Determining the locations and discontinuities in the derivatives of functions
Applied Numerical Mathematics
Detection of Edges in Spectral Data III--Refinement of the Concentration Method
Journal of Scientific Computing
Discontinuity detection in multivariate space for stochastic simulations
Journal of Computational Physics
Iterative methods based on spline approximations to detect discontinuities from Fourier data
Journal of Computational and Applied Mathematics
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
Sparsity Enforcing Edge Detection Method for Blurred and Noisy Fourier data
Journal of Scientific Computing
Hypothesis Testing for Fourier Based Edge Detection Methods
Journal of Scientific Computing
Iterative Design of Concentration Factors for Jump Detection
Journal of Scientific Computing
On the use of the polynomial annihilation edge detection for locating cracks in beam-like structures
Computers and Structures
Edge detection from truncated Fourier data using spectral mollifiers
Advances in Computational Mathematics
Journal of Computational Physics
Hi-index | 0.02 |
We are concerned with the detection of edges--the location and amplitudes of jump discontinuities of piecewise smooth data realized in terms of its discrete grid values. We discuss the interplay between two approaches. One approach, realized in the physical space, is based on local differences and is typically limited to low-order of accuracy. An alternative approach developed in our previous work [Gelb and Tadmor, Appl. Comp. Harmonic Anal., 7, 101---135 (1999)] and realized in the dual Fourier space, is based on concentration factors; with a proper choice of concentration factors one can achieve higher-orders--in fact in [Gelb and Tadmor, SIAM J. Numer. Anal., 38, 1389---1408 (2001)] we constructed exponentially accurate edge detectors. Since the stencil of these highly-accurate detectors is global, an outside threshold parameter is required to avoid oscillations in the immediate neighborhood of discontinuities. In this paper we introduce an adaptive edge detection procedure based on a cross-breading between the local and global detectors. This is achieved by using the minmod limiter to suppress spurious oscillations near discontinuities while retaining high-order accuracy away from the jumps. The resulting method provides a family of robust, parameter-free edge-detectors for piecewise smooth data. We conclude with a series of one- and two-dimensional simulations.