Two-dimensional imaging
A polynomial approach to linear algebra
A polynomial approach to linear algebra
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Applied numerical linear algebra
Applied numerical linear algebra
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Variational method for super-resolution optical flow
Signal Processing
Pyramid transform and scale-space analysis in image analysis
Proceedings of the 15th international conference on Theoretical Foundations of Computer Vision: outdoor and large-scale real-world scene analysis
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In this paper, we introduce a method to express a local linear operated in the neighbourhood of each point in the discrete space as a matrix transform. To derive matrix expressions, we develop a decomposition and construction method of the neighbourhood operations using algebraic properties of the noncommutative matrix ring. This expression of the transforms in image analysis clarifies analytical properties, such as the norm of the transforms. We show that the symmetry kernels for the neighbourhood operations have the symmetry matrix expressions.