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基于变分的主动轮廓图像分割方法
Alternative TitleVariational Active Contours for Image Segmentation
李小毛1,2
Department机器人学研究室
Thesis Advisor唐延东
ClassificationTP391.4
Keyword主动轮廓 Mumford-shah 模型 形状约束 梯度流 水平集
Call NumberTP391.4/L35/2008
Pages105页
Degree Discipline模式识别与智能系统
Degree Name博士
2008-05-30
Degree Grantor中国科学院沈阳自动化研究所
Place of Conferral沈阳
Abstract图像分割是图像处理中很重要的一个问题,是计算机视觉的基础。因为它能够简化信息的存储和表示,从而能够对获取的图像内容进行智能解释,所以在很多应用问题中,图像分割是必不可少的过程,如医学图像处理,环境三维重建及自动目标识别等。图像分割的方法有很多种,如边缘检测,阈值,区域融合,分水岭及马尔可夫随机场等。虽然这些方法有其各自特点,但是它们在图象分割过程中不能充分将图像底层信息与高层信息结合,从而无法模拟人类视觉系统智能性。当图像底层信息不足时,这些仅基于数据驱动的分割模型无法达到令人满意的结果。尽管某种具体图像分割方法不可能满足所有图像分割要求,但利用尽可能多的高层与底层信息,将图像分割成有意义和人们所期望的区域始终是研究者所追求的目标。图像分割问题的数学建模和计算中有两个关键因素。第一是建立合适的分割模型将分割边界和分割区域的作用有效结合。第二是利用最有效的方法将分割边界和分割区域的几何特征统一到分割模型中。基于变分原理的主动轮廓图像分割将图像视为连续函数。这就使得研究者可以从连续函数空间角度来研究图像分割问题。这同时也为研究者提供严格的数学工具,如微分几何、泛函分析和微分方程等。为此它能很好的解决上述两个问题。第一,Mumford-Shah(M-S)模型为基于变分的主动轮廓分割模型提供了一完整的数学理论框架,并且Mumford-Shah模型从信息论的角度也能得到合理解释。第二,水平集方法能有效的表示分割边界和分割区域的几何特征。与其它方法相比,变分主动轮廓在理论和实际计算过程中都具有显著的优势。首先它能直接处理和表示各种重要的几何特征,如梯度、切向量、曲率等,并且能有效模拟很多动态过程,如线性和非线性扩散等。再则其可以利用很多已有的丰富数值方法进行分析和计算。本文基于变分原理与偏微分方程方法,利用主动轮廓模型具有结合底层图像信息与高层先验知识的特点,将特定先验知识与主动轮廓分割模型进行有效结合以弥补底层图像信息的不足,从而使主动轮分割廓模型具有更强的智能性。本文主要从两点对变分主动轮廓分割模型展开了研究:1、演化轮廓的形状约束;2、演化轮廓的梯度下降流约束及其滤波实现。其主要工作包括以下四个方面的内容:第一,基于M-S模型和样条曲线的开边界检测。本章通过对演化轮廓引入合理边界条件,利用样条曲线表示待检测的开曲线,将一般开曲线的检测问题变为合理的图像分割问题,从而达到一般开曲线检测目的。此方法称为开扩散蛇模型。一般开曲线的检测具有很多应用领域,如:河流、道路、天际线、焊缝等检测。第二,方差主动轮廓模型。在目标跟踪应用中,跟踪目标的主要运动形式表现为平移。本章将此作为一种先验知识与主动轮廓模型结合,提出了一种方差主动轮廓模型(HV)。此模型的特点是轮廓在演化过程中具有平移优先和快速的良好特性。它比已有的主动轮廓模型更适于自动目标跟踪领域。第三,基于M-S模型和隐式曲面变分方法的一般梯度下降流滤波器。本章为一般梯度下降流求取提供了统一框架及解决方法。首先本章将H0梯度下降流和一般梯度下降流统一到Mumford-Shah模型框架中,从而将一般梯度下降流的求取转换为一个极小化泛函问题,并利用隐式曲面变分方法对此极小化泛函进行求解。另外本章从滤波器设计角度出发,通过对H0梯度下降流滤波可以得到一般梯度下降流。滤波器的实现体现了内嵌于一般梯度下降流的先验属性。根据此思想,本章将对应于HV和H1主动轮廓的內积空间顺序组合,对H0梯度下降流进行顺序滤波,提出了一种既具有全局平移优先性又具有局部光滑速度场的主动轮廓,称为HV1主动轮廓。它将H0,H1和HV主动轮廓统一起来。第四,形状保持主动轮廓模型及其应用。针对某些特定目标的检测,本章提出了形状保持主动轮廓模型。此模型能够达到分割即目标的目的,同时能够给出目标的定量描述。基于此模型,本章实现了具有椭圆、直线和平行四边形轮廓特征目标的检测。椭圆形状约束用于眼底图像分割。直线和平行四边行分别用于自动目标识别中的天际线检测和机场跑道跟踪。
Other AbstractImage segmentation is an fundamental problem of image processing and computer vision. For it can simplify the expression and storage of acquired images and makes possible the intelligent intrepretation of image contents, it is a necessary procedure for many applications, such as medical image processing, 3D reconstruction of environment and automatic target recognition. There have been many methods for image segmentation, such as edge detection, thresholding, region growing, watershed and markov random field. Although each method possesses its features, they can't fully combine low-level information with high-level information for image segmentation. Thus, they can not model the intelligence of human visual system. When the information of images is not sufficient or misleading, thses data driven segmentation methods can't obtain satisified results. Although it is impossible that a specified segmentation method is adopted for all image segmentation, image segmentation should utilize low-level and high-level information as much as possible to segment a given image into several desired and meaningful parts. This is the goal of many researchers. There are two key elements in the matematical modeling and computation of image segmentation problems. The first one is to formulate a model that appropritely combines the effects of both the edge set and its segmented regions. The other one is to find the efficient way to represent the geometric features of both the edge set and the regions in a segmentation model. The method of variational active contours for image segmentation takes images as a continuous function. Thus, image segmentation problems can be studied from the point of continuous function sapce and accounted for many existed strict mathematical tools, such as differential gometry, functional analysis and partial differential equations. Variational active contours can account for the two elements mentioned above very well. Firstly, The Mumford-Shah(M-S) model provides a whole framework of mathematical theory. We can also give a reasonable intepretation