AM-FM models images as a linear combination of positive amplitude modulated (AM) sinusoids with non-linear phase functions. In this paper, we develop a novel FM harmonics operator for revealing different levels of image structure detail. The new operator is defined in terms of known AM-FM demodulation techniques: dominant component analysis and channelized component analysis. We also show an example of image segmentation, where the new operator is used for tracking cardiac wall boundaries in Motion-mode (M-mode) ultrasound video.