Learning nonlinear image manifolds by global alignment of local linear models
Learning nonlinear image manifolds by global alignment of local linear models
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DOI：
10.1109/tpami.2006.166
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发表时间：
2006-08
影响因子：
23.6
通讯作者：
J. Verbeek
中科院分区：
文献类型：
--
作者：
J. Verbeek
基于外观的方法基于图像(区域)中像素值的统计模型，而不是基于几何对象模型，在计算机视觉中日益流行。在许多应用中，图像生成过程中的自由度(DOF)数远远低于图像中的像素数。如果存在将自由度映射到像素值的平滑函数，则图像被限制在嵌入在图像空间中的低维流形中。我们提出了一种基于因子分析器的概率混合的方法：1)对从流形上采样的图像的密度进行建模；2)恢复流形的全局参数。通过组合几个局部有效的线性映射，得到流形上的坐标和图像之间的全局非线性概率双向映射。我们提出了一种对现有方案进行改进的参数估计方案，并通过实验比较了所提出的方法在自组织映射、生成性地形映射和混合因子分析器中的应用。此外，我们还证明了该方法也适用于寻找同一流形的不同嵌入之间的映射
Appearance-based methods, based on statistical models of the pixel values in an image (region) rather than geometrical object models, are increasingly popular in computer vision. In many applications, the number of degrees of freedom (DOF) in the image generating process is much lower than the number of pixels in the image. If there is a smooth function that maps the DOF to the pixel values, then the images are confined to a low-dimensional manifold embedded in the image space. We propose a method based on probabilistic mixtures of factor analyzers to 1) model the density of images sampled from such manifolds and 2) recover global parameterizations of the manifold. A globally nonlinear probabilistic two-way mapping between coordinates on the manifold and images is obtained by combining several, locally valid, linear mappings. We propose a parameter estimation scheme that improves upon an existing scheme and experimentally compare the presented approach to self-organizing maps, generative topographic mapping, and mixtures of factor analyzers. In addition, we show that the approach also applies to finding mappings between different embeddings of the same manifold