基于单纯复形的流形上图像点对应
Simplicial Complex based Point Correspondence between Images warped onto Manifolds
摘要：
投影到流形上的扭曲图像的可用性的最近增加（例如，全向球形图像），加上高阶分配方法的成功，已经引发了对由于投影而变形的图像上的改进的高阶匹配算法的研究的兴趣。尽管目前，几种现有的方法“压平”此类3D图像以使用平面图/超图匹配方法，但它们仍然存在严重的失真和其他不期望的伪影，从而导致匹配不准确。或者，目前的平面方法不能平凡地扩展到有效地匹配点的图像扭曲到流形上。因此，在这些扭曲的图像上进行匹配仍然是一个艰巨的挑战。在本文中，我们提出的分配问题，找到一个双射映射之间的两个图诱导单纯复形，这是高阶类似的图。我们提出了一个约束二次分配问题（QAP），匹配每个p-骨架的单纯形复合体，从最高到最低的维度迭代。我们的方法的准确性和鲁棒性的合成和现实世界的球形/扭曲（投影）图像与已知的地面实况对应说明。我们显着优于现有的最先进的球形匹配方法在一组不同的数据集。
英文摘要：
Recent increase in the availability of warped images projected onto a manifold (e.g., omnidirectional spherical images), coupled with the success of higher-order assignment methods, has sparked an interest in the search for improved higher-order matching algorithms on warped images due to projection. Although currently, several existing methods "flatten" such 3D images to use planar graph / hypergraph matching methods, they still suffer from severe distortions and other undesired artifacts, which result in inaccurate matching. Alternatively, current planar methods cannot be trivially extended to effectively match points on images warped onto manifolds. Hence, matching on these warped images persists as a formidable challenge. In this paper, we pose the assignment problem as finding a bijective map between two graph induced simplicial complexes, which are higher-order analogues of graphs. We propose a constrained quadratic assignment problem (QAP) that matches each p-skeleton of the simplicial complexes, iterating from the highest to the lowest dimension. The accuracy and robustness of our approach are illustrated on both synthetic and real-world spherical / warped (projected) images with known ground-truth correspondences. We significantly outperform existing state-of-the-art spherical matching methods on a diverse set of datasets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
