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IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 48, NO. 5, MAY 2000 1379 Locally Monotonic Diffusion
 

Summary: IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 48, NO. 5, MAY 2000 1379
Locally Monotonic Diffusion
Scott T. Acton, Senior Member, IEEE
Abstract--Anisotropic diffusion affords an efficient, adaptive
signal smoothing technique that can be used for signal enhance-
ment, signal segmentation, and signal scale-space creation. This
paper introduces a novel partial differential equation (PDE)-based
diffusion method for generating locally monotonic signals. Unlike
previous diffusion techniques that diverge or converge to trivial sig-
nals, locally monotonic (LOMO) diffusion converges rapidly to well-
defined LOMO signals of the desired degree. The property of local
monotonicity allows both slow and rapid signal transitions (ramp
and step edges) while excluding outliers due to noise. In contrast
with other diffusion methods, LOMO diffusion does not require
an additional regularization step to process a noisy signal and uses
no ad hoc thresholds or parameters. In the paper, we develop the
LOMO diffusion technique and provide several salient properties,
including stability and a characterization of the root signals. The
convergence of the algorithm is well behaved (nonoscillatory) and
is independent of signal length, in contrast with the median filter. A

  

Source: Acton, Scott - Department of Electrical and Computer Engineering, University of Virginia

 

Collections: Computer Technologies and Information Sciences