Multidimensional energy operator for image processing

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Abstract
The 1-D nonlinear differential operator (Psi) (f) equals (f')2 - ff' has been recently introduced to signal processing and has been found very useful for estimating the parameters of sinusoids and the modulating signals of AM-FM signals. It is called an energy operator because it can track the energy of an oscillator source generating a sinusoidal signal. In this paper we introduce the multidimensional extension (Phi) (f) equals (parallel)$DELf(parallel)2 - f$DEL2f of the 1-D energy operator and briefly outline some of its applications to image processing. We discuss some interesting properties of the multidimensional operator and develop demodulation algorithms to estimate the amplitude envelope and instantaneous frequencies of 2-D spatially-varying AM-FM signals, which can model image texture. The attractive features of the multidimensional operator and the related amplitude/frequency demodulation algorithms are their simplicity, efficiency, and ability to track instantaneously- varying spatial modulation patterns.

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