Fidler Sanja, Skocaj Danijel, Leonardis Ales
Faculty of Computer and Information Science, University of Ljubljana, Slovenia.
IEEE Trans Pattern Anal Mach Intell. 2006 Mar;28(3):337-50. doi: 10.1109/TPAMI.2006.46.
Linear subspace methods that provide sufficient reconstruction of the data, such as PCA, offer an efficient way of dealing with missing pixels, outliers, and occlusions that often appear in the visual data. Discriminative methods, such as LDA, which, on the other hand, are better suited for classification tasks, are highly sensitive to corrupted data. We present a theoretical framework for achieving the best of both types of methods: An approach that combines the discrimination power of discriminative methods with the reconstruction property of reconstructive methods which enables one to work on subsets of pixels in images to efficiently detect and reject the outliers. The proposed approach is therefore capable of robust classification with a high-breakdown point. We also show that subspace methods, such as CCA, which are used for solving regression tasks, can be treated in a similar manner. The theoretical results are demonstrated on several computer vision tasks showing that the proposed approach significantly outperforms the standard discriminative methods in the case of missing pixels and images containing occlusions and outliers.
线性子空间方法，如主成分分析（PCA），能够对数据进行充分重构，为处理视觉数据中经常出现的缺失像素、异常值和遮挡提供了一种有效方式。另一方面，判别方法，如线性判别分析（LDA），更适合分类任务，但对损坏的数据高度敏感。我们提出了一个理论框架，以实现这两种方法的优势：一种将判别方法的判别能力与重构方法的重构特性相结合的方法，它能够处理图像中的像素子集，从而有效地检测和排除异常值。因此，所提出的方法能够以高崩溃点进行稳健分类。我们还表明，用于解决回归任务的子空间方法，如典型相关分析（CCA），也可以以类似的方式处理。在几个计算机视觉任务上展示了理论结果，表明在所提出的方法在处理缺失像素以及包含遮挡和异常值的图像时，显著优于标准判别方法。
