Mathematics

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Three Dimensional Edge Detection Using Wavelet and Shearlet Analysis
(2012) Schug, David Albert; O'Leary, Dianne P; Easley, Glenn R; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Edge detection determines the boundary of objects in an image. A sequence of images records a 2D representation of a scene changing over time, giving 3D data. New 3D edge detectors, particularly ones we developed using shearlets and hybrid shearlet-Canny algorithms, identify edges of complicated objects much more reliably than standard approaches, especially under high noise conditions. We also use edge information to track the position and velocity of objects using an optimization algorithm.
RECOVERY OF EDGES FROM SPECTRAL DATA WITH NOISE—A NEW PERSPECTIVE
(Copyright: Society for Industrial and Applied Mathematics, 2008) ENGELBERG, SHLOMO; TADMOR, EITAN
We consider the problem of detecting edges—jump discontinuities in piecewise smooth functions from their N-degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the “smoothness” scale of order 1/N, the noise scale of order √η, and the O(1) scale of the jump discontinuities. We use concentration factors which are adjusted to the standard deviation of the noise √η ≫ 1/N in order to detect the underlying O(1)-edges, which are separated from the noise scale √η ≪ 1.