Patch-Based Low-Rank Matrix Completion for Learning of Shape and Motion Models from Few Training Samples
Statistical models have opened up new possibilities for the automated analysis of images. However, the limited availability of representative training data, e.g. segmented images, leads to a bottleneck for the application of statistical models in practice
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Abstract. Statistical models have opened up new possibilities for the automated analysis of images. However, the limited availability of representative training data, e.g. segmented images, leads to a bottleneck for the application of statistical models in practice. In this paper, we propose a novel patch-based technique that enables to learn representative statistical models of shape, appearance, or motion with a high grade of detail from a small number of observed training samples using lowrank matrix completion methods. Our method relies on the assumption that local variations have limited effects in distant areas. We evaluate our approach on three exemplary applications: (1) 2D shape modeling of faces, (2) 3D modeling of human lung shapes, and (3) population-based modeling of respiratory organ deformation. A comparison with the classical PCA-based modeling approach and FEM-PCA shows an improved generalization ability for small training sets indicating the improved flexibility of the model. Keywords: Statistical modeling · High-dimension-low-sample-size problem · Low-rank matrix completion · Virtual samples
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Introduction
Statistical models play an important role in several tasks in computer vision and image analysis, such as image segmentation and object classification. These models aim to represent properties like shape or intensity of a class of objects based on a population of observed instances. However, collecting an adequately large and representative training population is often laborious and challenging, particularly if dimensionality and complexity of the observed objects increase. Therefore, many applications suffer from the high-dimension-low-sample-size (HDLSS) problem. In the application of statistical shape models (SSMs) [7] or eigenfaces (eigenimages) [27] for segmentation or recognition tasks, a small sample size results in a limited flexibility of the model and details can not be represented adequately (see Fig. 1). This paper proposes a method for statistical shape, appearance, and motion modeling with increased ability to adapt to local details, thus, increasing the c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part IV, LNCS 9908, pp. 712–727, 2016. DOI: 10.1007/978-3-319-46493-0 43
Patch-Based Low-Rank Matrix Completion for Learning of Shape Models
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Fig. 1. Example application of the patch-based modeling approach using only two training shapes: classical models only learn the global transition between the two shapes. The patch-based model combines local shape details, and can adapt to test shapes showing local properties of both shapes.
flexibility of models generated from few training samples. The method is based on the assumption of locality, i.e. we assume that local variations in shape, intensity, or motion have limited effects in distant areas. This allows the model to combine local variations observed in different training samples while preserving overall object properties, i.e. generating valid instances. During the learning phase, the objects are p
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