Measurement of shaft diameters by machine vision

Guang Wei; Qingchang Tan

doi:10.1364/AO.50.003246

Measurement of shaft diameters by machine vision

Guang Wei and Qingchang Tan

Applied Optics
Vol. 50,
Issue 19,
pp. 3246-3253
(2011)
•https://doi.org/10.1364/AO.50.003246

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Guang Wei and Qingchang Tan, "Measurement of shaft diameters by machine vision," Appl. Opt. 50, 3246-3253 (2011)

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Related Topics
Table of Contents Category
- Image Processing
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Digital image processing (100.2000)
- Detection (120.1880)
- Industrial inspection (150.3040)

About this Article
History
- Original Manuscript: January 18, 2011
- Revised Manuscript: April 12, 2011
- Manuscript Accepted: May 4, 2011
- Published: June 24, 2011

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Abstract

A machine vision method for accurately measuring the diameters of cylindrical shafts is presented. Perspective projection and the geometrical features of cylindrical shafts are modeled in order to enable accurate measurement of shaft diameters. Some of the model parameters are determined using a shaft of known diameter. The camera model itself includes radial and tangential distortions terms. Experiments were used to measure the accuracy of the proposed method and the effect of the position of the camera relative to the shaft, as well as other factors.

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		Position $a_{1}$		Position $a_{2}$		Position $a_{3}$
Shafts	$D_{1} / mm$	$D / mm$	$Δ D / mm$	$D / mm$	$Δ D / mm$	$D / mm$	$Δ D / mm$
1	38.088	38.1025	0.0145	38.0951	0.0071	38.0982	0.0102
2	37.715	37.7274	0.0124	37.7204	0.0054	37.7231	0.0081
3	37.672	37.6858	0.0138	37.6776	0.0056	37.6688	0.0032
4	36.868	36.8805	0.0125	36.8686	0.0006	36.8730	0.0050
5	36.541	36.5495	0.0085	36.5403	0.0007	36.5444	0.0034
6	35.652	35.6580	0.0060	35.6537	0.0017	35.6535	0.0015
7	35.376	35.3837	0.0077	35.3793	0.0033	35.3815	0.0055
8	35.346	35.3556	0.0096	35.3430	0.0030	35.3523	0.0063
9	35.238	35.2510	0.0130	35.2418	0.0038	35.2511	0.0131
10	34.550	34.5545	0.0045	34.5409	0.0091	34.5389	0.0111
11	33.451	33.4441	0.0069	33.4393	0.0117	33.4435	0.0075
12	33.440	33.4300	0.0100	33.4285	0.0115	33.4323	0.0077
13	32.461	32.4537	0.0073	32.4503	0.0107	32.4487	0.0123
14	32.441	32.4410	0.0000	32.4314	0.0096	32.4283	0.0127
15	31.480	31.4780	0.0020	31.4681	0.0119	31.4741	0.0059
16	31.467	31.4590	0.0080	31.4537	0.0133	31.4559	0.0111
17	30.468	30.4628	0.0052	30.4544	0.0136	30.4665	0.0015
18	30.459	30.4540	0.0050	30.4467	0.0123	30.4600	0.0010
Mean error			0.0082		0.0075		0.0071

Shafts	$D_{1} / mm$	$D / mm$	$Δ D / mm$
1	33.346	33.3406	0.0054
2	32.957	32.9503	0.0067
3	32.320	32.3135	0.0065

