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Summary: POLYNOMIAL FITTING FOR EDGE DETECTION IN
IRREGULARLY SAMPLED SIGNALS AND IMAGES
RICK ARCHIBALD, ANNE GELB, AND JUNGHO YOON§
Abstract. We propose a new edge detection method that is effective on multivariate irregular
data in any domain. The method is based on a local polynomial annihilation technique and can
be characterized by its convergence to zero for any value away from discontinuities. The method is
numerically cost efficient and entirely independent of any specific shape or complexity of boundaries.
Application of the minmod function to the edge detection method of various orders ensures a high
rate of convergence away from the discontinuities while reducing the inherent oscillations near the
discontinuities. It further enables distinction of jump discontinuities from steep gradients, even in in-
stances where only sparse non-uniform data is available. These results are successfully demonstrated
in both one and two dimensions.
Key words. minmod function, multivariate edge detection, Newton divided differencing, non-
uniform grids.
AMS subject classifications. 41A25,41A45,41A63.
1. Introduction. Edge detection is of fundamental importance in image anal-
ysis. In particular, a reliable and efficient edge detection method can both provide
the possibility of processing an image with high accuracy, as well as serve to simplify
the analysis of images by drastically reducing the amount of data to be processed.
Among the many common criteria relevant to edge detector performance, there are
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