Multiscale geometric image processing

Justin K. Romberg, Michael B. Wakin, Richard G. Baraniuk

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

19 Scopus citations


Since their introduction a little more than 10 years ago, wavelets have revolutionized image processing. Wavelet based algorithms define the state-of-the-art for applications including image coding (JPEG2000), restoration, and segmentation. Despite their success, wavelets have significant shortcomings in their treatment of edges. Wavelets do not parsimoniously capture even the simplest geometrical structure in images, and wavelet based processing algorithms often produce images with ringing around the edges. As a first step towards accounting for this structure, we will show how to explicitly capture the geometric regularity of contours in cartoon images using the wedgelet representation and a multiscale geometry model. The wedgelet representation builds up an image out of simple piecewise constant functions with linear discontinuities, We will show how the geometry model, by putting a joint distribution on the orientations of the linear discontinuities, allows us to weigh several factors when choosing the wedgelet representation: the error between the representation and the original image, the parsimony of the representation, and whether the wedgelets in the representation form "natural" geometrical structures. Finally, we will analyze a simple wedgelet coder based on these principles, and show that it has optimal asymptotic performance for simple cartoon images.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsT. Ebrahimi, T. Sikora
Number of pages8
Volume5150 II
StatePublished - 2003
EventVisual Communications and Image Processing 2003 - Lugano, Switzerland
Duration: Jul 8 2003Jul 11 2003


OtherVisual Communications and Image Processing 2003


  • Geometry in images
  • Image compression
  • Wedgelets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics


Dive into the research topics of 'Multiscale geometric image processing'. Together they form a unique fingerprint.

Cite this