基于图像不确定性信息的阈值分割方法研究
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摘要
图像分割是由图像处理向图像分析过渡的重要步骤，在图像处理技术中占有重要地位。图像分割同时也是一个经典的世界性难题，目前仍然还没有一种公认的通用的分割算法。阈值化是图像分割中最常用的方法之一，阈值化具有简单、直观、易于实现的特点，是图像分割研究和应用的一个热点。鉴于图像信息具有不确定性，如何处理好图像中的不确定性信息，以便获得更精确的分割结果是图像分割的一个难点。图像中的不确定性包括图像获取，传输，存储等过程中带来的随机性、模糊性、不完全性、不稳定性和不一致性等几个方面。本论文从图像拥有的统计信息、模糊信息和粗糙信息入手，针对现有的一些阈值化方法中存在的问题和不足进行探讨，提出了一些适应性更好的阈值分割算法。取得的主要研究成果如下：
1.针对运用图像统计信息的Otsu法不能有效分割小目标图像的缺点，提出了两种加权Otsu法。其一是利用邻域平滑直方图作为权值，对传统Otsu法加权，提出了一种邻域加权Otsu法，该方法在保证阈值点处类间方差尽可能大的同时，保证了阈值点尽量位于图像直方图的谷点位置；其二是结合梯度映射函数提出了一种梯度加权Otsu法，该方法将梯度信息加入到Otsu方法的目标函数中，使得最佳的阈值尽量位于目标和背景的边界处。
2.把运用图像统计信息的一维最小误差阈值法和一维最小交叉熵阈值法推广到二维情形，并舍弃传统二维方法中二维直方图内反对角线区域概率和近似为0的假设，提出了二维直线型最小误差阈值法和二维直线型最小交叉熵阈值法。
3.对运用图像模糊信息的最大模糊熵阈值分割法进行研究。针对该方法耗时太长的问题提出了一种快速算法，快速算法利用S型隶属函数和模糊熵的两个性质，将传统模糊熵阈值法的时间复杂度由O (L4)降到O (L3)；基于模糊熵的对偶概念——模糊能量，讨论了基于模糊能量的图像阈值分割法，为了增强基于模糊能量的阈值法的分割效果，提出了一种加权模糊能量阈值法。
4.对运用图像模糊信息的广义模糊熵阈值化方法进行研究。针对该方法中参数m的选取问题提出了一种利用优化算法自适应选取参数的方案，该方案可以根据具体图像自适应选取参数m，同时针对参数(a, b, d)穷举搜索费时的缺点，通过优化方法快速找到其最佳参数组合；将一维广义模糊熵阈值法推广到二维以提高算法的抗噪能力，二维方法通过定义图像的二维模糊隶属度函数，同时考虑图像的点灰度信息和像素点周围邻域内的平均灰度信息，可以有效去除图像中的高斯噪声。
5.对运用图像粗糙信息的粗糙熵阈值化方法进行研究。针对现有粗糙熵表述上的问题，提出了最小平方粗糙熵阈值分割法，该方法的最佳分割阈值取在图像中目标和背景的粗糙度为0处，目标函数的意义更为明确；针对一维粗糙熵阈值法仅考虑了图像中灰度信息的不足，建立了图像的二维粗糙集模型，提出了一种结合空间信息的二维粗糙熵图像阈值分割算法。
Image segmentation is the key step of the image processing to image analysis andplays an important role in image processing technology. There has no universal imagesegmentation method in the world at present and it’s still a classical worldwide proplem.Thresholding is one of the most commonly used methods and is the hot off the press inimage segmentation with characteristics of simple, intuitive and easy to be realized.Considering the uncertainty of the image information, it’s a difficult problem that howto deal with the uncertainty in the image and get more accurate segmentation results.The uncertainty of the image includes the randomness, fuzziness, incompleteness,instability and inconsistency by the process of image acquisition, transmission, andstorage etc. This paper discussed the problem and the shortcoming in the existingthresholding method and proposed some new thresholding algorithms with betterperformance based on the statistical information, fuzzy information and roughinformation in the image. Main research results are as follows,
1. Considering the classical Otsu method which uses the statistics information of theimage failed if the histogram is unimodal or close to unimodal, two modified Otsumethod were proposed. One novel method weighs the objective function of Otsumethod with the neighborhood gray level of the threshold, and selects a thresholdvalue that has small probabilities in its neighborhood area and also maximizes thebetween-classes variance in the gray-level histogram. The other new method weighsthe objective function of the Otsu method with the gray level and gradient mapping(GGM) function. It combines the gradient information to the objective function ofthe Otsu method and makes the optimal threshold near at the boundary of the objectand the background in an image.
