Nishino Ko, Nayar Shree K, Jebara Tony
Department of Computer Science, Columbia University, MC 0401, 1214 Amsterdam Avenue, New York, NY 10027, USA.
IEEE Trans Pattern Anal Mach Intell. 2005 Oct;27(10):1675-9. doi: 10.1109/TPAMI.2005.193.
Principal Component Analysis (PCA) is extensively used in computer vision and image processing. Since it provides the optimal linear subspace in a least-square sense, it has been used for dimensionality reduction and subspace analysis in various domains. However, its scalability is very limited because of its inherent computational complexity. We introduce a new framework for applying PCA to visual data which takes advantage of the spatio-temporal correlation and localized frequency variations that are typically found in such data. Instead of applying PCA to the whole volume of data (complete set of images), we partition the volume into a set of blocks and apply PCA to each block. Then, we group the subspaces corresponding to the blocks and merge them together. As a result, we not only achieve greater efficiency in the resulting representation of the visual data, but also successfully scale PCA to handle large data sets. We present a thorough analysis of the computational complexity and storage benefits of our approach. We apply our algorithm to several types of videos. We show that, in addition to its storage and speed benefits, the algorithm results in a useful representation of the visual data.
主成分分析（PCA）在计算机视觉和图像处理中被广泛应用。由于它在最小二乘意义上提供了最优线性子空间，因此已被用于各个领域的降维和子空间分析。然而，由于其固有的计算复杂性，其可扩展性非常有限。我们引入了一个将PCA应用于视觉数据的新框架，该框架利用了此类数据中通常存在的时空相关性和局部频率变化。我们不是将PCA应用于整个数据体（完整的图像集），而是将数据体划分为一组块，并对每个块应用PCA。然后，我们将与这些块对应的子空间分组并合并在一起。结果，我们不仅在视觉数据的最终表示中实现了更高的效率，而且成功地扩展了PCA以处理大型数据集。我们对我们方法的计算复杂性和存储优势进行了全面分析。我们将我们的算法应用于几种类型的视频。我们表明，除了存储和速度优势外，该算法还能生成视觉数据的有用表示。
