基于统计和谱图的图像阈值分割方法研究
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摘要
图像分割是图像处理与分析的关键环节,也是计算机视觉研究领域的一个经典难题。在一些图像分割的应用中,目标像素的灰度级有别于背景像素的灰度级。在这种情形下,阈值方法就成了-种简单而有效的图像分割方法。近年来,阈值分割受到了国内外研究者的广泛关注,并已被广泛应用于目标识别、机器视觉等领域。本文针对图像阈值分割方法进行了较为深入的研究,主要工作和研究成果如下：
(1)经典的统计阈值方法将目标和背景的方差和作为阈值选择的准则,仅仅考虑了方差和,对目标和背景具有较大方差差异的图像分割的效果不理想。针对此问题,首先提出了一种融合了方差和与方差差异的统计阈值方法,较好地解决了这类图像的分割问题。此外,针对目标和背景具有相似统计分布的特性,设计了一种统计阈值方法,并将其与图(graph)的等周常数联系起来,进一步说明了此方法的合理性。在一系列红外图像上的实验结果证实了它的有效性。
(2)近年来,基于谱图的图像分割技术成了图像分割领域一个新的研究热点。这类方法将图像映射为带权无向图,把图像分割问题转化为图划分问题,通过求图划分代价函数的最小值来获得对应图像的分割。等周图割是一种新近的图谱图像分割方法,它不属于阈值分割范畴,未能充分利用图像中像素点的灰度信息,直接应用到灰度图像的分割中效果不甚理想。为此,结合等周图割和阈值分割思想提出了一种二级阈值方法。此方法将等周图割中的等周率作为阈值选择的准则,并在此基础上,利用人类视觉感知的特性来缩小阈值搜索的范围,缩短分割时间,提升分割性能。此外,由于二级阈值方法只能将图像分割成两个部分,无法满足实际分割中将图像分成多个部分的需要。针对此问题,将基于等周图割的二级阈值方法扩展到多级阈值分割中,提出了一种快速有效的迭代策略来获得多个分割阈值,优化了等周率的计算,引入了聚类数自动确定的方法来选择合理的阈值个数。扩展后的多级阈值方法不仅能自动确定阂值个数,而且其时间复杂性与阈值个数无关,这使其避免了传统多级阈值方法的缺陷,即随着阈值个数的增大,分割性能不稳定且计算复杂度呈指数增长。在一系列图像上的实验结果表明了此方法的有效性。
(3)基于过渡区域的阈值分割方法是近年来兴起的一类图像分割方法。相对于图像的非过渡区域(目标和背景)而言,过渡区域具有更为频繁而强烈的灰度变化。根据图像过渡区域的特点,提出了一种基于灰度差异的过渡区域提取及阈值分割方法,将像素点的灰度级与其局部邻域的灰度均值之间的绝对差异作为描述子来刻画过渡区域。灰度差异仅笼统地反映了像素点与其邻域均值之间的差异,未能反映像素点与邻域内像素点之间的具体差异。为此,提出了一种改进的灰度差异作为过渡区域描述子,利用像素点与其邻域内像素点的绝对灰度差异之和来刻画过渡区域。在一系列图像上的实验结果表明,改进的灰度差异对过渡区域的刻画是行之有效的。另外,针对传统过渡区域描述子未同时考虑灰度变化的频率和幅度,对过渡区域刻画不完整的问题,提出了一种融合了局部复杂度和局部方差的过渡区域描述子。它利用局部复杂度来刻画局部窗口内灰度变化的频率,同时借助局部方差来反映灰度变化的幅度,最后将局部复杂度和局部方差归一化后综合为一个新的描述子。在红外以及文本等一系列图像上的实验结果表明,相对于传统的过渡区域描述子,综合后的描述子能更准确地刻画过渡区域。新方法准确地提取了图像的过渡区域,获得了更好的阈值分割结果,且抗噪性能更强。
(4)针对现有的过渡区域方法未考虑人类视觉感知特性的问题,提出了一种无监督的过渡区域提取方法。此方法先利用人类视觉感知的特性,结合图像的统计特征,以种无监督的方式来估计过渡区域的灰度范围,实现图像变换,然后利用局部方差作为描述子提取图像的过渡区域,进而获得最终的阈值分割结果。在工业无损检测等系列图像上的实验结果表明,图像变换过程保持了过渡区域的灰度变化,同时削弱了非过渡区域的灰度变化,简化了原图像,对后续的过渡区域提取大有裨益。新方法明显改善了过渡区域提取的准确性,获得了更好的分割结果。此外,将图像变换的思想借鉴到了传统阈值分割中,提出了3种无监督的范围受限的阈值方法。相对于传统方法,范围受限的方法用变换后的图像替代原图像作为分割对象,既符合人类视觉感知的特点,又缩小了阈值搜索的范围,节省了运算时间。变换后的图像更简单,有利于后续的阈值分割。在工业无损检测等系列图像上的实验结果表明,与它们对应的传统方法相比,范围受限的阈值方法分割效果更好,分割速度与传统方法相当。
Image segmentation is a key step in image processing and analysis, and a classic difficulty in computer vision. There are some applications of image segmentation, where gray levels of object pixels are distinctive from those of background ones. In this case, image thresholding becomes a simple and effective image segmentation approach. During last few years, image thresholding has gotten wide attention from researchers at home and abroad, and has been widely applied to a lot of fields, such as target recognition and machine vision. The paper does comparatively deep research on image thresholding, and its main works and research results are as follows:
