Title of article :
Differential morphology and image processing
Author/Authors :
Maragos، نويسنده , , P.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 1996
Abstract :
Image processing via mathematical morphology has
traditionally used geometry to intuitively understand morphological
signal operators and set or lattice algebra to analyze them
in the space domain. In this paper, we provide a unified view
and analytic tools for a recently growing part of morphological
image processing that is based on ideas from differential calculus
and dynamical systems. This part includes both recent and some
earlier ideas on using partial differential or difference equations
(PDEs) to model distance propagation or nonlinear multiscale
processes in images. We briefly review some nonlinear difference
equations that implement discrete distance transforms and relate
them to numerical solutions of the eikonal equation of optics.
We also review some nonlinear PDEs that model the evolution
of multiscale morphological operators and use morphological
derivatives. Among the new ideas presented, we develop some
general 2-0 maxhin-sum difference equations that model the
space dynamics of 2-D morphological systems (including the
distance computations) and some nonlinear signal transforms,
called slope transforms, that can analyze these systems in a
transform domain in ways conceptually similar to the application
of Fourier transforms to linear systems. Thus, distance transforms
are shown to be bandpass slope filters. We view the analysis of
the multiscale morphological PDEs and of the eikonal PDE solved
via weighted distance tranforms as a unified area in nonlinear
image processing, which we call differential morphology, and
briefly discuss its potential applications to image processing and
computer vision.
Journal title :
IEEE TRANSACTIONS ON IMAGE PROCESSING
Journal title :
IEEE TRANSACTIONS ON IMAGE PROCESSING