝P(β_t)＝1b，联合概率为P(α_s,β_t)＝n_st/N，其中n_st为扩展二维盒子阵列中盒子(s,t)中元素对的个数，(s,t)为盒子在扩展二维盒子阵列中的坐标；S2.4: Pairs of elements

Two elements in α _s and β _t respectively fall into the probability P(α _s )=P(β _t )=1b, the joint probability is P(α _s ,β _t )=n _st /N, where n _st is The number of element pairs in the box (s, t) in the extended two-dimensional box array, (s, t) is the coordinate of the box in the extended two-dimensional box array;

S2.5：计算

和

的非线性相关系数

计算公式为：S2.5: Calculation

and

The nonlinear correlation coefficient of

The calculation formula is:

${ρ ρ}_{j j,, k k}^{((i i))} = = 22 + + {Σ Σ}_{s the s = = 11}^{b b} {Σ Σ}_{t t = = 11}^{b b} P P (({α α}_{s the s},, {β β}_{t t})) {log log}_{b b} P P (({α α}_{s the s},, {β β}_{t t})) . .$

进一步地，在步骤S2.1之前，对一维离散随机变量和

进行预处理，预处理方法为：将一维离散随机变量和

中序号相同并且均为0的取值删除，取值个数N为删除后的取值个数。Further, before step S2.1, for a one-dimensional discrete random variable and

Perform preprocessing, the preprocessing method is: the one-dimensional discrete random variable and

The values with the same serial number and all 0 are deleted, and the number of values N is the number of values after deletion.

其中，所述盒子个数b根据公式b＝1.87×(N-1)^2/5确定。Wherein, the number b of boxes is determined according to the formula b=1.87×(N-1) ^2/5 .

本发明基于区域相关信息熵的图像分割质量评价方法，基于图像分割的本质，从区域之间的异质性角度，引入非线性的区域相关信息熵作为评价测度，通过对各个图像分割算法针对相同目标图像得到的图像分割结果，即各个图像区域，计算区域间的非线性相关信息熵，根据不同的区域相关信息熵来评价这些不同算法的分割质量，区域相关信息熵越小，对应的图像分割算法的图像分割质量越好。The image segmentation quality evaluation method based on region-related information entropy of the present invention is based on the essence of image segmentation, and from the perspective of heterogeneity between regions, introduces non-linear region-related information entropy as an evaluation measure. The image segmentation results obtained from the target image, that is, each image region, calculate the non-linear correlation information entropy between regions, and evaluate the segmentation quality of these different algorithms according to different region correlation information entropy, the smaller the region correlation information entropy, the corresponding image segmentation The better the image segmentation quality of the algorithm is.

本发明能够在闭区间[0,1]上给出定量的评价结果，并且由于区域相关信息熵可以对区域间的信息相关程度进行较为准确的度量，采用本发明得到的评价结果的具有较高的精度和有效性，适用于较为精确的图像分割质量评价场景，如医学图像等。The present invention can give quantitative evaluation results on the closed interval [0,1], and since the region-related information entropy can measure the degree of information correlation between regions more accurately, the evaluation results obtained by using the present invention have higher It is suitable for more accurate image segmentation quality evaluation scenarios, such as medical images.

附图说明Description of drawings

图1是本发明基于区域相关信息熵的图像分割质量评价方法一种具体实施方式流程图；Fig. 1 is a flow chart of a specific embodiment of the image segmentation quality evaluation method based on region-related information entropy of the present invention;

图2是实施例1合成图像的五种分割结果示意图；Fig. 2 is the five kinds of segmentation result schematic diagrams of synthetic image of embodiment 1;

图3是脑MR图像的典型切片；Figure 3 is a typical slice of a brain MR image;

图4是图3所示脑MR图像中脑白质的参考分割结果；Fig. 4 is the reference segmentation result of brain white matter in the brain MR image shown in Fig. 3;

图5是采用增量式Chan-Vese模型得到的脑MR图像中脑白质的分割结果；Fig. 5 is the segmentation result of brain white matter in the brain MR image obtained by using the incremental Chan-Vese model;

图6是采用阈值法得到的脑MR图像中脑白质的分割结果。Fig. 6 is the segmentation result of the white matter in the brain MR image obtained by using the threshold method.

具体实施方式Detailed ways

下面结合附图对本发明的具体实施方式进行描述，以便本领域的技术人员更好地理解本发明。需要特别提醒注意的是，在以下的描述中，当已知功能和设计的详细描述也许会淡化本发明的主要内容时，这些描述在这里将被忽略。Specific embodiments of the present invention will be described below in conjunction with the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when detailed descriptions of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

在描述本发明具体实施方式之前，先对本发明的技术原理进行简要介绍。Before describing the specific implementation of the present invention, the technical principle of the present invention will be briefly introduced.

设论域Ω＝[0,M′-1]×[0,N′-1]，M′,为

上的连通子集，考虑图像I:Ω→[0,L]，的分割问题。Suppose domain of discourse Ω=[0,M'-1]×[0,N'-1], M', for

On the connected subset, consider the image I:Ω→[0,L], segmentation problem.

