P. Maragos et Ac. Bovik, IMAGE DEMODULATION USING MULTIDIMENSIONAL ENERGY SEPARATION, Journal of the Optical Society of America. A, Optics, image science,and vision., 12(9), 1995, pp. 1867-1876
Locally narrow-band images can be modeled as two-dimensional (2D) spat
ial AM-FM signals with several applications in image texture analysis
and computer vision. We formulate an image-demodulation problem and pr
esent a solution based on the multidimensional energy operator Phi(f)
= parallel to del f parallel to(2)-f del(2)f This nonlinear operator i
s a multidimensional extension of the one-dimensional (1D) energy-trac
king operator psi(f) = (f')(2)-ff '', which has been found useful for
demodulating 1D AM-FM and speech signals. We discuss some interesting
properties of the multidimensional operator and develop a multidimensi
onal energy-separation algorithm to estimate the amplitude envelope an
d instantaneous frequencies of 2D spatially varying AM-FM signals. Exp
eriments are also presented on applying this 2D energy-demodulation al
gorithm to estimate the instantaneous amplitude contrast and spatial f
requencies of image textures bandpass filtered by means of Gabor filte
rs. The attractive features of the multidimensional energy operator an
d the 2D energy-separation algorithm are their simplicity, efficiency,
and ability to track instantaneously varying spatial-modulation patte
rns.