Commun. Comput. Phys., 5 (2009), pp. 694-711.


A High Order Method for Determining the Edges in the Gradient of a Function

Rishu Saxena 1*, Anne Gelb 1, Hans Mittelmann 1

1 Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, USA.

Received 1 October 2007; Accepted (in revised version) 30 November 2007
Available online 1 August 2008

Abstract

Detection of edges in piecewise smooth functions is important in many applications. Higher order reconstruction algorithms in image processing and post processing of numerical solutions to partial differential equations require the identification of smooth domains, creating the need for algorithms that will accurately identify discontinuities in a given function as well as those in its gradient. This work expands the use of the polynomial annihilation edge detector, (Archibald, Gelb and Yoon, 2005), to locate discontinuities in the gradient given irregularly sampled point values of a continuous function. The idea is to preprocess the given data by calculating the derivative, and then to use the polynomial annihilation edge detector to locate the jumps in the derivative. We compare our results to other recently developed methods.

AMS subject classifications: 41A10, 41A63, 41A58, 65D99

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Key words: Multivariate edge detection, derivative discontinuities, piecewise smooth functions, polynomial annihilation, non-uniform grids.

*Corresponding author.
Email: saxena@mathpost.asu.edu (R. Saxena), ag@math.asu.edu (A. Gelb), mittelmann@asu.edu (H. Mittelmann)
 

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