分割算法集T＝{T₁,T₂,…,T_m}，分别将图像I分割为Θ＝{Θ₁,Θ₂,…,Θ_m}，其中Segmentation algorithm set T={T ₁ ,T ₂ ,…,T _m }, respectively divide the image I into Θ={Θ ₁ ,Θ ₂ ,…,Θ _m }, where

${Θ Θ}_{i i} = = {\cup \cup}_{j j}^{{M m}_{i i}} {Ω Ω}^{((i i))}_{j j},, i i = = 1,2 1,2,, . . . . . .,, m m - - - - - - ((11))$

Ω⁽ⁱ⁾ _j为Θ_i中第j个区域，j＝1,2,…,M_i，M_i为Θ_i中区域个数。Ω ⁽ⁱ⁾ _j is the jth area in Θ _i , j=1,2,...,M _i , and M _i is the number of areas in Θ _i .

理想情况下，源图像中同质性的区域被精确地合并，异质性的区域被精确地分开，这些区域之间的信息相关程度是确定的。这种相关程度称为区域相关性。因此，如果不同分割算法所得结果中区域之间的区域相关性存在差异，那么这个差异是由于不同分割算法的结果造成的。换句话说，这个差异产生的原因是这些分割算法的性能（精度）不同。Ideally, homogeneous regions in the source image are accurately merged, heterogeneous regions are precisely separated, and the degree of information correlation between these regions is determined. This degree of correlation is called regional correlation. Therefore, if there is a difference in the region correlation between regions in the results obtained by different segmentation algorithms, then this difference is due to the results of different segmentation algorithms. In other words, the reason for this difference is the different performance (accuracy) of these segmentation algorithms.

如果某个分割结果Θ_a中区域Ω^(a) _j之间的区域相关性要低于另一分割结果Θ_b中各自区域Ω^(b) _j之间的区域相关性，则说明Θ_a中异质性区域比Θ_b中异质性区域被更准确地分开，也就是说分割算法T_a比T_b具有更好的分割性能。If the regional correlation between the region Ω ^(a) _j in a certain segmentation result Θ _a is lower than the regional correlation between the respective regions Ω ^(b) _j in another segmentation result Θ _b , it means that the difference in Θ _a The qualitative region is separated more accurately than the heterogeneous region in Θ _b , which means that the segmentation algorithm T _a has better segmentation performance than T _b .

由以上分析可知，若存在有效的区域相关性度量Φ，且From the above analysis, if there is an effective regional correlation measure Φ, and

Φ(Θ_a)＜Φ(Θ_b) （2）Φ(Θ _a )＜Φ(Θ _b ) (2)

则分割算法T_a的性能优于T_b，图像分割质量更优。Then the performance of the segmentation algorithm T _a is better than T _b , and the image segmentation quality is better.

上述的区域相关性度量必须能有效地度量区域上的非线性相关程度。本发明以区域Ω₁,Ω₂,…Ω_n之间的非线性相关信息熵Λ(Ω₁,Ω₂,…Ω_n)作为这种区域相关性度量，简称区域相关信息熵，可以对区域间的信息相关程度进行较为准确的度量。利用区域相关信息熵，式（2）可写为：The above-mentioned regional correlation measure must be able to effectively measure the non-linear correlation degree on the region. In the present invention, the non-linear correlation information entropy Λ(Ω ₁ ,Ω ₂ ,...Ω _n ) among regions Ω ₁ ,Ω ₂ ,…Ω _n is used as the regional correlation measure, referred to as regional correlation information entropy, which can be used for regional A more accurate measure of the degree of information correlation between them. Using region-related information entropy, formula (2) can be written as:

${Φ Φ}_{j j}^{{M m}_{a a}} (({Ω Ω}^{((a a))}_{j j})) < < {Φ Φ}_{i i}^{{M m}_{b b}} (({Ω Ω}^{((b b))}_{j j})) - - - - - - ((33))$

本发明中，称以区域相关信息熵为评价测度的图像分割质量评价方法为区域相关信息熵定量评价方法（Partition Entropy Quantitative Assessment，PEQA）。In the present invention, the image segmentation quality evaluation method using the region-related information entropy as the evaluation measure is called the region-related information entropy quantitative evaluation method (Partition Entropy Quantitative Assessment, PEQA).

图1是本发明基于区域相关信息熵的图像分割质量评价方法一种具体实施方式流程图。如图1所示，本发明基于区域相关信息熵的图像分割质量评价方法包括以下步骤：FIG. 1 is a flow chart of a specific embodiment of the image segmentation quality evaluation method based on region-related information entropy in the present invention. As shown in Figure 1, the image segmentation quality evaluation method based on region-related information entropy of the present invention comprises the following steps:

S101：采用待评价分割算法T₁和参考分割算法T₂分别将目标图像I进行分割，得到不同的分割结果Θ_i,i＝1,2，每个分割结果得到的区域个数记为M_i，分割结果

j＝1,2,…,Mi，Ω⁽ⁱ⁾ _j为分割结果Θ_i的区域。S101: Use the segmentation algorithm to be evaluated _T1 and the reference segmentation algorithm _T2 to segment the target image I respectively to obtain different segmentation results Θ _i , i=1, 2, and the number of regions obtained by each segmentation result is denoted as M _i , the result of segmentation

j=1,2,...,Mi, Ω ⁽ⁱ⁾ _j is the area of the segmentation result Θ _i .

