This paper presents a novel method for handling the effects of shape outliers in statistical shape analysis. Usually performed by a variant of classical principal component analysis (PCA), variability analysis may be highly affected by erroneous shapes. Principal components may thus imply aberrant modes, while eigenshapes may not accurately describe variability in a given set of shapes. Our robust analysis is performed using an elastic metric associated with the square-root velocity representation of shapes. This elastic shape analysis allows shape variability to be described with natural and intuitive deformations. The proposed method based on shape outlier detection applies the shape restoration procedure to rectify aberrant shapes. The resultant components are thus obtained from a tangent PCA on the restored database. By performing experiments based on MPEG-7 and HAND databases, we demonstrate that the proposed scheme is effective for shape variability analysis in the presence of outlying shapes. Our method is then compared with two existing schemes for robust data variability analysis: minimum covariance determinant-based PCA and projection pursuit-based PCA.

中文翻译：

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通过形状恢复实现可靠的正切PCA，用于形状变异性分析

本文提出了一种在统计形状分析中处理形状异常值影响的新方法。通常，通过经典主成分分析（PCA）的变体执行变异性分析，而形状可能会受到很大的影响。主成分可能因此暗示异常模式，而本征形状可能无法准确描述给定形状集合中的可变性。我们的稳健分析是使用与形状的平方根速度表示关联的弹性度量执行的。通过这种弹性形状分析，可以通过自然直观的变形来描述形状变化。所提出的基于形状离群值检测的方法应用形状恢复程序来纠正异常形状。因此，从还原的数据库上的切线PCA获得了所得的组件。通过执行基于MPEG-7和HAND数据库的实验，我们证明了所提出的方案对于存在异常形状的形状变异性分析是有效的。然后将我们的方法与用于鲁棒数据可变性分析的两种现有方案进行比较：基于最小协方差行列式的PCA和基于投影追踪的PCA。