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Differentiation of discrete multidimensional signals

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2 Author(s)
Farid, H. ; Comput. Sci. Dept., Dartmouth Coll., Hanover, NH, USA ; Simoncelli, E.P.

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.

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Image Processing, IEEE Transactions on  (Volume:13 ,  Issue: 4 )