S102：对于每个分割结果Θ_i中的M_i个区域

区域

中的像素用灰度值保持原值，将目标图像I中区域

外的像素灰度值全部记为0，得到

对应的扩展灰度图像（尺寸与目标图像I相同）。将每个区域

对应的扩展灰度图像以行优先法展开为一维离散随机变量

变量取值个数均为N，N为目标图像I的像素数量。计算两两随机变量

和

之间的非线性相关系数（Nonlinear Correlation Coefficient，NCC）

j,k＝1,2,…,M_i,j≠k，随机变量

与其自身的非线性相关系数

S102: For each of the M _i regions in the segmentation result Θ _i

area

The pixels in the gray value keep the original value, and the area in the target image I

The gray values of the pixels outside are all recorded as 0, and the obtained

Corresponding extended grayscale image (same size as target image I). will each area

The number of variable values is N, and N is the number of pixels of the target image I. Computing Pairwise Random Variables

and

Nonlinear Correlation Coefficient (NCC) between

j,k=1,2,...,M _i ,j≠k, random variable

The nonlinear correlation coefficient with itself

本步骤将每个区域转化为图像像素灰度值的一维离散随机变量，为保证每个一维离散随机变量的取值个数相同，将目标图像中区域外的像素灰度值记为0，这些像素称为0伪像素，从而得到整幅灰度图像，将灰度值作为变量，变量取值按行进行排列，即采用行优先法将整幅灰度图像展开为一维离散随机变量，这种展开方式与矩阵的行优先展开方式类似。根据每个区域对应的一维离散随机变量可以方便地求出区域之间的非线性相关系数。每个区域采用的图像像素灰度值范围相同，通常图像像素灰度值的取值范围为[0,255]。This step converts each area into a one-dimensional discrete random variable of image pixel gray value. In order to ensure that the number of values of each one-dimensional discrete random variable is the same, the pixel gray value outside the area in the target image is recorded as 0 , these pixels are called 0 pseudo-pixels, so as to obtain the entire grayscale image, the grayscale value is used as a variable, and the variable values are arranged in rows, that is, the entire grayscale image is expanded into a one-dimensional discrete random variable using the row-first method , which is similar to the row-major expansion of matrices. According to the one-dimensional discrete random variable corresponding to each region, the nonlinear correlation coefficient between regions can be easily calculated. The range of image pixel gray values used in each region is the same, usually the range of image pixel gray values is [0, 255].

S103：利用步骤S2中每个分割结果Θ_i的所有非线性相关系数构造分割结果Θ_i的非线性相关矩阵R_i：S103: Utilize all nonlinear correlation coefficients of each segmentation result Θ _i in step S2 to construct the nonlinear correlation matrix R _i of the segmentation result Θ _i :

${R R}_{i i} = = (\begin{matrix} 11 & {ρ ρ}_{1,2 1,2}^{((i i))} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {ρ ρ}_{11,, {M m}_{i i}}^{((i i))} \\ {ρ ρ}_{2,1 2,1}^{((i i))} & 11 & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & {ρ ρ}_{22,, {M m}_{i i}}^{((i i))} \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; & \cdot &Center Dot; \\ {ρ ρ}_{{M m}_{i i},, 11}^{((i i))} & {ρ ρ}_{{M m}_{i i},, 22}^{((i i))} & \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot; & 11 \end{matrix}) - - - - - - ((44))$

当所有区域间相关性最弱时，矩阵为单位矩阵；相关性最强时，矩阵中所有元素都为1。这表明，非线性相关矩阵蕴含了这M_i个区域之间的普遍相关性。When the correlation between all regions is the weakest, the matrix is an identity matrix; when the correlation is the strongest, all elements in the matrix are 1. This shows that the non-linear correlation matrix implies the general correlation among these M _i regions.

S104：计算每个非线性相关矩阵R_i的M_i个特征值λ_p,p＝1,2,…,M_i，根据特征值计算每个分割结果Θ_i的区域相关信息熵：S104: Calculate M _i eigenvalues λ _p , p=1, 2,..., M _i of each nonlinear correlation matrix R _i , and calculate the region-related information entropy of each segmentation result Θ _i according to the eigenvalues:

${Λ Λ}_{i i} = = 11 + + {Σ Σ}_{p p = = 11}^{{M m}_{u u}} \frac{{λ λ}_{p p}}{{M m}_{i i}} {log log}_{{M m}_{i i}} \frac{{λ λ}_{p p}}{{M m}_{i i}} - - - - - - ((55))$

（5）式中，非线性的区域相关信息熵具有对称性，并在闭区间[0,1]上表征这M_i个区域之间的普遍相关性。理想情况下，最弱相关时，每两个区域之间的非线性相关系数均为0，此时非线性的区域相关信息熵为0；最强相关时，每两个区域之间的非线性相关系数均为1，此时非线性的区域相关信息熵为1。In formula (5), the non-linear region-related information entropy has symmetry, and represents the general correlation among the M _i regions on the closed interval [0,1]. Ideally, when the correlation is the weakest, the nonlinear correlation coefficient between each two regions is 0, and the nonlinear region correlation information entropy is 0 at this time; when the correlation is the strongest, the nonlinear correlation coefficient between each two regions The correlation coefficients are all 1, and the non-linear regional correlation information entropy is 1 at this time.

S105：比较待评价分割算法T₁和参考分割算法T₂的区域相关信息熵，如果Λ₁＞Λ₂，则参考分割算法T₂得到的图像分割结果优于待评价分割算法T₁得到的图像分割结果的质量；如果Λ₁＜Λ₂，则待评价分割算法T₁得到的图像分割结果优于参考分割算法T₂得到的图像分割结果的质量；如果Λ₁＝Λ₂，则两种分割算法得到图像分割结果质量相同。S105: Comparing the region-related information entropy of the segmentation algorithm _T1 to be evaluated and the reference segmentation algorithm _T2 , if _Λ1 > _Λ2 , the image segmentation result obtained by the reference segmentation algorithm _T2 is better than the image obtained by the segmentation algorithm _T1 to be evaluated The quality of the segmentation result; if Λ ₁ < Λ ₂ , the image segmentation result obtained by the segmentation algorithm T ₁ to be evaluated is better than the quality of the image segmentation result obtained by the reference segmentation algorithm T ₂ ; if Λ ₁ = Λ ₂ , the two segmentation results The quality of the image segmentation results obtained by the algorithm is the same.