(1) Classic statistical thresholding methods use variance sum of object and background classes as criteria for threshold selection. They only take variance sum into account, and fail to achieve satisfactory results when segmenting a kind of images, where variance discrepancy between the object and background classes is large. To solve the problem, a new statistical thresholding method combining variance sum and variance discrepancy is proposed in this paper. In addition, we present another statistical method for some images having similar statistical distributions on the object and background, and relate it with isoperimetric constant of a graph. This further shows the rationality of our method, and experimental results on a series of infrared images demonstrate its effectiveness.
(2) Recently, image segmentation technique based on spectral graph is a new research hotspot. It regards an image as a weighted undirected graph, converts image segmentation problem into graph partitioning one, and implements image segmentation by minimizing certain cost function of graph partition. Among this kind of methods, isoperimetric cut is a newly developed one. However, the isoperimetric cut dose not belong to thresholding, and fail to adequately utilize gray level information of an image. This makes it unsuitable for gray level image segmentation. Here, we introduce the isoperimetric cut into image thresholding, and present a bilevel thresholding method for overcoming the above limitation. The proposed method uses isoperimetric ratio of the isoperimetric cut as criterion for threshold selection. Furthermore, characteristics of human visual perception are also utilized to reduce search range of thresholds, shorten segmentation time, and improve segmentation performance. The above bilevel thresholding method can only divide an image into two parts, and can not meet some practical segmentation tasks dividing an image into multiple parts. To solve the problem, we extend a bilevel method based on isoperimetric cut into multilevel thresholding. The extended method finds multiple thresholds by a fast and effective iterative scheme, simplifies computation of isoperimetric ratio, and introduces a way of automatically determining cluster number to adaptively choose reasonable threshold number. The new multilevel method can automatically determine threshold number, and its time complexity is independent of the threshold number. This makes our method avoid disadvantages of conventional multilevel thresholding ones, i.e., instability of segmentation performance and exponential growth of computational complexity with the increase of threshold number. Experimental results on a series of images show the effectiveness of our multilevel method.