Zhang	Heikkila	This Article
First $[\begin{matrix} x_{c} \\ y_{c} \\ z_{c} \end{matrix}] = R [\begin{matrix} x_{w} \\ y_{w} \\ z_{w} \end{matrix}] + t$	First $[\begin{matrix} x_{c} \\ y_{c} \\ z_{c} \end{matrix}] = R [\begin{matrix} x_{w} \\ y_{w} \\ z_{w} \end{matrix}] + t$	Fourth $[\begin{matrix} x_{c} \\ y_{c} \\ z_{c} \end{matrix}] = R [\begin{matrix} x_{w} \\ y_{w} \\ z_{w} \end{matrix}] + t$
Second $[\begin{matrix} x_{u} \\ y_{u} \end{matrix}] = \frac{1}{z_{c}} [\begin{matrix} x_{c} \\ y_{c} \end{matrix}]$	Second $[\begin{matrix} x_{u} \\ y_{u} \end{matrix}] = \frac{f}{z_{c}} [\begin{matrix} x_{c} \\ y_{c} \end{matrix}]$	Third $[\begin{matrix} x_{u} \\ y_{u} \end{matrix}] = \frac{1}{z_{c}} [\begin{matrix} x_{c} \\ y_{c} \end{matrix}]$
Third $[\begin{matrix} x_{d} \\ y_{d} \end{matrix}] = (1 + k_{1} r^{2} + k_{2} r^{4}) [\begin{matrix} x_{u} \\ y_{u} \end{matrix}]$ where $r = \sqrt{x_{u}^{2} + y_{u}^{2}}$	Third $[\begin{matrix} x_{u} \\ y_{u} \end{matrix}] = (1 + k_{1} r^{2} + k_{2} r^{4}) [\begin{matrix} x_{d} \\ y_{d} \end{matrix}] + [\begin{matrix} 2 p_{1} x_{d} y_{d} + (r^{2} + 2 x_{d}^{2}) \\ p_{1} (r^{2} + 2 y_{d}^{2}) + 2 p_{2} x_{d} y_{d} \end{matrix}]$ where $r = \sqrt{x_{d}^{2} + y_{d}^{2}}$	Second $[\begin{matrix} x_{u} \\ y_{u} \end{matrix}] = (1 + k_{1} r^{2} + k_{2} r^{4}) [\begin{matrix} x_{d} \\ y_{d} \end{matrix}] + [\begin{matrix} 2 p_{1} x_{d} y_{d} + p_{2} (r^{2} + 2 x_{d}^{2}) \\ p_{1} (r^{2} + 2 y_{d}^{2}) + 2 p_{2} x_{d} y_{d} \end{matrix}]$ where $r = \sqrt{x_{d}^{2} + y_{d}^{2}}$
Fourth $[\begin{matrix} x_{p} \\ y_{p} \\ 1 \end{matrix}] = [\begin{matrix} α & γ & c_{x} \\ 0 & β & c_{y} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} x_{d} \\ y_{d} \\ 1 \end{matrix}]$	Fourth $[\begin{matrix} x_{p} \\ y_{p} \\ 1 \end{matrix}] = [\begin{matrix} α / f & 0 & c_{x} \\ 0 & β / f & c_{y} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} x_{d} \\ y_{d} \\ 1 \end{matrix}]$	First $[\begin{matrix} x_{p} \\ y_{p} \\ 1 \end{matrix}] = [\begin{matrix} α & γ & c_{x} \\ 0 & β & c_{y} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} x_{d} \\ y_{d} \\ 1 \end{matrix}]$

		Position $a_{1}$		Position $a_{2}$		Position $a_{3}$
Shafts	$D_{1} / mm$	$D / mm$	$Δ D / mm$	$D / mm$	$Δ D / mm$	$D / mm$	$Δ D / mm$
1	38.088	38.1025	0.0145	38.0951	0.0071	38.0982	0.0102
2	37.715	37.7274	0.0124	37.7204	0.0054	37.7231	0.0081
3	37.672	37.6858	0.0138	37.6776	0.0056	37.6688	0.0032
4	36.868	36.8805	0.0125	36.8686	0.0006	36.8730	0.0050
5	36.541	36.5495	0.0085	36.5403	0.0007	36.5444	0.0034
6	35.652	35.6580	0.0060	35.6537	0.0017	35.6535	0.0015
7	35.376	35.3837	0.0077	35.3793	0.0033	35.3815	0.0055
8	35.346	35.3556	0.0096	35.3430	0.0030	35.3523	0.0063
9	35.238	35.2510	0.0130	35.2418	0.0038	35.2511	0.0131
10	34.550	34.5545	0.0045	34.5409	0.0091	34.5389	0.0111
11	33.451	33.4441	0.0069	33.4393	0.0117	33.4435	0.0075
12	33.440	33.4300	0.0100	33.4285	0.0115	33.4323	0.0077
13	32.461	32.4537	0.0073	32.4503	0.0107	32.4487	0.0123
14	32.441	32.4410	0.0000	32.4314	0.0096	32.4283	0.0127
15	31.480	31.4780	0.0020	31.4681	0.0119	31.4741	0.0059
16	31.467	31.4590	0.0080	31.4537	0.0133	31.4559	0.0111
17	30.468	30.4628	0.0052	30.4544	0.0136	30.4665	0.0015
18	30.459	30.4540	0.0050	30.4467	0.0123	30.4600	0.0010
Mean error			0.0082		0.0075		0.0071

Shafts	$D_{1} / mm$	$D / mm$	$Δ D / mm$
1	33.346	33.3406	0.0054
2	32.957	32.9503	0.0067
3	32.320	32.3135	0.0065

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