由于针对不同的目标图像，得到的区域相关信息熵存在差异，因此无法使用一个通用的标准值来判断图像分割结果质量，因此需要一个参考分割算法T₂来对待评价分割算法T₁进行对比。在实际应用中，可以选定一个参考分割算法T₂，计算其对多个目标图像的区域相关信息熵作为对比模板数据供用户选择使用。采用本发明，还可以对一个分割算法集T＝{T₁,T₂,…,T_m}的每个分割算法计算区域相关信息熵，根据区域相关信息熵的大小即可对分割算法集中每个分割算法的图像分割质量进行排序。Due to differences in the obtained region-related information entropy for different target images, a common standard value cannot be used to judge the quality of image segmentation results. Therefore, a reference segmentation algorithm T ₂ is needed to compare the segmentation algorithm T ₁ to be evaluated. In practical applications, a reference segmentation algorithm T ₂ can be selected, and its region-related information entropy for multiple target images can be calculated as comparison template data for users to choose and use. With the present invention, it is also possible to calculate the region-related information entropy for each segmentation algorithm in a segmentation algorithm set T={T ₁ , T ₂ ,...,T _m }, and to calculate the region-related information entropy for each segmentation algorithm set according to the size of the region-related information entropy. The image segmentation quality of each segmentation algorithm is ranked.

本实施方式中，由于每个区域都表示为一维离散随机变量，因此步骤S102中的非线性相关系数

可以采用等概率法进行盒子划分的方式计算。具体计算过程包括步骤：In this embodiment, since each region is expressed as a one-dimensional discrete random variable, the nonlinear correlation coefficient in step S102

It can be calculated by using the equal probability method for box division. The specific calculation process includes steps:

S2.1：一维离散随机变量

和中的取值个数为N，

和

分别表示

和

的第w,1≤w≤N个取值，分别将

和的取值按从小到大排列。S2.1: One-dimensional discrete random variable

and The number of values in is N,

and

Respectively

and

The w, 1≤w≤N value of the w, 1≤w≤N, respectively

and The values of are arranged in ascending order.

在步骤S2.1之前还可以对一维离散随机变量

和

进行预处理，预处理方法为：将一维离散随机变量

和

中序号相同并且均为0的取值删除，取值个数N为删除后的取值个数。经过预处理后可以降低0伪像素的个数，使计算得到的非线性相关系数

更为准确。Before step S2.1, one-dimensional discrete random variable can also be

and

Perform preprocessing, the preprocessing method is: the one-dimensional discrete random variable

and

The values with the same serial number and all 0 are deleted, and the number of values N is the number of values after deletion. After preprocessing, the number of 0 pseudo pixels can be reduced, so that the calculated nonlinear correlation coefficient

more accurate.

S2.2：分别将

和

中的取值依次划分为b个盒子，前b-1个盒子中每个盒子的元素个数均为

第b个盒子中元素个数为

表示向下取整。即第一组

个取值构成第一个盒子，第二组

个取值构成第二个盒子，依次类推，最后一个盒子即第b个盒子中取值个数为

得到的每个盒子记为α_s,1≤s≤b，

得到的每个盒子记为β_t,1≤t≤b，将每个盒子中的最小值和最大值作为该盒子的阈值。S2.2: Respectively

and

The values in are divided into b boxes in turn, and the number of elements in each box in the first b-1 boxes is

The number of elements in the bth box is

Indicates rounding down. i.e. the first group

values form the first box, the second group

values constitute the second box, and so on, the number of values in the last box, the bth box, is

Each box obtained is denoted as α _s , 1≤s≤b,

Each obtained box is denoted as β _t , 1≤t≤b, and the minimum and maximum values in each box are used as the threshold of the box.

S2.3：将

的每个盒子分别和的每个盒子组合，构成b×b的扩展二维盒子阵列，依据每个盒子的阈值，将N个取值对

放入扩展二维盒子阵列中。S2.3: Will

Each box of Combination of each box of b to form a b×b extended two-dimensional box array, according to the threshold of each box, the N value pairs

into an extended 2D box array.

表1为扩展二维盒子阵列的示意表。Table 1 is a schematic diagram of the extended two-dimensional box array.

α₁,β₁ α ₁ , β ₁ α₁,β₂ α ₁ , β ₂ …… α₁,β_b α ₁ ,β _b α₂,β₁ α ₂ , β ₁ α₂,β₂ α ₂ , β ₂ …… α₂,β_b α ₂ ,β _b …… …… …… …… α_b,β₁ α _b ,β ₁ α_b,β₂ α _b ,β ₂ …… α_b,β_b α _b , β _b

表1Table 1

S2.4：取值对

中的两个取值分别落入α_s和β_t中概率P(α_s)＝P(β_t)＝1/b，联合概率为P(α_s,β_t)＝n_st/N，其中n_st为盒子阵列中盒子(s,t)中元素对的个数。(s,t)即是盒子在b×b的扩展二维盒子阵列的坐标。S2.4: value pairs

Two values in α _s and β _t respectively fall into the probability P(α _s )=P(β _t )=1/b, the joint probability is P(α _s ,β _t )=n _st /N, where n _st is the number of element pairs in the box (s, t) in the box array. (s, t) are the coordinates of the extended two-dimensional box array of the box at b×b.

