IEEE Trans Pattern Anal Mach Intell. 2018 Nov;40(11):2668-2681. doi: 10.1109/TPAMI.2017.2784421. Epub 2017 Dec 18.
A set of images depicting faces with different expressions or in various ages consists of components that are shared across all images (i.e., joint components) imparting to the depicted object the properties of human faces as well as individual components that are related to different expressions or age groups. Discovering the common (joint) and individual components in facial images is crucial for applications such as facial expression transfer and age progression. The problem is rather challenging when dealing with images captured in unconstrained conditions in the presence of sparse non-Gaussian errors of large magnitude (i.e., sparse gross errors or outliers) and contain missing data. In this paper, we investigate the use of a method recently introduced in statistics, the so-called Joint and Individual Variance Explained (JIVE) method, for the robust recovery of joint and individual components in visual facial data consisting of an arbitrary number of views. Since the JIVE is not robust to sparse gross errors, we propose alternatives, which are (1) robust to sparse gross, non-Gaussian noise, (2) able to automatically find the individual components rank, and (3) can handle missing data. We demonstrate the effectiveness of the proposed methods to several computer vision applications, namely facial expression synthesis and 2D and 3D face age progression 'in-the-wild'.
一组描绘不同表情或不同年龄段人脸的图像包含跨所有图像共享的成分（即联合成分），这些成分赋予所描绘对象人脸的属性以及与不同表情或年龄组相关的个体成分。发现人脸图像中的共同（联合）和个体成分对于面部表情转移和年龄增长等应用至关重要。当处理在存在大量稀疏非高斯误差（即稀疏总误差或异常值）和缺失数据的非约束条件下捕获的图像时，问题相当具有挑战性。在本文中，我们研究了最近在统计学中引入的一种方法，即所谓的 Joint and Individual Variance Explained (JIVE) 方法，用于稳健恢复由任意数量视图组成的视觉人脸数据中的联合和个体成分。由于 JIVE 对稀疏总误差不稳健，我们提出了一些替代方法，这些方法：1. 对稀疏总误差、非高斯噪声具有鲁棒性；2. 能够自动找到个体成分的秩；3. 能够处理缺失数据。我们展示了所提出的方法在几个计算机视觉应用中的有效性，即面部表情合成以及 2D 和 3D 人脸年龄增长“野外”。
