| A new theory of multidimensional AM-FM signal modeling is presented in this dissertation. AM-FM image functions generalize the 2D Fourier transform kernel by admitting arbitrarily varying amplitude and phase modulations. Thus, they are inherently capable of capturing essential nonstationary, yet locally coherent image structures. Often, such nonstationarities contribute significantly to visual perception and interpretation. Recently, AM-FM signal modeling has been successfully applied to a number of problems characterized by such nonstationarities. Examples include speech recognition and analysis, image texture modeling, analysis, and segmentation, 3D shape from texture, and phase-based computational stereopsis.; The first half of the dissertation focuses on the fundamental motivation and principles of AM-FM modeling. Foundations are developed for analyzing modulations in arbitrarily dimensioned continuous and discrete signals using nonlinear demodulation operators related to the Teager-Kaiser operator. In the second half of the dissertation, practical approaches are presented for extracting AM-FM sub-image information from digital images and for computing multi-component AM-FM image representations. Biologically motivated multiband Gabor filter banks are used for isolating AM-FM image multi-components on a spatio-spectrally localized basis, and optimal filters are designed for tracking multi-components across the filterbank channel responses using a statistical state-space component model. Techniques for recovering the essential structure of an image from its computed AM-FM representation are also developed.; Two main computational paradigms are presented in detail. The first, called dominant component analysis, delivers estimates of the emergent frequencies and dominant amplitude modulations of an image. These estimates are useful in a variety of image processing and machine vision tasks, including shape from texture and texture-based stereopsis. Texture segmentation using the estimated dominant component modulating functions is also demonstrated. In the second main paradigm, full multi-component AM-FM image representations are computed. Exciting future applications of such representations include AM-FM-based image and video coding for multimedia communications and CD-ROM mass storage systems. |
