Differentiation of discrete multidimensional signals

We describe the design of finite-size linear-phase separable kernels for differentiation of discrete multidimensional signals. The problem is formulated as an optimization of the rotation-invariance of the gradient operator, which results in a simultaneous constraint on a set of one-dimensional low-...

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Bibliographic Details
Published in:IEEE transactions on image processing 2004-04, Vol.13 (4), p.496-508
Main Authors: Farid, H., Simoncelli, E.P.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Biomedical imaging
Computer Simulation
Constraint optimization
Derivatives
Detection, estimation, filtering, equalization, prediction
Differential equations
Differentiation
Digital filters
Exact sciences and technology
Image edge detection
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image processing
Information Storage and Retrieval - methods
Information, signal and communications theory
Kernels
Lattices
Models, Statistical
Multidimensional systems
Numerical Analysis, Computer-Assisted
Numerical simulation
Operators
Optimization
Pattern Recognition, Automated
Prefilters
Reproducibility of Results
Sampling methods
Sensitivity and Specificity
Signal and communications theory
Signal Processing, Computer-Assisted
Signal sampling
Signal, noise
Stochastic Processes
Telecommunications and information theory
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Description
Summary:We describe the design of finite-size linear-phase separable kernels for differentiation of discrete multidimensional signals. The problem is formulated as an optimization of the rotation-invariance of the gradient operator, which results in a simultaneous constraint on a set of one-dimensional low-pass prefilter and differentiator filters up to the desired order. We also develop extensions of this formulation to both higher dimensions and higher order directional derivatives. We develop a numerical procedure for optimizing the constraint, and demonstrate its use in constructing a set of example filters. The resulting filters are significantly more accurate than those commonly used in the image and multidimensional signal processing literature.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2004.823819