Mathematics and Cognition Seminar
joint with
Computational and Applied Math Proseminar

Department of Mathematics, Arizona State University

Tuesday, February 1, 2000, 12:00 p.m. in GWC Room 604

Anne Gelb

Department of Mathematics

Edge detection: reconstruction of piecewise smooth functions from their spectral data

Abstract Detection of object edges in machine vision depends on the determination of discontinuities in the intensity, color, texture etc of an otherwise smoothly varying visual image. Reconstruction methods using both pseudo-spectral coefficients and physical space interpolants have been discussed extensively in the literature, and it is clear that an a-priori knowledge of the jump discontinuity location is essential for any reconstruction technique to yield spectrally accurate results with high resolution near the discontinuities. Hence detection of the jump discontinuities is critical for all methods. A new localized reconstruction method is formulated incorporating the detection of edges and a localized reconstruction technique. The method is robust and highly accurate, yielding spectral accuracy up to a small neighborhood of the jump discontinuities. Results are shown in one and two dimensions. Current investigation of a method yielding spectral accuracy up to the jump discontinuities are also discussed.

For further information please contact: mittelmann@asu.edu