Outline
Human Vision: Modeling the Primary Visual Pathway
Primary Visual Pathway
Cortical Receptive Field Data
Gabor Model
Gabor Functions
Gaussian Derivative Model
Gaussian Derivative Functions
A Gaussian Derivative Based Transform
Discrete 1D DGT
Non-orthogonality
MMSE Decomposition
Separable 2D Transform
Basis Selection - Spatial
Basis Selection - Derivative Order
Spectral Distribution
Uniform Spectral Distribution
Perfect Reconstruction
Transform Coding Example
Summary
On the Optimality of Hermite Functions
Heisenberg
Locality
A Common Joint Uncertainty Metric
Gabor Functions
Hermite Functions
Gaussian Derivative Functions
Minimizing The Joint Uncertainty Product
Calculus of Variations
Hermite Functions
Second Variation
Direct Evaluation of the Joint Uncertainty
Hermite Functions
Gaussian Derivatives
Joint Uncertainty Product Comparison
Summary