2. Two dimensional methods were presented for the minimum error thresholdingmethod and the minimum cross entropy method, which utilize the statisticsinformation of the image. And discarding the hypothesis that sum of the probabilityin the back diagonal area in the2D histogram are zero, two dimensional linear typeminimum error thresholding method and two dimensional linear type minimumcross entropy method were proposed.
3. A fast algorithm for the maximum fuzzy entropy thresholding method based on thefuzzy information of the image is presented. The new algorithm reduces the timecomplexity of the maximum fuzzy entropy thresholding method fromO (L4)toO (L3)based on the two properties of the S-type membership function and the fuzzy entropy. Based on the dual conception of the fuzzy entropy, the maximumfuzzy energy image thresholding method was discussed. To enhance theperformance of the maximum fuzzy energy thresholding method, a weightedmethod was proposed.
4. The generalized fuzzy entropy thresholding method used fuzzy information of theimage was studied. And an adaptive preferences algorithm for the patameter m ofthe generalized fuzzy entropy thresholding method is proposed by the optimizationalgorithm. The new algorithm can select the parameter m for an image adaptivelyand find the optimal parameter combination (a, b, d)with the optimizationalgorithm fastly. To improve the noise immunity of the generalized fuzzy entropythresholding method, the two dimensional generalized fuzzy entropy thresholdingmethod is suggested by the definition of the two dimensional fuzzy membershipfunction for an image. Two dimensional method can remove the Gassion noiseeffectively by considering not only the gray value but also the average gray value ofthe neighbourhood.
5. In the last section, we discussed the rough entropy thresholding method whichutilized the rough information of the image. The minimum square rough entropy isgiven for the expression problem of the existing rough entropy. The optimalthreshold of the minimum square rough entropy thresholding method is at the grayvalue that the roughness of the object and the background are zeros. To considermore information of the image, the two dimensional rough entropy thresholdingmethod is presented based on the two dimensional rough model of the image withthe spatial information.
1.针对运用图像统计信息的Otsu法不能有效分割小目标图像的缺点，提出了两种加权Otsu法。其一是利用邻域平滑直方图作为权值，对传统Otsu法加权，提出了一种邻域加权Otsu法，该方法在保证阈值点处类间方差尽可能大的同时，保证了阈值点尽量位于图像直方图的谷点位置；其二是结合梯度映射函数提出了一种梯度加权Otsu法，该方法将梯度信息加入到Otsu方法的目标函数中，使得最佳的阈值尽量位于目标和背景的边界处。
2.把运用图像统计信息的一维最小误差阈值法和一维最小交叉熵阈值法推广到二维情形，并舍弃传统二维方法中二维直方图内反对角线区域概率和近似为0的假设，提出了二维直线型最小误差阈值法和二维直线型最小交叉熵阈值法。
3.对运用图像模糊信息的最大模糊熵阈值分割法进行研究。针对该方法耗时太长的问题提出了一种快速算法，快速算法利用S型隶属函数和模糊熵的两个性质，将传统模糊熵阈值法的时间复杂度由O (L4)降到O (L3)；基于模糊熵的对偶概念——模糊能量，讨论了基于模糊能量的图像阈值分割法，为了增强基于模糊能量的阈值法的分割效果，提出了一种加权模糊能量阈值法。
4.对运用图像模糊信息的广义模糊熵阈值化方法进行研究。针对该方法中参数m的选取问题提出了一种利用优化算法自适应选取参数的方案，该方案可以根据具体图像自适应选取参数m，同时针对参数(a, b, d)穷举搜索费时的缺点，通过优化方法快速找到其最佳参数组合；将一维广义模糊熵阈值法推广到二维以提高算法的抗噪能力，二维方法通过定义图像的二维模糊隶属度函数，同时考虑图像的点灰度信息和像素点周围邻域内的平均灰度信息，可以有效去除图像中的高斯噪声。
5.对运用图像粗糙信息的粗糙熵阈值化方法进行研究。针对现有粗糙熵表述上的问题，提出了最小平方粗糙熵阈值分割法，该方法的最佳分割阈值取在图像中目标和背景的粗糙度为0处，目标函数的意义更为明确；针对一维粗糙熵阈值法仅考虑了图像中灰度信息的不足，建立了图像的二维粗糙集模型，提出了一种结合空间信息的二维粗糙熵图像阈值分割算法。