for M-S model from the point of information theory. Secondly, the level set mehtod can represent the geometry of both the edge set and its segmented regions effectively. Compared with other approaches, the method of variational active contours has remarkable advantages in both theory and computation. Firstly, It allows to directly express and handle important geometric features, such as gradients, tangents and curvatures. It can also simulate many dynamic processes, such as linear and nonlinear diffusions. Secondly, in terms of computation, it can benefit from the existing wealthy numerical method for analysis and computation. Based on variational principle and partial differential equation methods and according to the feature of combining low-level information with high-level prior knowledge of active contours, in the thesis, specified prior knowledge is combined with active contour models effectively to cover the insufficient or misleading low-level information of acquired images. This entitles the active contours more intelligence. In the thesis the main research on variational active contours includes: 1. shape restraint for evolving active contours, 2. the restraint for the gradient descent flow of evolving active contours and the filter implementation of the gradient descent flow. The main contents and contributions are summarized as follows. 1. Open boundary detection using B-Spline Curve based on M-S model. Based on M-S model, the open boundary detection, represented by B-Spline curve, becomes a minimal partition problem by introducing two constraint equations for the open evolving curve. The method is called open diffusion snake. It has many applications, such as the detection of road, river, skyline and welding line. 2. Variance active contour. The major motion of tracked objects is translation for many automatic object tracking applications. According to this prior knowledge, a new active contour called variance active contour (denoted by HV) is proposed. It prefers translation when the curve evolves and can be implemented easily and fastly. Thus it is very suitable for automatic object tracking. 3. Filtering for generalized gradient descent flows based on M-S model and variational method on implicit surfaces. In this section, a whole framework and its implementation for general gradient descent flows are proposed. Firstly, the relation between the H0 gradient descent flow and general gradient flows is integrated into the M-S framework. Thus, the acquisition of general gradient descent flows becomes a minimal functional problem which is intrinsically solved using variational method on implicit surfaces. In addition, from the point of filter design, general gradient descent flows can be obtained by filtering the H0 gradient descent flow. The implementation of filter embodies the prior information of general gradient descent flows. According to this idea, a new active contour called HV1 active contour is proposed, integrating the H0, H1 and HV active contours. It possesses the properties of global transformation and local smooth velocity fields by sequentially combining the inner products relative to HV and H1 active contours to filter the H0 gradient descent flow. 4. Shape preserving active contour and its application. This section proposes the shape preserving active contour model for specified objects detection. It can detect the given object correctly and characterize the object shape quantificationally via its shape parameters simultaneously. According to shape preserving active contour, the automatic detection for the objects with elliptic shape, beeline and parallelogram boundary are realized. The elliptic shape restraint is used to papilla segmentation. Beeline and parallelogram are applied to skyline detection for automatic target recognition and runway tracking respectively.
Language中文
Contribution Rank1
Document Type学位论文
Identifierhttp://ir.sia.cn/handle/173321/422
Collection机器人学研究室
Affiliation1.中国科学院沈阳自动化研究所
2.中国科学院研究生院
Recommended Citation
GB/T 7714
李小毛. 基于变分的主动轮廓图像分割方法[D]. 沈阳. 中国科学院沈阳自动化研究所,2008.
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