Image and video processing are forms of signal processing. Signal processing allows a set of characteristics or parameters related to the image or video to be obtained. Signal processing including analog signal processing, discrete time signal processing, and digital signal processing, which may involve a one-dimensional (“1D”), two-dimensional (“2D”) or three-dimensional (“3D”) input signal to which signal processing techniques are applied.
Signal processing techniques include transform-based processing such as discrete or integral transforms which were implemented prior to AM-FM processing. As an example, a 1D analysis of transform-based processing includes the use of short-time Fourier Transform (“STFT”) for non-stationary signals. When using STFT, the fast Fourier Transform (“FFT”) of different time intervals of the signals is used to determine the frequency and phase content. Thus, the STFT is a convenient 2D representation that provides frequency content information at different time intervals. A disadvantage is that the STFT cannot be effectively generalized to images and videos. For example, using STFT for images would produce a four-dimensional (“4D”) representation and using STFT for video would produce a six-dimensional (“6D”) representation.
The discrete Wavelet Transform (“DWT”) has also been used for transform-based image processing. Unlike Fourier Transforms, Wavelet Transforms are based on specific functions defined at different scales and durations. Thus, the DWT is a space-frequency representation of the input signal and it is related to harmonic analysis is as in Fourier Transform. While FFT uses equally spaced frequency division, DWT uses logarithmic divisions of the frequency. A disadvantage is that DWT does not measure frequency content directly.
The development of accurate methods for estimating amplitude-modulation frequency-modulation image decompositions is of great interest due to is potentially significant impact on image analysis applications including in the areas of signal, image and video processing. Applications in signal processing include speech signal analysis. Image processing applications include shape from shading, image pattern analysis, image interpolation, fingerprint classification, image retrieval in digital libraries, image segmentation, and damaged image texture repairs. Applications in video processing include cardiac image segmentation, motion estimation, and motion reconstruction, to name a few.
Accurate system and methods for estimating AM-FM components are important due to their potentially significant impact on various applications. Thus, there is demand for improved AM-FM demodulation for both stationary and non-stationary processing for use in a variety of contexts and applications. The present invention satisfies this demand.