Spectral Generalized Multi-dimensional Scaling

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• 作者：Yonathan Aflalo ; Anastasia Dubrovina…
• 刊名：International Journal of Computer Vision
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：118
• 期：3
• 页码：380-392
• 全文大小：2,812 KB
• 刊物类别：Computer Science
• 刊物主题：Computer Imaging, Vision, Pattern Recognition and Graphics
  Artificial Intelligence and Robotics
  Image Processing and Computer Vision
  Pattern Recognition
  
• 出版者：Springer Netherlands
• ISSN：1573-1405
• 卷排序：118

文摘

Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances between each pair of points in the set. Distances in the target space can be computed analytically in this setting. Generalized MDS is an extension that allows mapping one metric space into another, that is, MDS into target spaces in which distances are evaluated numerically rather than analytically. Here, we propose an efficient approach for computing such mappings between surfaces based on their natural spectral decomposition, where the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS procedure enables efficient embedding by incorporating smoothness of the metric structure into the problem, thereby substantially reducing the complexity involved in its solution while practically overcoming its non-convex nature. The method is compared to existing techniques that compute dense correspondence between shapes. Numerical experiments of the proposed method demonstrate its efficiency and accuracy compared to state-of-the-art approaches especially when isometry invariance is a dominant property.KeywordsSpectral domainGMDSShape matching