Duquesne K, Nauwelaers N, Claes P, Audenaert E A
Department Human Structure and Repair, University Ghent, Corneel Heymanslaan 10, Ghent 9000, Belgium; Department Orthopaedic Surgery and Traumatology, Ghent University Hospital, Corneel Heymanslaan 10, Ghent B-9000, Belgium.
Medical Imaging Research Center, MIRC, University Hospitals Leuven, Herestraat 49 - 7003, Leuven 3000, Belgium; Department of Electrical Engineering, ESAT/PSI, KU Leuven, Kasteelpark Arenberg 10 - box 2441, Leuven 3001, Belgium.
Comput Methods Programs Biomed. 2022 Jun;220:106812. doi: 10.1016/j.cmpb.2022.106812. Epub 2022 Apr 12.
The most widespread statistical modeling technique is based on Principal Component Analysis (PCA). Although this approach has several appealing features, it remains hampered by its linearity. Principal Polynomial Analysis (PPA) can capture non-linearity in a sequential algorithm, while maintaining the interesting properties of PCA. PPA is, however, computationally expensive in handling shape surface data. To this end, we propose Principal Polynomial Shape Analysis (PPSA) as an adjusted approach for non-linear shape analyzes. The aim of this study was to assess PPSA's features, its model boundaries and its general applicability.
PCA and PPSA-based shape models were investigated on one verification and three model evaluation experiments. In the verification experiment, the estimated mean of the PCA and PPSA model on a data set of synthetic lower limbs of different lengths in different poses were compared to the real mean. Further, the PCA-based and PPSA shape models were tested for three challenging cases namely for shape model creation of gait marker data, for regression analysis on aging faces and for modeling pose variation in full body scans. For the latter, additionally a Fundamental Coordinate Model (FCM) and a PPSA model on Fundamental Coordinate(FC) space was created. The performances were evaluated based on model-based accuracy, generalization, compactness and specificity.
In the verification experiment, the scaling error reduced from 75% to below 1% when employing PPSA instead of PCA for a training set with 180° angular variation. For the model evaluation experiments, the PPSA models described the data as accurate and generalized as the PCA-based shape models. The PPSA models were slightly more compact and specific (up to 30%) than the PCA-based models. In regression, PCA and PPSA-based parameterizations explained a similar amount of variation. Lastly, for the full body scans, applying PPSA to parameterizations improved the compactness and accuracy.
PPSA describes the non-linear relationships between principal variations in a parameterized space. Compared to standard PCA-based shape models, capturing the non-linearity reduced the nonsense information in the shape components and improved the description of the data mean.
最广泛应用的统计建模技术基于主成分分析（PCA）。尽管这种方法有几个吸引人的特点，但它仍然受限于其线性特性。主多项式分析（PPA）可以在一个顺序算法中捕捉非线性，同时保持PCA的有趣特性。然而，PPA在处理形状表面数据时计算成本很高。为此，我们提出主多项式形状分析（PPSA）作为一种用于非线性形状分析的调整方法。本研究的目的是评估PPSA的特征、其模型边界及其一般适用性。
在一个验证实验和三个模型评估实验中研究了基于PCA和PPSA的形状模型。在验证实验中，将不同姿势下不同长度的合成下肢数据集上PCA和PPSA模型的估计均值与真实均值进行比较。此外，针对三个具有挑战性的案例测试了基于PCA和PPSA的形状模型，即步态标记数据的形状模型创建、衰老面部的回归分析以及全身扫描中的姿势变化建模。对于后者，还在基本坐标（FC）空间中创建了一个基本坐标模型（FCM）和一个PPSA模型。基于基于模型的准确性、泛化性、紧凑性和特异性对性能进行评估。
在验证实验中，对于具有180°角度变化的训练集，采用PPSA而非PCA时，缩放误差从75%降至1%以下。对于模型评估实验，PPSA模型对数据的描述与基于PCA的形状模型一样准确且具有泛化性。PPSA模型比基于PCA的模型稍微更紧凑且更具特异性（高达30%）。在回归分析中，基于PCA和PPSA的参数化解释的变异量相似。最后，对于全身扫描，将PPSA应用于参数化提高了紧凑性和准确性。
PPSA描述了参数化空间中主变化之间的非线性关系。与基于标准PCA的形状模型相比，可以捕捉非线性减少了形状成分中的无意义信息并改善了数据均值的描述。