(3) Image thresholding based on transition region is a newly developed image segmentation technique. As compared with non-transition region (i.e., object and background regions), transition region of an image has more frequent and stronger gray level changes. On the basis of the characteristic of transition region, a transition region extraction and thresholding method based on gray level difference is proposed in this paper. The proposed method uses absolute difference between a pixel's gray level and the gray level average of its local neighborhood window as a descriptor for depicting transition region. The above gray level difference is very rough, and can not reflect the detailed difference between the pixel and other pixels in its neighborhood. Hence we present a modified gray level difference as a new transition region descriptor. The descriptor uses the sum of absolute gray level difference between the pixel and each pixel in its neighborhood to characterize transition region. Experimental results on a variety of images show that the modified gray level difference is effective on transition region description. In addition, conventional transition region descriptors do not take frequency and degree of gray level changes into account simultaneously, and fail to depict transition region comprehensively. To solve the problem, we present a new descriptor integrating local complexity and local variance. It uses local complexity to reflect frequency of gray level changes in local neighborhood window, meanwhile utilizes local variance to degree of the changes. Then local complexity and local variance are combined as a new transition region descriptor after being normalized respectively. Experimental results on a variety of images including infrared and text ones show that the new descriptor can depict transition region more accurately, as compared with conventional ones. And the corresponding method extracts transition region more accurately, obtains better thresholding results, and has stronger noise immunity.
(4) Existing image thresholding methods based on transition region do not consider characteristics of human visual perception. An unsupervised transition region extraction and thresholding method is proposed to solve this problem. The proposed method first utilizes characteristics of human visual perception and statistical characteristics of an image to estimate gray level range of transition region for implementing image transformation in an unsupervised way, then uses local variance as descriptor to extract transition region, and finally obtains thresholding result. Experimental results on a variety of images including industrial nondestructive testing ones show that image transformation preserves gray level changes of transition region, meanwhile weakens gray level changes of non-transition region. This simplifies the original image, which should be helpful for subsequent transition region extraction. The new method obviously improves accuracy of transition region extraction, and obtains better sgemnetation results. In addition, we introduce the above image transformation into conventional thresholding, and present three unsupervised range-constrained thresholding methods. As compared with conventional approaches, range-constrained methods implement thresholding on the transformed image instead of the original one. This not only coincides with human visual perception, but also reduces search range of thresholds and saves computational time. The transformed image is simper than the original one, which should be helpful for subsequent image thresholding. Experimental results on a variety of images including nondestructive testing ones show that range-constrained methods have better segmentation quality, and segmentation speed is comparative with their counterparts.
