Image demodulation using multidimensional energy separation

Locally narrow-band images can be modeled as two-dimensional (2D) spatial AM–FM signals with several applications in image texture analysis and computer vision. We formulate an image-demodulation problem and present a solution based on the multidimensional energy operator Fs f d ­ k=fk2 2 f=2f . This nonlinear operator is a multidimensional extension of the one-dimensional (1D) energy-tracking operator Cs f d ­ s f 0 d2 2 ff 00, 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 multidimensional energy-separation algorithm to estimate the amplitude envelope and instantaneous frequencies of 2D spatially varying AM–FM signals. Experiments are also presented on applying this 2D energy-demodulation algorithm to estimate the instantaneous amplitude contrast and spatial frequencies of image textures bandpass filtered by means of Gabor filters. The attractive features of the multidimensional energy operator and the 2D energy-separation algorithm are their simplicity, efficiency, and ability to track instantaneously varying spatial-modulation patterns.