Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual...

Area of Science:

• Computational neuroscience
• Image processing
• Information theory

Background:

• Two-dimensional spatial linear filters face uncertainty relations limiting resolution in orientation, spatial frequency, and position.
• General uncertainty principles govern the trade-offs in extracting information from images.

Purpose of the Study:

• To identify an optimal family of 2D filters that minimize joint uncertainty.
• To investigate if these optimal filters describe receptive fields in the mammalian visual cortex.

Main Methods:

• Developed an optimal 2D filter family using exponentiated bivariate second-order polynomials.
• Analyzed filter properties including orientation bandwidth, spatial frequency bandwidth, and spatial dimensions.
• Compared filter characteristics to receptive-field profiles of simple cells in mammalian visual cortex.

Main Results:

• An optimal 2D filter family was derived, generalizing Gabor's elementary functions.
• These filters occupy irreducible volumes in a 4D information hyperspace, enabling efficient sampling.
• Receptive fields of mammalian visual cortex simple cells align well with this optimal filter family.

Conclusions:

• Mammalian visual neurons may optimize general uncertainty relations for joint spatial and spectral information resolution.
• The observed variety and correlations in receptive field properties suggest constraints and a division of labor in information processing.