Active Contour Models综述：医学图像形状描述方法

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本文档是一篇关于"Active Contour Models (ACMs)"的综述文章，主要关注于图像分割中的轮廓描述方法，特别是针对医学图像的形状描述。标题"Active_Contour_Models(review)"明确了文章的核心内容，即对主动轮廓模型的理论背景、应用及其在医疗图像分析中的重要性进行深入探讨。首先，文章介绍了几个关键概念。"Scale Space"是处理图像尺度变化的一种工具，它有助于在不同尺度下提取物体边缘和特征，为ACMs提供了一个基础框架。ACMs本身则是动态模型，通过能量函数驱动，能够自动追踪图像中的对象轮廓，如蛇算法（snakes）就是一种广泛应用的ACM实例。接着，文章详细回顾了不同的形状描述方法。这些方法包括： 1. **链码**（ChainCodes）：用于编码二维空间中的线性路径，便于存储和比较形状的拓扑结构。 2. **签名**（Signatures）：通过组合局部特征来形成整体形状的标识符，可以抵抗噪声影响。 3. **弦**（Chords）：描述轮廓曲线上的点对之间的关系，可用于简单形状描述。 4. **多边形逼近和凸包**：将复杂形状近似为简单几何形状，方便分析。 5. **样条曲线**（Splines），包括B-Splines和Overhauser Splines，它们提供了光滑的形状表示，适用于描绘连续的轮廓。 6. **Medial Shape Representation**：基于图像内部结构来描述形状，强调中心区域的特性。形状的量化描述部分涵盖了面积、紧凑度、曲率、弯曲能量等基本特征，这些都是评估轮廓稳定性和匹配度的重要参数。此外，文章还讨论了**分形描述符**，如分形维数估计和分形签名，这些能捕捉形状的复杂性和自相似性。全球形状描述则涉及**傅立叶描述符**和**矩**，前者利用频率域特性来分析形状的周期性和细节，后者通过计算图像矩阵的统计属性来刻画形状。**Hough变换**作为一种全局搜索方法，也被用来检测和定位特定形状，尤其是在轮廓检测中很常见。这篇综述文档不仅概述了ACMs的基本原理和应用，还深入剖析了医学图像分析中常见的形状描述方法，为理解和设计更有效的轮廓分割算法提供了丰富的参考资源。

Chapter 1

Introduction

Magnetic resonance (MR) imaging has become an increasingly popularimage acquisitionmethod,

as it is able to produce very detailed cross-sectional images of the human body while being non-

ionizing and non-invasive. When visualized, the images are analyzed by clinicians and other ex-

perts with respect to certain complex relationships, such as deformations and distinguishing be-

tween normals and abnormals. In order to describe an image quantitatively, it is ﬁrst segmented

into its constituent parts. The extracted objects are then characterized and described in terms of

volumetric measurements and other shape descriptions. One major medical task is the quantiﬁca-

tion of deformations of the brain for special diseases such as epilepsy, schizophrenia or multiple

sclerosis. Thisinformationisusually obtainedmanually bythe analysisof the imagesat a computer

terminal. However, highdemand on expert time poses an urgent need to automaticallypost-process

the extremely large three-dimensional data sets and image-derived data and to extract inter- and

intra-observer independent and reproducible meaningful information. Post-processing should be

carefully designed and validated to enhance interpretative and decision-making processes in med-

ical applications in order to increase faithful extraction of both scientiﬁc and clinical information

contained in medical images.

Thispaper presents a hierarchical approachfor shape descriptionof MR images of the humanbrain,

combining two recently developed and powerful techniques in image processing: differential in-

variants in scale space, and active contour models.

