Phase unwrapping algorithms for use in a true real-time optical body sensor system for use during radiotherapy

James Parkhurst; Gareth Price; Phil Sharrock; Christopher Moore

doi:10.1364/AO.50.006430

Applied Optics
Vol. 50,
Issue 35,
pp. 6430-6439
(2011)
•https://doi.org/10.1364/AO.50.006430

Phase unwrapping algorithms for use in a true real-time optical body sensor system for use during radiotherapy

James Parkhurst, Gareth Price, Phil Sharrock, and Christopher Moore

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James Parkhurst, Gareth Price, Phil Sharrock, and Christopher Moore, "Phase unwrapping algorithms for use in a true real-time optical body sensor system for use during radiotherapy," Appl. Opt. 50, 6430-6439 (2011)

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- Image Processing
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About this Article
History
- Original Manuscript: May 31, 2011
- Manuscript Accepted: September 6, 2011
- Published: December 2, 2011
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 7, Iss. 2

Abstract

An evaluation of the suitability of eight existing phase unwrapping algorithms to be used in a real-time optical body surface sensor based on Fourier fringe profilometry is presented. The algorithms are assessed on both the robustness of the results they give and their speed of execution. The algorithms are evaluated using four sets of real human body surface data, each containing five-hundred frames, obtained from patients undergoing radiotherapy, where fringe discontinuity is significant. We also present modifications to an existing algorithm, noncontinuous quality-guided path algorithm (NCQUAL), in order to decrease its execution time by a factor of 4 to make it suitable for use in a real-time system. The results obtained from the modified algorithm are compared with those of the existing algorithms. Three suitable algorithms were identified: two-stage noncontinuous quality-guided path algorithm (TSNCQUAL)—the modified algorithm presented here—for online processing and Flynn’s minimum discontinuity algorithm (FLYNN) and preconditioned conjugate gradient method (PCG) algorithms for enhanced accuracy in off-line processing.

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	Number of Discontinuities
	Dataset 1		Dataset 2		Dataset 3		Dataset 4		Total
Algorithm	Mean	Sdev	Mean	Sdev	Mean	Sdev	Mean	Sdev	Mean	Sdev of mean
gold	0	0.3	499	275	37	196	1399.5	542.4	483.9	651.3
qual	0	0.3	315.8	46.8	2.6	9.4	175.4	55.5	123.5	152.2
ncqual	0	0.3	302.1	40.1	2.6	9.2	169.3	86.1	118.5	145.8
tsncqual	0	0.2	302.3	40.1	2.6	9.2	169.2	86.1	118.5	145.8
mcut	0	0.3	499	275	37	196	1399.5	542.4	483.9	651.3
flynn	0.8	2	156.3	22.7	6.2	15.6	80.6	16.2	61	73.2
mgrid	16.1	32.8	449.2	139.6	54.4	80.4	164.1	67.7	170.9	195.8
pcg	0	0	309.5	41.3	1.9	8.7	79.8	10.5	97.8	146
lpnorm	0	0	361.5	105.4	1.8	8.5	86.3	26.5	112.4	170.9

	Percentage Area Unwrapped
	Dataset 1		Dataset 2		Dataset 3		Dataset 4		Total
Algorithm	Mean	Sdev	Mean	Sdev	Mean	Sdev	Mean	Sdev	Mean	Sdev of mean
gold	100	0	99.3	1	99.9	0.5	97.9	2.9	99.3	1.3
qual	100	0	99.6	0.1	100	0	99.7	0.3	99.8	0.1
ncqual	100	0	99.6	0	100	0	99.8	0.3	99.8	0.1
tsncqual	100	0	99.6	0	100	0	99.8	0.2	99.9	0.1
mcut	100	0	99.3	1	99.9	0.5	97.9	2.9	99.3	1.3
flynn	100	0	99.8	0	100	0	99.9	0	99.9	0
mgrid	99.6	2.3	99.2	1.7	99.1	2.1	99.2	1.6	99.3	0.3
pcg	100	0	99.6	0	100	0	99.9	0	99.9	0
lpnorm	100	0	99.6	0.1	100	0	99.9	0	99.9	0.1

	Execution Time (milliseconds)
Algorithm	Dataset 1	Dataset 2	Dataset 3	Dataset 4	Mean
gold	11.7	12.8	13.7	14.6	13.4
qual	57.8	85.7	76.1	77.9	80.5
ncqual	32.3	35.8	38.9	43.4	38.4
tsncqual	6.9	8.9	8.5	10.3	8.9
mcut	30.6	32.1	32.4	34.1	32.5
flynn	3083.8	2769.0	1616.0	1655.3	2007.8
mgrid	105.2	107.7	109.6	113.4	109.4
pcg	591.9	594.7	596.5	601.2	596.5
lpnorm	5404.1	5412.5	5365.2	5368.5	5383.3

	Number of Discontinuities
	Dataset 1		Dataset 2		Dataset 3		Dataset 4		Total
Algorithm	Mean	Sdev	Mean	Sdev	Mean	Sdev	Mean	Sdev	Mean	Sdev of mean
gold	0	0.3	499	275	37	196	1399.5	542.4	483.9	651.3
qual	0	0.3	315.8	46.8	2.6	9.4	175.4	55.5	123.5	152.2
ncqual	0	0.3	302.1	40.1	2.6	9.2	169.3	86.1	118.5	145.8
tsncqual	0	0.2	302.3	40.1	2.6	9.2	169.2	86.1	118.5	145.8
mcut	0	0.3	499	275	37	196	1399.5	542.4	483.9	651.3
flynn	0.8	2	156.3	22.7	6.2	15.6	80.6	16.2	61	73.2
mgrid	16.1	32.8	449.2	139.6	54.4	80.4	164.1	67.7	170.9	195.8
pcg	0	0	309.5	41.3	1.9	8.7	79.8	10.5	97.8	146
lpnorm	0	0	361.5	105.4	1.8	8.5	86.3	26.5	112.4	170.9

	Percentage Area Unwrapped
	Dataset 1		Dataset 2		Dataset 3		Dataset 4		Total
Algorithm	Mean	Sdev	Mean	Sdev	Mean	Sdev	Mean	Sdev	Mean	Sdev of mean
gold	100	0	99.3	1	99.9	0.5	97.9	2.9	99.3	1.3
qual	100	0	99.6	0.1	100	0	99.7	0.3	99.8	0.1
ncqual	100	0	99.6	0	100	0	99.8	0.3	99.8	0.1
tsncqual	100	0	99.6	0	100	0	99.8	0.2	99.9	0.1
mcut	100	0	99.3	1	99.9	0.5	97.9	2.9	99.3	1.3
flynn	100	0	99.8	0	100	0	99.9	0	99.9	0
mgrid	99.6	2.3	99.2	1.7	99.1	2.1	99.2	1.6	99.3	0.3
pcg	100	0	99.6	0	100	0	99.9	0	99.9	0
lpnorm	100	0	99.6	0.1	100	0	99.9	0	99.9	0.1

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