Covariance properties under natural image transformations for the generalised Gaussian derivative model for visual...

Area of Science:

• Computational Neuroscience
• Computer Vision
• Image Processing

Background:

• Covariance (equivariance) describes how image operators behave under transformations.
• Generalised Gaussian derivative models are used for receptive fields in the primary visual cortex and lateral geniculate nucleus.
• Geometric invariance at higher visual levels is enabled by covariance properties.

Purpose of the Study:

• To present a theory of geometric covariance properties in vision.
• To analyze the covariance properties of generalised Gaussian derivative models for receptive fields.
• To explore implications for biological vision and natural image transformations.

Main Methods:

• Developed a theory of geometric covariance for vision.
• Analyzed generalised Gaussian derivative models for receptive fields.
• Investigated covariance under spatial scaling, affine, Galilean, and temporal scaling transformations.

Main Results:

• The generalised Gaussian derivative model exhibits true covariance under various spatial and temporal transformations.
• Covariance properties allow vision systems to approximate handling of image/video deformations from multiple views.
• The theory connects receptive field shapes to image structure variabilities under natural transformations.

Conclusions:

• The presented theory has implications for understanding biological vision.
• It suggests a link between receptive field shape variability and image structure variability.
• Experimentally testable hypotheses are formulated regarding receptive field properties in the primary visual cortex.