(1)经典的统计阈值方法将目标和背景的方差和作为阈值选择的准则,仅仅考虑了方差和,对目标和背景具有较大方差差异的图像分割的效果不理想。针对此问题,首先提出了一种融合了方差和与方差差异的统计阈值方法,较好地解决了这类图像的分割问题。此外,针对目标和背景具有相似统计分布的特性,设计了一种统计阈值方法,并将其与图(graph)的等周常数联系起来,进一步说明了此方法的合理性。在一系列红外图像上的实验结果证实了它的有效性。
(2)近年来,基于谱图的图像分割技术成了图像分割领域一个新的研究热点。这类方法将图像映射为带权无向图,把图像分割问题转化为图划分问题,通过求图划分代价函数的最小值来获得对应图像的分割。等周图割是一种新近的图谱图像分割方法,它不属于阈值分割范畴,未能充分利用图像中像素点的灰度信息,直接应用到灰度图像的分割中效果不甚理想。为此,结合等周图割和阈值分割思想提出了一种二级阈值方法。此方法将等周图割中的等周率作为阈值选择的准则,并在此基础上,利用人类视觉感知的特性来缩小阈值搜索的范围,缩短分割时间,提升分割性能。此外,由于二级阈值方法只能将图像分割成两个部分,无法满足实际分割中将图像分成多个部分的需要。针对此问题,将基于等周图割的二级阈值方法扩展到多级阈值分割中,提出了一种快速有效的迭代策略来获得多个分割阈值,优化了等周率的计算,引入了聚类数自动确定的方法来选择合理的阈值个数。扩展后的多级阈值方法不仅能自动确定阂值个数,而且其时间复杂性与阈值个数无关,这使其避免了传统多级阈值方法的缺陷,即随着阈值个数的增大,分割性能不稳定且计算复杂度呈指数增长。在一系列图像上的实验结果表明了此方法的有效性。
(3)基于过渡区域的阈值分割方法是近年来兴起的一类图像分割方法。相对于图像的非过渡区域(目标和背景)而言,过渡区域具有更为频繁而强烈的灰度变化。根据图像过渡区域的特点,提出了一种基于灰度差异的过渡区域提取及阈值分割方法,将像素点的灰度级与其局部邻域的灰度均值之间的绝对差异作为描述子来刻画过渡区域。灰度差异仅笼统地反映了像素点与其邻域均值之间的差异,未能反映像素点与邻域内像素点之间的具体差异。为此,提出了一种改进的灰度差异作为过渡区域描述子,利用像素点与其邻域内像素点的绝对灰度差异之和来刻画过渡区域。在一系列图像上的实验结果表明,改进的灰度差异对过渡区域的刻画是行之有效的。另外,针对传统过渡区域描述子未同时考虑灰度变化的频率和幅度,对过渡区域刻画不完整的问题,提出了一种融合了局部复杂度和局部方差的过渡区域描述子。它利用局部复杂度来刻画局部窗口内灰度变化的频率,同时借助局部方差来反映灰度变化的幅度,最后将局部复杂度和局部方差归一化后综合为一个新的描述子。在红外以及文本等一系列图像上的实验结果表明,相对于传统的过渡区域描述子,综合后的描述子能更准确地刻画过渡区域。新方法准确地提取了图像的过渡区域,获得了更好的阈值分割结果,且抗噪性能更强。
(4)针对现有的过渡区域方法未考虑人类视觉感知特性的问题,提出了一种无监督的过渡区域提取方法。此方法先利用人类视觉感知的特性,结合图像的统计特征,以种无监督的方式来估计过渡区域的灰度范围,实现图像变换,然后利用局部方差作为描述子提取图像的过渡区域,进而获得最终的阈值分割结果。在工业无损检测等系列图像上的实验结果表明,图像变换过程保持了过渡区域的灰度变化,同时削弱了非过渡区域的灰度变化,简化了原图像,对后续的过渡区域提取大有裨益。新方法明显改善了过渡区域提取的准确性,获得了更好的分割结果。此外,将图像变换的思想借鉴到了传统阈值分割中,提出了3种无监督的范围受限的阈值方法。相对于传统方法,范围受限的方法用变换后的图像替代原图像作为分割对象,既符合人类视觉感知的特点,又缩小了阈值搜索的范围,节省了运算时间。变换后的图像更简单,有利于后续的阈值分割。在工业无损检测等系列图像上的实验结果表明,与它们对应的传统方法相比,范围受限的阈值方法分割效果更好,分割速度与传统方法相当。
Image segmentation is a key step in image processing and analysis, and a classic difficulty in computer vision. There are some applications of image segmentation, where gray levels of object pixels are distinctive from those of background ones. In this case, image thresholding becomes a simple and effective image segmentation approach. During last few years, image thresholding has gotten wide attention from researchers at home and abroad, and has been widely applied to a lot of fields, such as target recognition and machine vision. The paper does comparatively deep research on image thresholding, and its main works and research results are as follows:
(1) Classic statistical thresholding methods use variance sum of object and background classes as criteria for threshold selection. They only take variance sum into account, and fail to achieve satisfactory results when segmenting a kind of images, where variance discrepancy between the object and background classes is large. To solve the problem, a new statistical thresholding method combining variance sum and variance discrepancy is proposed in this paper. In addition, we present another statistical method for some images having similar statistical distributions on the object and background, and relate it with isoperimetric constant of a graph. This further shows the rationality of our method, and experimental results on a series of infrared images demonstrate its effectiveness.
