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.