Projective rectification of infrared images from air-cooled condenser temperature measurement by using projection profile features and cross-ratio invariability

Lijun Xu; Lulu Chen; Xiaolu Li; Tao He

doi:10.1364/AO.53.006482

Applied Optics
Vol. 53,
Issue 28,
pp. 6482-6493
(2014)
•https://doi.org/10.1364/AO.53.006482

Projective rectification of infrared images from air-cooled condenser temperature measurement by using projection profile features and cross-ratio invariability

Lijun Xu, Lulu Chen, Xiaolu Li, and Tao He

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Lijun Xu, Lulu Chen, Xiaolu Li, and Tao He, "Projective rectification of infrared images from air-cooled condenser temperature measurement by using projection profile features and cross-ratio invariability," Appl. Opt. 53, 6482-6493 (2014)

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Abstract

In this paper, we propose a projective rectification method for infrared images obtained from the measurement of temperature distribution on an air-cooled condenser (ACC) surface by using projection profile features and cross-ratio invariability. In the research, the infrared (IR) images acquired by the four IR cameras utilized are distorted to different degrees. To rectify the distorted IR images, the sizes of the acquired images are first enlarged by means of bicubic interpolation. Then, uniformly distributed control points are extracted in the enlarged images by constructing quadrangles with detected vertical lines and detected or constructed horizontal lines. The corresponding control points in the anticipated undistorted IR images are extracted by using projection profile features and cross-ratio invariability. Finally, a third-order polynomial rectification model is established and the coefficients of the model are computed with the mapping relationship between the control points in the distorted and anticipated undistorted images. Experimental results obtained from an industrial ACC unit show that the proposed method performs much better than any previous method we have adopted. Furthermore, all rectified images are stitched together to obtain a complete image of the whole ACC surface with a much higher spatial resolution than that obtained by using a single camera, which is not only useful but also necessary for more accurate and comprehensive analysis of ACC performance and more reliable optimization of ACC operations.

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	Camera 1		Camera 2		Camera 3		Camera 4
Coefficients	$a_{i}$	$b_{i}$	$a_{i}$	$b_{i}$	$a_{i}$	$b_{i}$	$a_{i}$	$b_{i}$
1	$2.86 E + 01$	$5.14 E + 00$	$2.53 E + 01$	$- 8.40 E + 01$	$- 3.35 E + 00$	$4.98 E + 00$	$- 2.85 E + 00$	$- 7.53 E + 00$
2	$- 1.01 E - 01$	$1.00 E + 00$	$- 8.27 E - 02$	$8.92 E - 01$	$- 8.98 E - 03$	$9.98 E - 01$	$2.24 E - 02$	$9.95 E - 01$
3	$5.64 E - 10$	$- 1.37 E - 12$	$4.35 E - 09$	$- 5.05 E - 08$	$- 7.92 E - 11$	$- 4.02 E - 10$	$- 3.01 E - 10$	$2.46 E - 09$
4	$8.15 E - 01$	$- 7.15 E - 03$	$9.21 E - 01$	$3.15 E - 02$	$1.04 E + 00$	$4.47 E - 02$	$1.05 E + 00$	$7.82 E - 02$
5	$1.35 E - 04$	$1.66 E - 07$	$4.12 E - 05$	$4.28 E - 05$	$- 6.58 E - 05$	$- 1.48 E - 05$	$- 2.01 E - 04$	$5.19 E - 05$
6	$5.37 E - 05$	$- 4.54 E - 07$	$9.72 E - 05$	$4.98 E - 06$	$1.03 E - 04$	$4.21 E - 06$	$9.08 E - 05$	$7.31 E - 06$
7	$- 1.51 E - 13$	$4.15 E - 16$	$2.55 E - 14$	$1.72 E - 12$	$5.07 E - 14$	$2.56 E - 13$	$3.80 E - 13$	$1.11 E - 12$
8	$- 7.10 E - 13$	$1.55 E - 14$	$- 1.93 E - 12$	$- 2.37 E - 12$	$7.73 E - 14$	$- 1.76 E - 13$	$- 6.34 E - 13$	$2.82 E - 13$
9	$9.58 E - 09$	$- 4.46 E - 11$	$- 4.79 E - 09$	$1.47 E - 09$	$- 2.51 E - 08$	$- 1.33 E - 09$	$- 9.90 E - 09$	$1.93 E - 09$
10	$- 2.04 E - 08$	$1.68 E - 10$	$- 3.54 E - 08$	$- 2.26 E - 09$	$- 4.61 E - 08$	$- 1.83 E - 09$	$- 3.61 E - 08$	$- 3.09 E - 09$

