Multiscale wedgelet image analysis: Fast decompositions and modeling

Justin K. Romberg, Michael Wakin, Richard Baraniuk

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

51 Scopus citations

Abstract

The most perceptually important features in images are geometrical, the most prevalent being the smooth contours ("edges") that separate different homogeneous regions and delineate distinct objects. Although wavelet based algorithms have enjoyed success in many areas of image processing, they have significant short-comings in their treatment of edges. Wavelets do not parsimoniously capture even the simplest geometrical structure in images, and as a result wavelet based processing algorithms often produce images with ringing around the edges. The multiscale wedgelet framework is a first step towards explicitly capturing geometrical structure in images. The framework has two components: decomposition and representation. The multiscale wavelet decomposition divides the image into dyadic blocks at different scales and projects these image blocks onto wedgelets - simple piecewise constant functions with linear discontinuities. The multiscale wedgelet representation is an approximation of the image built out of wedgelets from the decomposition. In choosing the wedgelets to form the representation, we can weigh several factors: the error between the representation and the original image, the parsimony of the representation, and whether the wedgelets in the representation form "natural" geometrical structure. In this paper, we show that an efficient multiscale wedgelet decomposition is possible if we carefully choose the set of possible wedgelet orientations. We also present a modeling framework that makes it possible to incorporate simple geometrical constraints into the choice of wedgelet representation, resulting in parsimonious image approximations with smooth contours.

Original languageEnglish
Title of host publicationIEEE International Conference on Image Processing
Volume3
StatePublished - Jan 1 2002
EventInternational Conference on Image Processing (ICIP'02) - Rochester, NY, United States
Duration: Sep 22 2002Sep 25 2002

Other

OtherInternational Conference on Image Processing (ICIP'02)
CountryUnited States
CityRochester, NY
Period9/22/029/25/02

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Hardware and Architecture
  • Electrical and Electronic Engineering

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