1.1 Scale Space

Over the last few years, multiscale approaches in image analysis have proved to be useful in terms

of describing images at varying levels of resolution. The fundamental concept of multiscale image

processing was developed by Marr [63] as a concept in human vision, with extensions by Witkin

[108] in terms of scale space. The underlying image can be represented by a family of images on

variouslevels of innerspatial scale. These are obtained by convolutionwith the Gaussian kernel as

the lowest order, rescaling operator, and its linear partial derivatives. A continuous scale space is

constructed to enable local image analysis in a robust way, while at the same time global features

are captured through the extra scale degree of freedom. Each pixel in the original image can be

tracked through an iso-intensity extremal path along increasing



in a manner thought to emulate

the multi-resolutionmechanism in the human eye (see Lifshitz and Pizer [58], Simmons et al. [93]

12 Chapter 1. Introduction

and Gerig et al. [38]). An improved descriptionuses higher ordermultiscale differential invariants,

as presented by Romeny et al. [96, 97], which aretrue image descriptorsthat resemble the receptive

ﬁeld proﬁles in the human front-end visual system and are invariant with respect to the chosen

coordinatesystem and lineartransformationsof the image intensity. Forexample, convolutionwith

the Laplacian-of-Gaussian implements the well-known Marr-Hildreth operator [64] at a range of

scales forming the basis for edge-focusing.

1.2 Active Contour Models

Active contours or snakes were ﬁrst introduced by Kass et al. [52, 51, 98]. They are a segmentation

tool based on minimizingthe energy of a continuoussplinecontoursubjectto constraintsonboth its

autonomous shape and external forces derived from a superposedimage that pull the active contour

toward image features such as lines and edges. The contour is initially placed near an edge under

consideration, then image forces and user-deﬁned external constraints draw the contour towards

image features. During the following optimization process, the active contour is deformed with

respect to the features to be localized. There are several optimization approaches for active contour

models, including a variational approach by Kass et al. [52], dynamic programming by Amini [1],

the greedy algorithm by Williams and Shah [107], genetic algorithms by Cootes et al. [28], and

stochastic relaxation techniques by Rueckert [86, 85].

1.3 Contributions of this Work

Classic curvature-minimizing active contour models are often incapable of extracting complex

shapes with points of high curvature. This paper presents a new active contour model which over-

comes this problem and which can be applied to image segmentation as well as shape description

in order to allow for quantitative and qualitative studies of shape measurements at multiple scales.

Scale space continuation in active contour models provides the ability to capture image features at

the adequate scale. Multiscale differential operators are integrated into the model’s energy func-

tional. Whereas the image intensity gradient attracts the spline contour to image features, the

isophote curvature of the image intensity function is used for matching the contour curvature. This

novel curvature matching approach appears to be very useful for the extraction of very complex

and strongly curved objects such as brain contours.

Using an initial active contour model, several implicit optimization processes with differently reg-

ularized energy functions with respect to scale areperformed. The results are formulated in a multi-

scale hierarchy and are qualitatively and quantitatively evaluated with respect to the rate of change

of the model’s shape in scale space.

1.4 Overview



Chapter 2 presents several classic shape representation and description techniques. Three

main shape description types are discussed: simple local techniques, global methods (e.g.

Fourier series), and distance transforms for inter-shape comparisons.



Chapter3 gives an overviewovermultiscaleimage processingtechniquesin terms of contour

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Active Contour Models综述：医学图像形状描述方法

active_contour_splitBregman.zip_active contour_主动轮廓模型_图像分割_水平集 分

active_contour_toolbox.zip_2D contour_active_active contour_cont

Snakes_Active_Contour_models_Image_Process_GVF

active_contour_usage.rar_contour_主动轮廓_主动轮廓模型_蛇 matlab_蛇模型

Geodesic_Active_Contour_gac_

AMT.zip_AMT_active contour_contour matlab_contour matlab code

snake_test.rar_2D contour_Snakes _active contour_contour

P091Geodesic_Active_Contour.rar_matlab测地线_主动轮廓模型_测地线_测地线 matlab

snk.rar_active contour_contour image

activeContour_WithoutEdges.rar_active contour_contour detection

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