闭合轮廓建模的傅里叶-香农方法

Claudia Bonciu, Christophe Léger, Jacques Thiel
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引用次数: 16

摘要

本文描述了一种连续闭合轮廓的建模方法。初始输入数据集由二维(2-D)点组成,这些点可以在极坐标系中表示为离散函数。该方法利用这些数据点之间的Shannon插值得到全局连续轮廓模型。利用Shannon插值核与周期函数的傅里叶级数极坐标展开(FSPD)之间的联系,得到了轮廓的最小描述。香农插值核允许在样本和傅立叶频域上直接解释轮廓平滑。针对主动建模技术中经常遇到的变形点源问题,提出了一种局部变形方法。每个局部变形在以变形点源为中心的角扇形中进行。所有邻近的特征样本都被置换,以尽量减少变形扇区外新创建模型的振荡。无论变形源的数量和强度如何,这种变形技术都保持了轮廓的频率特征。通过这种方式,该技术诱导了频率建模约束,可以随后在主动检测和建模环境中使用。综合数据和实际数据的实验证明了该方法的有效性。该方法目前用于从超声心尖图像中获得心脏左心室的轮廓模型。这项工作是一个更大项目的一部分,其目的是分析左心室的空间和时间变形。二维傅里叶-香农模型被用作更复杂的三维和四维傅里叶模型的基础,能够自动恢复心脏左心室在心脏周期中的运动和变形。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Fourier–Shannon approach to closed contours modelling

This paper describes a modelling method for continuous closed contours. The initial input data set consists of two-dimensional (2-D) points, which may be represented as a discrete function in a polar coordinate system. The method uses the Shannon interpolation between these data points to obtain the global continuous contour model. A minimal description of the contour is obtained using the link between the Shannon interpolation kernel and the Fourier series of polar development (FSPD) for periodic functions. The Shannon interpolation kernel allows the direct interpretation of the contour smoothness in terms of both samples and Fourier frequency domains.

In order to deal with deformation point sources, often encountered in active modelling techniques, a method of local deformation is proposed. Each local deformation is performed in an angular sector centred on the deformation point source. All the neighbouring characteristic samples are displaced in order to minimize the oscillations of the newly created model outside the deformation sector. This deformation technique preserves the frequency characteristics of the contour, regardless of the number and the intensity of deformation sources. In this way, the technique induces a frequency modelling constraint, which may be subsequently used in an active detection and modelling environment.

Experiments on synthetic and real data prove the efficiency of the proposed technique. The method is currently used to model contours of the left ventricle of the heart obtained from ultrasound apical images. This work is part of a larger project, the aim of which is to analyse the space and time deformations of the left ventricle. The 2-D Fourier–Shannon model is used as a basis for more complex three-dimensional and four-dimensional Fourier models, able to recover automatically the movement and deformation of the left ventricle of the heart during a cardiac cycle.

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