A theoretical insight into morphological operations in surface measurement by introducing the slope transform
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Shan Lou, Xiang-qian Jiang, Wen-han Zeng, Paul J. Scott. A theoretical insight into morphological operations in surface measurement by introducing the slope transform[J]. Journal of Zhejiang University Science A, 2015, 16(5): 395-403.
@article{title="A theoretical insight into morphological operations in surface measurement by introducing the slope transform",
author="Shan Lou, Xiang-qian Jiang, Wen-han Zeng, Paul J. Scott",
journal="Journal of Zhejiang University Science A",
volume="16",
number="5",
pages="395-403",
year="2015",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1400223"
}
%0 Journal Article
%T A theoretical insight into morphological operations in surface measurement by introducing the slope transform
%A Shan Lou
%A Xiang-qian Jiang
%A Wen-han Zeng
%A Paul J. Scott
%J Journal of Zhejiang University SCIENCE A
%V 16
%N 5
%P 395-403
%@ 1673-565X
%D 2015
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1400223
TY - JOUR
T1 - A theoretical insight into morphological operations in surface measurement by introducing the slope transform
A1 - Shan Lou
A1 - Xiang-qian Jiang
A1 - Wen-han Zeng
A1 - Paul J. Scott
J0 - Journal of Zhejiang University Science A
VL - 16
IS - 5
SP - 395
EP - 403
%@ 1673-565X
Y1 - 2015
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1400223
Abstract: As one of the tools for surface analysis, morphological operations, although not as popular as linear convolution operations (e.g., the Gaussian filter), are really useful in mechanical surface reconstruction, surface filtration, functional simulation, etc. By introducing the slope transform originally developed for signal processing into the field of surface metrology, an analytic capability is gained for morphological operations, paralleling that of the Fourier transform in the context of linear convolution. Using the slope transform, the tangential dilation is converted into the addition in the slope domain, just as by the Fourier transform, the convolution switches into the multiplication in the frequency domain. Under the theory of the slope transform, the slope and curvature changes of the structuring element to the operated surface can be obtained, offering a deeper understanding of morphological operations in surface measurement. The analytical solutions to the tangential dilation of a sine wave and a disk by a disk are derived respectively. An example of the discretized tangential dilation of a sine wave by the disks with two different radii is illustrated to show the consistency and distinction between the tangential dilation and the classical dilation.
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CLC number: TB9; TG8
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2015-04-15
Cited: 0
Clicked: 7584
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