A Kernelized Multi-level Localization Method for Flexible Shape Modeling with Few Training Data

Statistical shape models (SSMs) are a standard generative shape modeling technique and they are still successfully employed in modern deep learning-based solutions for data augmentation purposes or as shape priors. However, with few training samples they often fail to represent local shape variations. Recently, a new state-of-the-art method has been proposed to alleviate this problem via a multi-level model localization scheme using distance-based covariance manipulations and Grassmannian-based level fusion during model training. This method significantly improves a SSMs performance, but heavily relies on costly eigendecompositions of large covariance matrices. In this paper, we derive a novel computationally-efficient formulation of the original method using ideas from kernel theory and randomized eigendecomposition. The proposed extension leads to a multi-level localization method for large-scale shape modeling problems that preserves the key characteristics of the original method while also improving its performance. Furthermore, our extensive evaluation on two publicly available data sets reveals the benefits of Grassmannian-based level fusion in contrast to a method derived from the popular Gaussian Process Morphable Models framework.