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Analyzing image structure by multidimensional frequency modulation
M. S. Pattichis and A. C. Bovik
IEEE Transactions on Pattern Analysis and Machine Intelligence
Keywords: Theory and models, Image Processing and Computer Vision, Image models.
Abstract
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.
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