【作者】 叶伟；

【导师】 宋志坚；

【作者基本信息】 复旦大学 ， 生物医学工程， 2009， 硕士

【摘要】 图像分割是将图像按性质划分为相似的区域,并且从中提取出感兴趣的区域用于后期操作的过程,图像分割方法有应用于轮廓提取的二项分割方法以及全局划分的多相分割方法。在过去20年的发展中,出现了很多有效的二相分割方法,其发展较为成熟;而起步较晚的多相图像分割方法是当前国内外研究的热点之一。本文的研究主要集中于水平集方法、Mumford-Shah模型及最小生成树(简称MST)分割方法这些可以用于多相分割的方法中。水平集方法使用高维上的零集作为活动轮廓,改变水平集函数的取值使轮廓移动,其轮廓可自动分裂及合并,具备良好的拓扑性。使用多个水平集函数的变分水平集方法是其在多相分割中的应用。Mumford-Shah模型是应用于多相分割的区域划分准则,该模型分析了图像中边缘的成因。Chan-Vese方法(简称CV方法)是使用水平集函数对Mumford-Shah模型的一种简化,适用于二相分割。MCV方法及多层水平集方法是CV方法在多相分割中的应用。基于图论中MST的FH方法,在MST的计算中引入了区域面积,调节区域间合并的难易,该方法能有效去除噪声的影响,并具有很好的计算速度。这些多相分割方法中,基于水平集及Mumford-Shah的分割方法均需要较为复杂的数值过程,其计算时间会随着相位的增多而急剧增加,在处理较多聚类时会非常耗时,难以达到实时应用。而基于图论中MST的分割方法虽然具有较好的分割速度,但是其结果较为粗糙、冗杂,并且往往存在不合理的狭长区域及杂乱区域。我们的研究从基于MST的FH方法出发,结合Mumford-Shah模型中对于图像中区域及边缘的认识,改进FH方法。我们通过考虑图像中区域间的结合程度以及各区域的几何性质,计算区域间基于结合度的权值并将之加入到最小生成树图像分割方法的区域合并判断公式中,改进了其合并判断的量度。新的合并公式可以使相互结合较好的区域更易于合并,使得边缘较简单的区域保留下来。相关实验显示了我们的方法能够有效地去除MST方法中普遍存在的狭长区域及杂乱区域,并得到平滑连续的区域边缘。我们的方法得到的区域划分更加符合现实三维空间中的各个物体。在文章的结尾处,对各种分割方法的优缺点及存在的问题做了讨论,并展望了未来的发展方向。更多还原

【Abstract】 The technology of Image Segmentation aims on partition regions on their property, extract interested objects from the image and for post processing using. The Image Segmentation methods include 2-phase segmentation methods used in extracting contours and multiphase segmentation methods used in region partition. With the development in the past 20 years, many effective 2-phase segmentation methods were published and most of them are mature. But the methods used in multiphase segmentation were start later and this research area is one of the hot issues in the fields of image processing now. This dissertation presented some studies concentrated in these topics: the level set method, the Mumford-Shah model, the minimum spanning tree (MST) based segmentation method. All these methods can be used in multiphase segmentation.The level set method use the 0 level sets in the high dimension as the active contour and move the contour by resetting the value of the level set function. The level set method is a topology free method whose contour can split and merge automatically. The variational level set method is a multiphase level set segmentation method. The Mumford-Shah model is a multiphase segmentation based region partition criterion, the model discussed the formation of edge in the image. The Chan-Vese method (CV method) use the level set function to simplify the Mumford-Shah model and can be used in the 2-phase segmentation. MCV method and multilayer level set method are based on CV method and used in multiphase segmentation. The MST based FH method put the area of the region as a factor into merging criteria and use the factor to control the difficulty of regions’ merging. The method can be used in noised image and have fast computing speed.Among these multiphase segmentation methods, the level set based methods and Mumford-Shah based methods always have complex numerical computation step and their computing time will increase sharply with the augment of phases’ amount, these methods are very time-consuming while dealing with a big amount of clustering, they can not be used in real-time segmentation. The MST based segmentation methods have good computing speed, but the results are coarse and have complex structure, further more, long-and-narrow regions and tanglesome regions are often exist in the results.Our research started with the MST based FH methods, use the knowledge of region and edge from the Mumford-Shah model to improve the FH method. We take a good consideration about the connectivity of neighboring regions and the geometric properties of each region, by computing weights between regions according to them and adding the weights into the region merging criteria. The improved criteria can make the regions with higher connectivity combine easier, reserve the regions with simply contours in the result. The experiments show our method can eliminate the long-and-narrow regions and tanglesome regions which are ubiquitous in the previous MST based methods, and the contours of our results are simple and smooth. The partition of our method is closer to the real objects in the 3 dimension space.In the end of this paper, we also discussed these segmentation methods’ properties and problems, gave the long-term outlook for Image Segmentation.更多还原