Polynomial Fitting for Edge Detection in Irregularly Sampled Signals and Images

Authors:
Rick Archibald;Anne Gelb;Jungho Yoon
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2005

Citing 0
Cited 16

Reconstruction of Piecewise Smooth Functions from Non-uniform Grid Point Data

Journal of Scientific Computing
Determining the locations and discontinuities in the derivatives of functions

Applied Numerical Mathematics
Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of 1/n

Journal of Computational Physics
Discontinuity detection in multivariate space for stochastic simulations

Journal of Computational Physics
Edge Detection by Adaptive Splitting

Journal of Scientific Computing
Improved Total Variation-Type Regularization Using Higher Order Edge Detectors

SIAM Journal on Imaging Sciences
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids

Journal of Computational Physics
Brief paper: Set membership approximation of discontinuous nonlinear model predictive control laws

Automatica (Journal of IFAC)
Iterative Filtering Decomposition Based on Local Spectral Evolution Kernel

Journal of Scientific Computing
Mode Decomposition Evolution Equations

Journal of Scientific Computing
Edge Detection by Adaptive Splitting II. The Three-Dimensional Case

Journal of Scientific Computing
Hypothesis Testing for Fourier Based Edge Detection Methods

Journal of Scientific Computing
Uncertainty Quantification given Discontinuous Model Response and a Limited Number of Model Runs

SIAM Journal on Scientific Computing
The detection and recovery of discontinuity curves from scattered data

Journal of Computational and Applied Mathematics
On the use of the polynomial annihilation edge detection for locating cracks in beam-like structures

Computers and Structures
Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions

Journal of Computational Physics

Quantified Score

Hi-index	0.03

Visualization

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 instances where only sparse nonuniform data is available. These results are successfully demonstrated in both one and two dimensions.