根据步骤S2.4可以得出改进的联合熵为：According to step S2.4, the improved joint entropy can be obtained as:

$H h (({X x}_{j j,, w w}^{((i i))},, {X x}_{k k,, w w}^{((i i))})) = = - - {Σ Σ}_{s the s = = 11}^{b b} {Σ Σ}_{t t = = 11}^{b b} P P (({α α}_{s the s},, {β β}_{t t})) {log log}_{b b} P P (({α α}_{s the s},, {β β}_{t t})) - - - - - - ((66))$

S2.5：根据（4）式得到

和

的非线性相关系数

的计算公式，计算

和

的非线性相关系数

计算公式为：S2.5: According to formula (4) get

and

The nonlinear correlation coefficient of

calculation formula, calculate

and

The nonlinear correlation coefficient of

The calculation formula is:

${ρ ρ}_{j j,, k k}^{((i i))} = = 22 + + {Σ Σ}_{s the s = = 11}^{b b} {Σ Σ}_{t t = = 11}^{b b} P P (({α α}_{s the s},, {β β}_{t t})) {log log}_{b b} P P (({α α}_{s the s},, {β β}_{t t})) - - - - - - ((77))$

（2）式中，非线性相关系数在闭区间[0,1]上表征两个变量的普遍相关性。当两个变量相关性最弱时，对应的数值对在b×b的扩展二维盒子阵列中均匀分布，非线性相关系数的理想值为0；当两个变量相关性最强时，对应的数值对在b×b的扩展二维X-Y盒子阵列中成对角线分布，非线性相关系数的理想值为1。当然在实际应用中，由于盒子数以及数值计算本身误差的影响，实际上很难取得0或1。In formula (2), the nonlinear correlation coefficient represents the universal correlation of two variables on the closed interval [0,1]. When the correlation between the two variables is the weakest, the corresponding value pairs are evenly distributed in the b×b extended two-dimensional box array, and the ideal value of the nonlinear correlation coefficient is 0; when the correlation between the two variables is the strongest, the corresponding Pairs of values are distributed diagonally in a b×b array of extended 2D X-Y boxes, ideally with a non-linear correlation coefficient of 1. Of course, in practical applications, due to the influence of the number of boxes and the error of numerical calculation itself, it is actually difficult to obtain 0 or 1.

需要指出的是，盒子的不同划分，计算出的非线性相关系数将会有所不同。每一个盒子代表了一个基本事件，因而盒子个数也就是基本事件总数。这样按照变量分布特征及有关客观因素事先定出基本事件数及各种事件的划分，才是比较合理的途径。但实际工作中往往面对的只是一系列数据，一般只有按以往的经验来划定。本实施方式选用的确定盒子个数的经验公式为：It should be pointed out that the calculated nonlinear correlation coefficient will be different for different divisions of the box. Each box represents a basic event, so the number of boxes is the total number of basic events. In this way, it is a more reasonable way to determine the number of basic events and the division of various events in advance according to the distribution characteristics of variables and related objective factors. However, in actual work, what is often faced is only a series of data, and generally it can only be delineated according to past experience. The empirical formula for determining the number of boxes selected in this embodiment is:

b＝1.87×(N-1)^2/5 （8）b＝1.87×(N-1) ^2/5 (8)

在实际应用中，可以根据（8）式的经验公式计算盒子个数供参考，以确定盒子个数。In practical applications, the number of boxes can be calculated according to the empirical formula of formula (8) for reference to determine the number of boxes.

表2是常用数据个数对应的盒子总数参考表。Table 2 is a reference table of the total number of boxes corresponding to the number of commonly used data.

元素个数number of elements 40-6040-60 100100 200200 400400 800800 10001000 15001500 20002000 50005000 1000010000 盒子总数total number of boxes 6-86-8 7-97-9 1616 2020 2727 2727 3535 3939 5656 7474

表2Table 2

实施例1Example 1

图2是实施例1合成图像的五种分割结果示意图。如图2所示，以浅灰色表示背景，以深灰色表示前景。将合成图像划分为a至e五种分割结果，得到左右所示的两个区域，将区域的外部所有像素全部用0值代替，在图像中显示为黑色区域，然后扩展为整个图像区域，保证了左右两个区域具有完全相同的采样点，满足非线性相关系数的计算要求。FIG. 2 is a schematic diagram of five kinds of segmentation results of the synthesized image in Embodiment 1. As shown in Figure 2, the background is represented by light gray, and the foreground is represented by dark gray. Divide the composite image into five segmentation results from a to e, and obtain the two areas shown on the left and right, replace all pixels outside the area with 0 values, display them as black areas in the image, and then expand them to the entire image area, ensuring The left and right regions have exactly the same sampling points, which meets the calculation requirements of the nonlinear correlation coefficient.

表3是采用本发明得到的分割结果a至e两个子区域的区域相关信息熵。Table 3 shows the region-related information entropy of the two sub-regions of the segmentation results a to e obtained by using the present invention.

分割结果Segmentation result aa bb cc dd ee 相关信息熵relevant information entropy 0.45570.4557 0.38820.3882 0.32250.3225 0.36270.3627 0.35690.3569

表3table 3

值得注意的是，为了满足非线性相关系数计算过程中对变量采样个数相同的要求，上面的方法直接以0替换区域外部的像素，称为0伪像素，这对结果的精确性将产生一定的影响。为了将这个影响降低到最小，可在计算前去掉共同区域上的0伪像素。It is worth noting that in order to meet the requirement of the same number of variables sampled during the calculation of the nonlinear correlation coefficient, the above method directly replaces the pixels outside the area with 0, which is called 0 pseudo-pixels, which will have a certain impact on the accuracy of the results. Impact. In order to minimize this effect, 0 pseudo-pixels on common areas can be removed before calculation.

