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International Journal of Computer Vision
Shape from Texture Using Local Spectral Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIAM Journal on Scientific Computing
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Elementary Differential Equations With Mathematica
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Am-fm image models
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IEEE Transactions on Signal Processing
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IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Statistical AM-FM models, extended Kalman filter demodulation,Cramer-Rao bounds, and speech analysis
IEEE Transactions on Signal Processing
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IEEE Transactions on Signal Processing
Multidimensional quasi-eigenfunction approximations and multicomponent AM-FM models
IEEE Transactions on Image Processing
Oriented texture completion by AM-FM reaction-diffusion
IEEE Transactions on Image Processing
Fingerprint classification using an AM-FM model
IEEE Transactions on Image Processing
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Pattern Recognition Letters
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IEEE Transactions on Signal Processing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
FM filters for modulation domain image processing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Multiscale AM-FM analysis of pneumoconiosis X-ray images
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Multiscale AM-FM demodulation and image reconstruction methods with improved accuracy
IEEE Transactions on Image Processing
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Tree image growth analysis using instantaneous phase modulation
EURASIP Journal on Advances in Signal Processing - Special issue on recent advances in theory and methods for nonstationary signal analysis
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We develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images. We begin with the widely accepted definition of the instantaneous frequency vector (IF) as the gradient of the phase and define the instantaneous frequency gradient tensor (IFGT) as the tensor of component derivatives of the IF vector. Frequency modulation bounds are derived and interpreted in terms of the eigendecomposition of the IFGT. Using the IFGT, we derive the ordinary differential equations (ODEs) that describe image flowlines. We study the diagonalization of the ODEs of multidimensional frequency modulation on the IFGT eigenvector coordinate system and suggest that separable transforms can be computed along these coordinates. We illustrate these new methods of image pattern analysis on textured and fingerprint images. We envision that this work will find value in applications involving the analysis of image textures that are nonstationary yet exhibit local regularity. Examples of such textures abound in nature.