Manifold Learning via the Principle Bundle Approach

Chen Yun Lin, Arin Minasian, Xin Jessica Qi, Hau Tieng Wu

Research output: Contribution to journalArticlepeer-review


In this paper, we propose a novel principal bundle model and apply it to the image denoising problem. This model is based on the fact that the patch manifold admits canonical groups actions such as rotation. We introduce an image denoising algorithm, called the diffusive vector non-local Euclidean median (dvNLEM), by combining the traditional nonlocal Euclidean median (NLEM), the rotational structure in the patch space, and the diffusion distance. A theoretical analysis of dvNLEM, as well as the traditional nonlocal Euclidean median (NLEM), is provided to explain why these algorithms work. In particular, we show how accurate we could obtain the true neighbors associated with the rotationally invariant distance (RID) and Euclidean distance in the patch space when noise exists, and how we could apply the diffusion geometry to stabilize the selected metric. The dvNLEM is applied to an image database of 1,361 images and a comparison with the NLEM is provided. Different image quality assessments based on the error-sensitivity or the human visual system are applied to evaluate the performance.

Original languageEnglish (US)
Article number21
JournalFrontiers in Applied Mathematics and Statistics
StatePublished - Jun 25 2018


  • diffusion geometry
  • image denoising
  • non-local means
  • patch size
  • principal bundles

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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