Image segmentation is the key step of the image processing to image analysis andplays an important role in image processing technology. There has no universal imagesegmentation method in the world at present and it’s still a classical worldwide proplem.Thresholding is one of the most commonly used methods and is the hot off the press inimage segmentation with characteristics of simple, intuitive and easy to be realized.Considering the uncertainty of the image information, it’s a difficult problem that howto deal with the uncertainty in the image and get more accurate segmentation results.The uncertainty of the image includes the randomness, fuzziness, incompleteness,instability and inconsistency by the process of image acquisition, transmission, andstorage etc. This paper discussed the problem and the shortcoming in the existingthresholding method and proposed some new thresholding algorithms with betterperformance based on the statistical information, fuzzy information and roughinformation in the image. Main research results are as follows,
1. Considering the classical Otsu method which uses the statistics information of theimage failed if the histogram is unimodal or close to unimodal, two modified Otsumethod were proposed. One novel method weighs the objective function of Otsumethod with the neighborhood gray level of the threshold, and selects a thresholdvalue that has small probabilities in its neighborhood area and also maximizes thebetween-classes variance in the gray-level histogram. The other new method weighsthe objective function of the Otsu method with the gray level and gradient mapping(GGM) function. It combines the gradient information to the objective function ofthe Otsu method and makes the optimal threshold near at the boundary of the objectand the background in an image.
2. Two dimensional methods were presented for the minimum error thresholdingmethod and the minimum cross entropy method, which utilize the statisticsinformation of the image. And discarding the hypothesis that sum of the probabilityin the back diagonal area in the2D histogram are zero, two dimensional linear typeminimum error thresholding method and two dimensional linear type minimumcross entropy method were proposed.
3. A fast algorithm for the maximum fuzzy entropy thresholding method based on thefuzzy information of the image is presented. The new algorithm reduces the timecomplexity of the maximum fuzzy entropy thresholding method fromO (L4)toO (L3)based on the two properties of the S-type membership function and the fuzzy entropy. Based on the dual conception of the fuzzy entropy, the maximumfuzzy energy image thresholding method was discussed. To enhance theperformance of the maximum fuzzy energy thresholding method, a weightedmethod was proposed.
4. The generalized fuzzy entropy thresholding method used fuzzy information of theimage was studied. And an adaptive preferences algorithm for the patameter m ofthe generalized fuzzy entropy thresholding method is proposed by the optimizationalgorithm. The new algorithm can select the parameter m for an image adaptivelyand find the optimal parameter combination (a, b, d)with the optimizationalgorithm fastly. To improve the noise immunity of the generalized fuzzy entropythresholding method, the two dimensional generalized fuzzy entropy thresholdingmethod is suggested by the definition of the two dimensional fuzzy membershipfunction for an image. Two dimensional method can remove the Gassion noiseeffectively by considering not only the gray value but also the average gray value ofthe neighbourhood.
5. In the last section, we discussed the rough entropy thresholding method whichutilized the rough information of the image. The minimum square rough entropy isgiven for the expression problem of the existing rough entropy. The optimalthreshold of the minimum square rough entropy thresholding method is at the grayvalue that the roughness of the object and the background are zeros. To considermore information of the image, the two dimensional rough entropy thresholdingmethod is presented based on the two dimensional rough model of the image withthe spatial information.
引文
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