如图2所示，在分割结果a和b中，得到的前景中存在属于背景的像素，因此前景与背景的的相关性较强，导致区域相关信息熵较大；在分割结果d和e中，得到的背景中存在属于前景的像素，因此背景与前景的相关性较强，同样也导致区域相关信息熵较大；在分割结果c中，前景与背景被很好地区分开，因此得到区域相关信息熵较小。As shown in Figure 2, in the segmentation results a and b, there are pixels belonging to the background in the obtained foreground, so the correlation between the foreground and the background is strong, resulting in a large area-related information entropy; in the segmentation results d and e , there are pixels belonging to the foreground in the obtained background, so the correlation between the background and the foreground is strong, which also leads to a large area related information entropy; in the segmentation result c, the foreground and the background are well separated, so the area correlation The information entropy is small.

按照表2中得到的区域相关信息熵对五种分割结果质量进行排序，得到c>e>d>b>a，其中分割结果b、d、e的区域相关信息熵较接近。从图2所示的五种分割结果可以看出，分割结果a中，前景中属于背景的像素最多，图像分割质量较差，分割结果b相对较少，并且分割结果b中前景中属于背景的像素数量，与分割结果d、e中背景中属于前景的像素数量较为接近，而分割结果c中前景与背景中均未出现对方的像素，图像分割质量最好。可见，采用本发明得到的区域相关信息熵得到的图像分割质量评价结果与实际结果一致。According to the region-related information entropy obtained in Table 2, the quality of the five segmentation results is sorted, and c>e>d>b>a is obtained, and the region-related information entropy of the segmentation results b, d, and e is relatively close. From the five segmentation results shown in Figure 2, it can be seen that in the segmentation result a, the pixels belonging to the background in the foreground are the most, the image segmentation quality is poor, and the segmentation result b is relatively small, and the pixels belonging to the background in the foreground in the segmentation result b The number of pixels is close to the number of pixels belonging to the foreground in the background in the segmentation results d and e, but in the segmentation result c, there are no opposite pixels in the foreground and background, and the image segmentation quality is the best. It can be seen that the image segmentation quality evaluation result obtained by using the region-related information entropy obtained by the present invention is consistent with the actual result.

实施例2Example 2

实施例2采用软件体膜（即合成图像）来验证本文分割质量评价方法本身的有效性。体膜具有客观性好、可重复性强、结果稳定等优点。如果采用真实图像则研究结果常受限于具体的应用，并且由于需要人工参与从而引入主观偏差。当然，合成图像中必须要把应用领域中的知识结合进来，才能准确反映客观问题。Example 2 uses the software body membrane (that is, the synthetic image) to verify the validity of the segmentation quality evaluation method in this paper. Body film has the advantages of good objectivity, strong repeatability, and stable results. If real images are used, the research results are often limited to specific applications, and subjective bias is introduced due to the need for human participation. Of course, knowledge in the application field must be incorporated in the composite image in order to accurately reflect objective problems.

本实施例采用的软件体膜为核磁共振（Magnetic Resonance，MR）（T1）图像，分辨率为512×512，含5%高斯噪声。图3是脑MR图像的典型切片。图3所示的区域为已知脑白质区域。图4是图3所示脑MR图像中脑白质的参考分割结果。图4用于对其他算法的分割结果进行参考对比。本实施例分别对采用增量式Chan-Vese模型和传统的阈值法得到的图像分割结果进行评价。The software body membrane used in this embodiment is a magnetic resonance (Magnetic Resonance, MR) (T1) image with a resolution of 512×512 and 5% Gaussian noise. Figure 3 is a typical slice of a brain MR image. The regions shown in Figure 3 are known white matter regions. FIG. 4 is a reference segmentation result of white matter in the brain MR image shown in FIG. 3 . Figure 4 is used to compare the segmentation results of other algorithms for reference. In this embodiment, the image segmentation results obtained by using the incremental Chan-Vese model and the traditional threshold method are respectively evaluated.

增量式Chan-Vese模型分割中，初始轮廓为圆，Chan-Vese模型参数μ＝1.0,υ＝0，窄带宽度δ＝6，窄带失效阈值ξ＝2，对于每一次的迭代采用迎风有限差分离散公式进行求解，其中时间步长Δt＝1.0。图5是采用增量式Chan-Vese模型得到的脑MR图像中脑白质的分割结果。如图5所示，该图像分割结果与图4所示的参考分割结果较为接近，图像分割质量较为理想。In incremental Chan-Vese model segmentation, the initial contour is a circle, Chan-Vese model parameters μ=1.0, υ=0, narrowband width δ=6, narrowband failure threshold ξ=2, and upwind finite difference is used for each iteration The discrete formulation was solved with a time step of Δt = 1.0. Fig. 5 is the segmentation result of the white matter in the brain MR image obtained by using the incremental Chan-Vese model. As shown in Figure 5, the image segmentation result is relatively close to the reference segmentation result shown in Figure 4, and the image segmentation quality is ideal.

阈值法可以简单地提取图像中的处于高灰度的脑白质。为比较不同阈值对分割结果的影响，对图3进行了10次图像分割，所采用的阈值T从57.5到80.0。Thresholding method can simply extract white matter in high gray level in the image. In order to compare the impact of different thresholds on the segmentation results, the image segmentation in Figure 3 was performed 10 times, and the threshold T used was from 57.5 to 80.0.

