Group theoretical methods in image processing
Group theoretical methods in image processing
The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Foundations of semi-differential invariants
International Journal of Computer Vision
Using Symbolic Computation to Find Algebraic Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
Similarity and Affine Invariant Distances Between 2D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Transformation Invariance in Pattern Recognition-Tangent Distance and Tangent Propagation
Neural Networks: Tricks of the Trade, this book is an outgrowth of a 1996 NIPS workshop
On Affine Invariance in the Beltrami Framework for Vision
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
A Common Framework for Steerability, Motion Estimation and Invariant Feature Detection
A Common Framework for Steerability, Motion Estimation and Invariant Feature Detection
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We present a complete system of functionally independent invariants for Abelian Lie transformation groups acting on an image. The invariants are based on measurements, given by inner product of predesigned functions and the image. We build on steerable filters and adopt a Lie theoretical approach that is applicable to any dimensionality. A complete characterization of Lie measurement invariants of a general irreducible component of the group, termed block invariants, is provided. We show that invariants for the entire group can be taken as the union of the invariants of its components. The system is completed by deriving invariants between components of the group, termed cross invariants.