Differentiation of Discrete Multi-Dimensional Signals
Published in:
IEEE Transactions on Image Processing
13(4): 496-508, April 2004.
© IEEE Signal Processing Society.
Short conference papers:
caip-97, icip-94
We describe the design of finite-size linear-phase separable kernels
for differentiation of discrete multi-dimensional 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 lowpass 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 multi-dimensional signal processing literature.
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