AM-FM analysis methods have been used in several biomedical imaging applications. In this paper, we are interested in the development of AM-FM analysis methods for small components, regions of interests (ROIs), and segmented objects. For detecting small components, we propose the use of a new multi-scale AM-FM edge and peak analysis system. The new system uses the product of gradient estimates from multiple scales. For small ROIs, we propose the use of a new nested optimization scheme. We show that separable designs based on 1-D designs with 15 coefficients can lead to excellent AMFM estimates. ©2009 IEEE.