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Exploiting manifold geometry in hyperspectral imagery

机译：在高光谱影像中利用流形几何

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摘要

A new algorithm for exploiting the nonlinear structure of hyperspectral imagery is developed and compared against the de facto standard of linear mixing. This new approach seeks a manifold coordinate system that preserves geodesic distances in the high-dimensional hyperspectral data space. Algorithms for deriving manifold coordinates, such as isometric mapping (ISOMAP), have been developed for other applications. ISOMAP guarantees a globally optimal solution, but is computationally practical only for small datasets because of computational and memory requirements. Here, we develop a hybrid technique to circumvent ISOMAP's computational cost. We divide the scene into a set of smaller tiles. The manifolds derived from the individual tiles are then aligned and stitched together to recomplete the scene. Several alignment methods are discussed. This hybrid approach exploits the fact that ISOMAP guarantees a globally optimal solution for each tile and the presumed similarity of the manifold structures derived from different tiles. Using land-cover classification of hyperspectral imagery in the Virginia Coast Reserve as a test case, we show that the new manifold representation provides better separation of spectrally similar classes than one of the standard linear mixing models. Additionally, we demonstrate that this technique provides a natural data compression scheme, which dramatically reduces the number of components needed to model hyperspectral data when compared with traditional methods such as the minimum noise fraction transform.
机译：提出了一种利用高光谱图像非线性结构的新算法，并将其与事实上的线性混合标准进行了比较。这种新方法寻求在高维高光谱数据空间中保留测地距离的流形坐标系。已经为其他应用开发了用于得出歧管坐标的算法，例如等距映射（ISOMAP）。 ISOMAP保证了全局最佳解决方案，但由于计算和内存需求，仅在小型数据集上具有计算实用性。在这里，我们开发了一种混合技术来规避ISOMAP的计算成本。我们将场景分为一组较小的图块。然后将源自各个图块的歧管对齐并缝合在一起以重新完成场景。讨论了几种对齐方法。这种混合方法利用了以下事实：ISOMAP保证了每个图块的全局最佳解决方案以及从不同图块派生的流形结构的假定相似性。使用弗吉尼亚海岸保护区的高光谱影像的土地覆盖分类作为测试案例，我们显示出新的流形表示比标准线性混合模型之一能更好地分离光谱相似的类别。此外，我们证明了该技术提供了一种自然的数据压缩方案，与传统方法（例如最小噪声分数变换）相比，该方法大大减少了建模高光谱数据所需的组件数量。

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