A generalized L2-spline filter

Dariusz Janecki

doi:10.1016/j.measurement.2009.01.020

A generalized L2-spline filter

2009-07-01

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Dariusz Janecki *

DOI：10.1016/j.measurement.2009.01.020

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This paper presents a generalization of the L-2-spline filter developed by Krystek [M. Krystek, Form filtering by splines, Measurement 18 (1996) 9-15]. Here, we assume that the distance between the spline nodes is much bigger than the profile sampling interval. Owing to this, the conditioning factor of the equations applied to determine the filter parameters does not depend on the sampling interval, and the number of such equations is relatively small. If the functional defining the spline parameters does not include the penalty for curve bending energy, the interval between the spline nodes should be exactly twice as small as the desired cutoff wavelength. If the cost of the bending energy is taken into account, we obtain a filter that is practically time-invariant for a case when the distance between the nodes is equal to one sixth of the cutoff wavelength. In this case, the filter frequency transmission characteristic is almost the same as the one proposed by Krystek. The analyzed spline filter is able to reduce the edge effect significantly. (C) 2009 Elsevier Ltd. All rights reserved.

Keyword:

Spline filter

Mean line

Edge effect

Transmission characteristic

A generalized L2-spline filter

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