(2) Recently, image segmentation technique based on spectral graph is a new research hotspot. It regards an image as a weighted undirected graph, converts image segmentation problem into graph partitioning one, and implements image segmentation by minimizing certain cost function of graph partition. Among this kind of methods, isoperimetric cut is a newly developed one. However, the isoperimetric cut dose not belong to thresholding, and fail to adequately utilize gray level information of an image. This makes it unsuitable for gray level image segmentation. Here, we introduce the isoperimetric cut into image thresholding, and present a bilevel thresholding method for overcoming the above limitation. The proposed method uses isoperimetric ratio of the isoperimetric cut as criterion for threshold selection. Furthermore, characteristics of human visual perception are also utilized to reduce search range of thresholds, shorten segmentation time, and improve segmentation performance. The above bilevel thresholding method can only divide an image into two parts, and can not meet some practical segmentation tasks dividing an image into multiple parts. To solve the problem, we extend a bilevel method based on isoperimetric cut into multilevel thresholding. The extended method finds multiple thresholds by a fast and effective iterative scheme, simplifies computation of isoperimetric ratio, and introduces a way of automatically determining cluster number to adaptively choose reasonable threshold number. The new multilevel method can automatically determine threshold number, and its time complexity is independent of the threshold number. This makes our method avoid disadvantages of conventional multilevel thresholding ones, i.e., instability of segmentation performance and exponential growth of computational complexity with the increase of threshold number. Experimental results on a series of images show the effectiveness of our multilevel method.
(3) Image thresholding based on transition region is a newly developed image segmentation technique. As compared with non-transition region (i.e., object and background regions), transition region of an image has more frequent and stronger gray level changes. On the basis of the characteristic of transition region, a transition region extraction and thresholding method based on gray level difference is proposed in this paper. The proposed method uses absolute difference between a pixel's gray level and the gray level average of its local neighborhood window as a descriptor for depicting transition region. The above gray level difference is very rough, and can not reflect the detailed difference between the pixel and other pixels in its neighborhood. Hence we present a modified gray level difference as a new transition region descriptor. The descriptor uses the sum of absolute gray level difference between the pixel and each pixel in its neighborhood to characterize transition region. Experimental results on a variety of images show that the modified gray level difference is effective on transition region description. In addition, conventional transition region descriptors do not take frequency and degree of gray level changes into account simultaneously, and fail to depict transition region comprehensively. To solve the problem, we present a new descriptor integrating local complexity and local variance. It uses local complexity to reflect frequency of gray level changes in local neighborhood window, meanwhile utilizes local variance to degree of the changes. Then local complexity and local variance are combined as a new transition region descriptor after being normalized respectively. Experimental results on a variety of images including infrared and text ones show that the new descriptor can depict transition region more accurately, as compared with conventional ones. And the corresponding method extracts transition region more accurately, obtains better thresholding results, and has stronger noise immunity.
(4) Existing image thresholding methods based on transition region do not consider characteristics of human visual perception. An unsupervised transition region extraction and thresholding method is proposed to solve this problem. The proposed method first utilizes characteristics of human visual perception and statistical characteristics of an image to estimate gray level range of transition region for implementing image transformation in an unsupervised way, then uses local variance as descriptor to extract transition region, and finally obtains thresholding result. Experimental results on a variety of images including industrial nondestructive testing ones show that image transformation preserves gray level changes of transition region, meanwhile weakens gray level changes of non-transition region. This simplifies the original image, which should be helpful for subsequent transition region extraction. The new method obviously improves accuracy of transition region extraction, and obtains better sgemnetation results. In addition, we introduce the above image transformation into conventional thresholding, and present three unsupervised range-constrained thresholding methods. As compared with conventional approaches, range-constrained methods implement thresholding on the transformed image instead of the original one. This not only coincides with human visual perception, but also reduces search range of thresholds and saves computational time. The transformed image is simper than the original one, which should be helpful for subsequent image thresholding. Experimental results on a variety of images including nondestructive testing ones show that range-constrained methods have better segmentation quality, and segmentation speed is comparative with their counterparts.
引文
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