The Riesz transform and simultaneous representations of phase, energy and orientation in spatial vision

Area of Science:

• Computer Vision
• Image Processing
• Computational Neuroscience

Background:

• Early visual processing models use quadrature filters for 1-D signals.
• 2-D phase representations in image signals have been underexplored.

Purpose of the Study:

• To introduce and explore 2-D phase representations using the Riesz transform.
• To demonstrate the Riesz transform's utility in image analysis and pattern recognition.

Main Methods:

• Utilized the Riesz transform to generate two transformed signals from an original 1-D image signal.
• Applied Singular Value Decomposition (SVD) to higher-order derivatives for property representation.
• Investigated signal autocorrelation functions for filter responses.

Main Results:

• The Riesz transform enables representation of orientation, phase, and energy as a 3-D vector.
• SVD of derivatives effectively captures image properties.
• Riesz transform simplifies Bayesian computations for spatial orientation.
• Demonstrated utility in estimating spatial orientation of second-order image signals.

Conclusions:

• The Riesz transform provides a robust framework for 2-D image signal analysis.
• It offers a general tool for 2-D visual pattern recognition by representing phase, orientation, and energy orthogonally.