Demodulation of images modeled by amplitude-frequency modulations using multidimensional energy separation

Locally narrowband images can be modeled as 2D spatial AM-FM signals with several applications in image texture analysis and computer vision. In this paper we formulate such an image demodulation problem, and present a solution based on the multidimensional energy operator Φ(f)=||∇f||²-f∇²f. We discuss some interesting properties of this multidimensional operator and develop multidimensional energy separation algorithms 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 via 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