Mei Lin, Figl Michael, Rueckert Daniel, Darzi Ara, Edwards Philip
Dept. of Biosurgery and Surgical Technology Imperial College London, UK.
Med Image Comput Comput Assist Interv. 2008;11(Pt 1):425-33. doi: 10.1007/978-3-540-85988-8_51.
Statistical shape modelling is a popular technique in medical imaging, but the issue of sample size sufficiency is not generally considered. Also the number of principal modes retained is often chosen simply to cover a percentage of the total variance. We show that these simple rules are unreliable. We propose a new method that uses bootstrap replication and a t-test comparison with noise to decide whether each mode direction has stabilised. We establish mode correspondence by minimising the distance between the space spanned by the replicates and their mean. By retaining only stable modes, our method distinguishes real anatomical variation from modes dominated by random noise. This provides a lower stopping rule when the sample is small and converges as the sample size increases. We use this convergence to determine sample sufficiency. For validation we use synthetic datasets of the left ventricle generated with a known number of structural modes and added noise. Our stopping rule detected the correct number of modes to retain where other methods failed. The methods were also tested on real 2D (22 points) and 3D (500 points) face data, retaining 24 and 70 modes with sample sufficiency being reached at approximately 50 and 150 samples respectively. For a 3D database of the left ventricle (527 points), 319 samples are not sufficient, but at this level we can retain around 55 stable modes. Our method provides a principled foundation for appropriate selection of the number of modes to retain and determination of sample size sufficiency for statistical shape modelling.
统计形状建模是医学成像中的一种常用技术，但样本量充足性问题通常未被考虑。此外，保留的主模式数量通常只是简单地选择以覆盖总方差的一定百分比。我们表明这些简单规则并不可靠。我们提出了一种新方法，该方法使用自助重复抽样和与噪声的t检验比较来确定每个模式方向是否已稳定。我们通过最小化重复抽样所跨越的空间与其均值之间的距离来建立模式对应关系。通过仅保留稳定模式，我们的方法将真实的解剖变异与由随机噪声主导的模式区分开来。当样本量较小时，这提供了一个更低的停止规则，并随着样本量的增加而收敛。我们利用这种收敛来确定样本充足性。为了进行验证，我们使用了具有已知数量结构模式并添加了噪声的左心室合成数据集。我们的停止规则在其他方法失败的情况下检测到了要保留的正确模式数量。这些方法还在真实的2D（22个点）和3D（500个点）面部数据上进行了测试，分别保留了24个和70个模式，样本充足性分别在大约50个和150个样本时达到。对于左心室的3D数据库（527个点），319个样本是不够的，但在这个水平上我们可以保留大约55个稳定模式。我们的方法为合理选择要保留的模式数量以及确定统计形状建模的样本量充足性提供了一个有原则的基础。