Inclined Angles of Vertical Lines (degree)	$v_{1} (v_{1}^{'})$	$v_{2} (v_{2}^{'})$	$v_{3} (v_{3}^{'})$	$v_{4} (v_{4}^{'})$	$v_{5} (v_{5}^{'})$	$v_{6} (v_{6}^{'})$	$v_{7} (v_{7}^{'})$	$v_{8} (v_{8}^{'})$	$v_{9} (v_{9}^{'})$	$v_{10} (v_{10}^{'})$	$v_{11} (v_{11}^{'})$
$α_{v}$	78.98	79.06	79.98	80.06	80.99	80.99	82.00	82.00	83.02	83.02	84.04
$α_{v^{'}}$	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00
$e_{v}$	6.80	6.02	5.22	4.40	3.56	2.69	6.80	6.02	5.22	4.40	3.56
$e_{v^{'}}$	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

Inclined Angles of Horizontal Lines (degree)	$h_{1} (h_{1}^{'})$	$h_{2} (h_{2}^{'})$	$h_{3} (h_{3}^{'})$	$h_{4} (h_{4}^{'})$	$h_{5} (h_{5}^{'})$	$h_{6} (h_{6}^{'})$
$α_{h}$	6.80	6.02	5.22	4.40	3.56	2.69
$α_{h^{'}}$	$- 0.20$	$- 0.22$	$- 0.24$	$- 0.26$	$- 0.28$	$- 0.30$
$e_{h}$	6.80	6.02	5.22	4.40	3.56	2.69
$e_{h^{'}}$	0.20	0.22	0.24	0.26	0.28	0.30

Inclined Angles of Vertical Lines (degree)	$v_{1} (v_{1}^{'})$	$v_{2} (v_{2}^{'})$	$v_{3} (v_{3}^{'})$	$v_{4} (v_{4}^{'})$	$v_{5} (v_{5}^{'})$	$v_{6} (v_{6}^{'})$	$v_{7} (v_{7}^{'})$	$v_{8} (v_{8}^{'})$	$v_{9} (v_{9}^{'})$	$v_{10} (v_{10}^{'})$	$v_{11} (v_{11}^{'})$
$α_{v}$	96.98	96.98	96.03	96.03	95.01	93.98	93.03	92.07	90.96	90.00	89.04
$α_{v^{'}}$	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00
$e_{v}$	6.98	6.98	6.03	6.03	5.01	3.98	3.03	2.07	0.96	0.00	0.96
$e_{v^{'}}$	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

Inclined Angles of Horizontal Lines (degree)	$h_{1} (h_{1}^{'})$	$h_{2} (h_{2}^{'})$	$h_{3} (h_{3}^{'})$	$h_{4} (h_{4}^{'})$	$h_{5} (h_{5}^{'})$	$h_{6} (h_{6}^{'})$
$α_{h}$	4.09	3.92	3.74	3.56	3.37	3.18
$α_{h^{'}}$	$- 0.10$	$- 0.19$	$- 0.27$	$- 0.35$	$- 0.43$	$- 0.51$
$e_{h}$	4.09	3.92	3.74	3.56	3.37	3.18
$e_{h^{'}}$	0.10	0.19	0.27	0.35	0.43	0.51

Inclined Angles of Vertical Lines (degree)	$v_{1}^{'}$ ( $v_{1}^{''}$ )	$v_{2}^{'}$ ( $v_{2}^{''}$ )	$v_{3}^{'}$ ( $v_{3}^{''}$ )	$v_{4}^{'}$ ( $v_{4}^{''}$ )	$v_{5}^{'}$ ( $v_{5}^{''}$ )	$v_{6}^{'}$ ( $v_{6}^{''}$ )	$v_{7}^{'}$ ( $v_{7}^{''}$ )	$v_{8}^{'}$ ( $v_{8}^{''}$ )	$v_{9}^{'}$ ( $v_{9}^{''}$ )	$v_{10}^{'}$ ( $v_{10}^{''}$ )	$v_{11}^{'}$ ( $v_{11}^{''}$ )
$α_{v p g}$	86.97	86.97	86.97	86.97	86.02	88.01	88.01	86.97	86.97	88.96	88.96
$α_{v p p r}$	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00	90.00
$e_{v p g}$	3.03	3.03	3.03	3.03	3.98	1.99	1.99	3.03	3.03	1.04	1.04
$e_{v p p r}$	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

Inclined Angles of Horizontal Lines (degree)	$h_{1}^{'}$ ( $h_{1}^{''}$ )	$h_{2}^{'}$ ( $h_{2}^{''}$ )	$h_{3}^{'}$ ( $h_{3}^{''}$ )	$h_{4}^{'}$ ( $h_{4}^{''}$ )	$h_{5}^{'}$ ( $h_{5}^{''}$ )	$h_{6}^{'}$ ( $h_{6}^{''}$ )
$α_{h p g}$	0.18	$- 0.53$	0.35	$- 0.92$	$- 1.08$	$- 1.23$
$α_{h p p r}$	$- 0.70$	$- 0.50$	$- 0.31$	$- 0.11$	0.08	0.28
$e_{h p g}$	0.18	0.53	0.35	0.92	1.08	1.23
$e_{h p p r}$	0.70	0.50	0.31	0.11	0.08	0.28

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Applied Optics