表4是每次图像分割采用的阈值。Table 4 is the threshold used for each image segmentation.

分割次数Number of splits ⅠI ⅡII ⅢIII ⅣIV ⅤⅤ ⅥⅥ ⅦVII ⅧVIII ⅨⅨ ⅩⅩ 阈值TThreshold T 57.557.5 60.060.0 62.562.5 65.065.0 67.567.5 70.070.0 72.572.5 75.075.0 77.577.5 80.080.0

表4Table 4

图6是采用阈值法得到的脑MR图像中脑白质的分割结果。如图6所示，由于脑组织的灰度分布特点，阈值法并不能得到非常满意的结果。Fig. 6 is the segmentation result of the white matter in the brain MR image obtained by using the threshold method. As shown in Figure 6, due to the gray distribution characteristics of brain tissue, the threshold method cannot obtain very satisfactory results.

表5是采用四种评价方法对参考分割结果以及增量式Chan-Vese模型和阈值法得到的图像分割结果得到的评价数据。Table 5 is the evaluation data obtained by using four evaluation methods on the reference segmentation results and the image segmentation results obtained by the incremental Chan-Vese model and the threshold method.

表5table 5

表5续Table 5 continued

表5所示的四种评价方法中，PEQA表示本发明提出的基于区域相关信息熵的评价方法；其他三种是目前常用的评价方法，基于区域灰度对比度的评价方法（Gray Contrast Measurement,GCM），基于区域一致性的评价方法（UniformityMeasurement,UM）和基于最终测试精度的评价方法（Relative UltimateMeasurement Accuracy,RUMA）。最终测试精度是以面积差异为测度的，由于实施例2采用的是体膜合成图像，因此该评价方法具有较为可靠的评价结果。Among the four evaluation methods shown in Table 5, PEQA represents the evaluation method based on the region-related information entropy proposed by the present invention; the other three are evaluation methods commonly used at present, and the evaluation method (Gray Contrast Measurement, GCM ), an evaluation method based on regional consistency (UniformityMeasurement, UM) and an evaluation method based on final test accuracy (Relative Ultimate Measurement Accuracy, RUMA). The final test accuracy is measured by the area difference. Since the embodiment 2 uses the body membrane composite image, this evaluation method has relatively reliable evaluation results.

从表5中的评价数据看来，以增量式Chan-Vese模型得到的图像分割结果为最优，并且与已知的参考分割结果非常接近，符合Chan-Vese模型具有较高分割精度的事实。阈值法的分割结果中，阈值为67.5和70.0时的图像分割结果Ⅴ和Ⅵ的评价数据在四种评价方法中均分别达到最小值，表明此时得到的图像分割结果相对较好，与图6所示结果相符；但这两个评价数据均要比以增量式Chan-Vese模型得到的图像分割结果和参考分割结果的评价数据大一些，与阈值法在医学图像中的分割效果差的事实相符。阈值过大或过小时，图像分割结果基本失去意义，在表5中对应的评价数据也都相对较大。From the evaluation data in Table 5, the image segmentation result obtained by the incremental Chan-Vese model is the best, and it is very close to the known reference segmentation results, which is consistent with the fact that the Chan-Vese model has higher segmentation accuracy . Among the segmentation results of the threshold method, the evaluation data of the image segmentation results V and VI when the threshold value is 67.5 and 70.0 respectively reached the minimum value in the four evaluation methods, indicating that the image segmentation results obtained at this time are relatively good, as shown in Figure 6 The results shown are consistent; but the two evaluation data are larger than the image segmentation results obtained by the incremental Chan-Vese model and the evaluation data of the reference segmentation results, which is consistent with the fact that the segmentation effect of the threshold method in medical images is poor match. If the threshold is too large or too small, the image segmentation results will basically lose meaning, and the corresponding evaluation data in Table 5 are relatively large.

从表5中可以看出，本发明所提出的PEQA方法可以在闭区间[0,1]上给出定量评价。It can be seen from Table 5 that the PEQA method proposed by the present invention can give quantitative evaluation on the closed interval [0,1].

由于RUMA的评价结果可靠性较高，因此以其评价数据作为参考数据，从GCM和UM的评价数据来看，GCM相对要准确一些，UM可靠性较低，并且GCM和UM对于该医学图像的评价效果都要远逊于PEQA；而RUMA的数据则表明，PEQA给出的评价与RUMA的评价完全一致，进一步证明了PEQA评价方法的有效性。并且与RUMA相比，PEQA能够在闭区间[0,1]上给出定量的评价结果，并且该评价结果具有较高的精度，对图像分割结果的评价更为直观与准确。Since the evaluation results of RUMA are highly reliable, the evaluation data of RUMA are used as reference data. Judging from the evaluation data of GCM and UM, GCM is relatively more accurate, while UM is less reliable. The evaluation effect is far inferior to that of PEQA; while the data of RUMA shows that the evaluation given by PEQA is completely consistent with that of RUMA, which further proves the effectiveness of the PEQA evaluation method. And compared with RUMA, PEQA can give quantitative evaluation results on the closed interval [0,1], and the evaluation results have higher precision, and the evaluation of image segmentation results is more intuitive and accurate.

