This dissertation is focused on the development of robust and efficient Amplitude-Modulation Frequency-Modulation (AM-FM) demodulation methods for image and video processing (there is currently a patent pending that covers the AM-FM methods and applications described in this dissertation). The motivation for this research lies in the wide number of image and video processing applications that can significantly benefit from this research. A number of potential applications are developed in the dissertation. First, a new, robust and efficient formulation for the instantaneous frequency (IF) estimation: a variable spacing, local quadratic phase method (VS-LQP) is presented. VS-LQP produces much more accurate results than current AM-FM methods. At significant noise levels (SNR \u3c 30dB), for single component images, the VS-LQP method produces better IF estimation results than methods using a multi-scale filterbank. At low noise levels (SNR \u3e 50dB), VS-LQP performs better when used in combination with a multi-scale filterbank. In all cases, VS-LQP outperforms the Quasi-Eigen Approximation algorithm by significant amounts (up to 20dB). New least squares reconstructions using AM-FM components from the input signal (image or video) are also presented. Three different reconstruction approaches are developed: (i) using AM-FM harmonics, (ii) using AM-FM components extracted from different scales and (iii) using AM-FM harmonics with the output of a low-pass filter. The image reconstruction methods provide perceptually lossless results with image quality index values bigger than 0.7 on average. The video reconstructions produced image quality index values, frame by frame, up to more than 0.7 using AM-FM components extracted from different scales. An application of the AM-FM method to retinal image analysis is also shown. This approach uses the instantaneous frequency magnitude and the instantaneous amplitude (IA) information to provide image features. The new AM-FM approach produced ROC area of 0.984 in classifying Risk 0 versus Risk 1, 0.95 in classifying Risk 0 versus Risk 2, 0.973 in classifying Risk 0 versus Risk 3 and 0.95 in classifying Risk 0 versus all images with any sign of Diabetic Retinopathy. An extension of the 2D AM-FM demodulation methods to three dimensions is also presented. New AM-FM methods for motion estimation are developed. The new motion estimation method provides three motion estimation equations per channel filter (AM, IF motion equations and a continuity equation). Applications of the method in motion tracking, trajectory estimation and for continuous-scale video searching are demonstrated. For each application, we discuss the advantages of the AM-FM methods over current approaches
