MRA-based wavelet frames and applications: Image segmentation and surface reconstruction

Bin Dong, Zuowei Shen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Theory of wavelet frames and their applications to image restoration problems have been extensively studied for the past two decades. The success of wavelet frames in solving image restoration problems, which includes denoising, deblurring, inpainting, computed tomography, etc., is mainly due to their capability of sparsely approximating piecewise smooth functions such as images. However, in contrast to the wide applications of wavelet frame based approaches to image restoration problems, they are rarely used for some image/data analysis tasks, such as image segmentation, registration and surface reconstruction from unorganized point clouds. The main reason for this is the lack of geometric interpretations of wavelet frames and their associated transforms. Recently, geometric meanings of wavelet frames have been discovered and connections between the wavelet frame based approach and the differential operator based variational model were established.1 Such discovery enabled us to extend the wavelet frame based approach to some image/data analysis tasks that have not yet been studied before. In this paper, we will provide a unified survey of the wavelet frame based models for image segmentation and surface reconstruction from unorganized point clouds. Advantages of the wavelet frame based approach are illustrated by numerical experiments.

Original languageEnglish (US)
Title of host publicationIndependent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering X
DOIs
StatePublished - Dec 1 2012
EventIndependent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering X - Baltimore, MD, United States
Duration: Apr 25 2012Apr 27 2012

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume8401
ISSN (Print)0277-786X

Other

OtherIndependent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering X
CountryUnited States
CityBaltimore, MD
Period4/25/124/27/12

Keywords

  • (tight) wavelet frames
  • Image segmentation
  • split Bregman algorithm
  • surface reconstruction
  • variational method

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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  • Cite this

    Dong, B., & Shen, Z. (2012). MRA-based wavelet frames and applications: Image segmentation and surface reconstruction. In Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering X [840102] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8401). https://doi.org/10.1117/12.923203