尽管上面对本发明说明性的具体实施方式进行了描述，以便于本技术领域的技术人员理解本发明，但应该清楚，本发明不限于具体实施方式的范围，对本技术领域的普通技术人员来讲，只要各种变化在所附的权利要求限定和确定的本发明的精神和范围内，这些变化是显而易见的，一切利用本发明构思的发明创造均在保护之列。Although the illustrative specific embodiments of the present invention have been described above, so that those skilled in the art can understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, As long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are included in the protection list.

Claims

1. an image segmentation quality evaluation method based on region-related information entropy, is characterized in that, comprises the following steps:

S1: Segment the target image I using the segmentation algorithm T ₁ to be evaluated and the reference segmentation algorithm T ₂ to obtain different segmentation results Θ _i , i=1, 2, and the number of regions obtained by each segmentation result is denoted as M _i , the result of segmentation

Θ_{i} = \cup_{j}^{m_{i}} Ω_{j}^{(i)}, j = 1,2, . . ., m_{i},

is the region of the segmentation result Θ _i ;

S2: For each segmentation result Θ _i in M _i regions

area

The pixels in the gray value maintain the original value, and the area

The gray values of the pixels outside are all recorded as 0, and the obtained

Corresponding extended grayscale image; each region

The number of variable values is N, and N is the number of pixels of the target image I; calculate two random variables

and

The nonlinear correlation coefficient between

Random Variables

The nonlinear correlation coefficient with itself

S3: Utilize all nonlinear correlation coefficients of each segmentation result Θ _i in step S2 to construct the nonlinear correlation matrix R _i of the segmentation result Θ _i :

{R R}_{i i} = = (\begin{matrix} 11 & {ρ ρ}_{1,2 1,2}^{((i i))} & \cdot &Center Dot; \cdot \cdot \cdot \cdot & {ρ ρ}_{11,, {M m}_{i i}}^{((i i))} \\ {ρ ρ}_{2,1 2,1}^{((i i))} & 11 & \cdot &Center Dot; \cdot \cdot \cdot \cdot & {ρ ρ}_{22,, {M m}_{i i}}^{((i i))} \\ \cdot \cdot & \cdot \cdot & \cdot \cdot & \cdot \cdot \\ \cdot \cdot & \cdot \cdot & \cdot \cdot & \cdot \cdot \\ \cdot \cdot & \cdot \cdot & \cdot \cdot & \cdot \cdot \\ {ρ ρ}_{{M m}_{i i},, 11}^{((i i))} & {ρ ρ}_{{M m}_{i i},, 22}^{((i i))} & \cdot &Center Dot; \cdot \cdot \cdot \cdot & 11 \end{matrix})

S4: Calculate M _i eigenvalues λ _p , p=1,2,...,M _i of each nonlinear correlation matrix R _i , and calculate the region-related information entropy of each segmentation result Θ _i according to the eigenvalues:

{Λ Λ}_{i i} = = 11 + + {Σ Σ}_{p p = = 11}^{{M m}_{u u}} \frac{{λ λ}_{p p}}{{M m}_{i i}} {log log}_{{M m}_{i i}} \frac{{λ λ}_{p p}}{{M m}_{i i}};;

S5: Comparing the region-related information entropy of the segmentation algorithm _T1 to be evaluated and the reference segmentation algorithm _T2 , if _Λ1 > _Λ2 , the image segmentation result obtained by the reference segmentation algorithm _T2 is better than the image obtained by the segmentation algorithm _T1 to be evaluated The quality of the segmentation result; if Λ ₁ < Λ ₂ , the image segmentation result obtained by the segmentation algorithm T ₁ to be evaluated is better than the quality of the image segmentation result obtained by the reference segmentation algorithm T ₂ ; if Λ ₁ = Λ ₂ , the two segmentation results The quality of the image segmentation results obtained by the algorithm is the same.

2. The image segmentation quality evaluation method according to claim 1, characterized in that, in the step S2, the value range of the image pixel gray value is [0, 255].

3. image segmentation quality assessment method according to claim 1, is characterized in that, in described step S2, non-linear correlation coefficient

S2.1: One-dimensional discrete random variable and The number of values in is N,

and

Respectively

and

The w, 1≤w≤N value of the w, 1≤w≤N, respectively

and The values of are arranged from small to large;

S2.2: Respectively

and

, the number of elements in the bth box is Each box obtained is denoted as α _s , 1≤s≤b,

Each obtained box is recorded as β _t , 1≤t≤b, and the minimum and maximum values in each box are used as the threshold of the box;

S2.3: Will

Each box of

Combination of each box of b to form a b×b extended two-dimensional box array, according to the threshold of each box, the N value pairs into the extended 2D box array;

S2.4: value pairs

Two values in α _s and β _t respectively fall into the probability P(α _s )=P(β _t )=1/b, the joint probability is P(α _s ,β _t )=n _st /N, where n _st is the number of value pairs in the box (s, t) in the extended two-dimensional box array, and (s, t) is the coordinate of the box in the extended two-dimensional box array;

S2.5: Calculation and The nonlinear correlation coefficient of

The calculation formula is:

{ρ ρ}_{j j,, k k}^{((i i))} = = 22 + + {Σ Σ}_{s the s = = 11}^{b b} {Σ Σ}_{t t = = 11}^{b b} P P (({α α}_{s the s},, {β β}_{t t})) {log log}_{b b} P P (({α α}_{s the s},, {β β}_{t t})) . .

4. The image segmentation quality evaluation method according to claim 3, characterized in that, said steps also include: before step S2.1, one-dimensional discrete random variable

and

and

5. The image segmentation quality evaluation method according to any one of claims 3 to 4, wherein the number b of boxes is determined according to the formula b=1.87×(N-1) ^2/5 .