Fixed window aggregation AD-census algorithm for phase-based stereo matching

Shengming Zhang; Mingxiong Wu; Yanxue Wu; Gaoxu Wu; Fei Liu

doi:10.1364/AO.58.008950

Applied Optics
Vol. 58,
Issue 32,
pp. 8950-8958
(2019)
•https://doi.org/10.1364/AO.58.008950

Fixed window aggregation AD-census algorithm for phase-based stereo matching

Shengming Zhang, Mingxiong Wu, Yanxue Wu, Gaoxu Wu, and Fei Liu

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Shengming Zhang, Mingxiong Wu, Yanxue Wu, Gaoxu Wu, and Fei Liu, "Fixed window aggregation AD-census algorithm for phase-based stereo matching," Appl. Opt. 58, 8950-8958 (2019)

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Abstract

Phase-based stereo matching (PSM) is a vital step in binocular structured light. PSM is hard to strike a balance between efficiency and accuracy, especially because of the absolute phase matrix’s (APM) double data type. It means that PSM needs more run time and memory than conventional intensity images’ stereo matching. In this paper, we propose a modified absolute difference (AD)-Census algorithm called the fixed window aggregation AD-Census (FWA-AD-Census) to balance the contradiction between efficiency and accuracy in PSM. The FWA-AD-Census aggregates matching cost in a fixed support window instead of an adaptive support window in AD-Census. We analyze the reason why PSM is more suitable to aggregate the matching cost in a fixed support window. Simulations and experiments are conducted to verify the FWA-AD-Census’s performances by comparing the FWA-AD-Census with two other local stereo matching algorithms. One is the AD-Census, which is more accurate but less efficient. Its matching cost is aggregated in an adaptive support window. Another is the sum of absolute difference (SAD), which is more efficient but less accurate, and its matching cost is aggregated in a fixed support window. Theoretical analysis and experimental results both indicate that the proposed algorithm can achieve similar accuracy to the AD-Census with less run time.

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Comparison Item	APM	Intensity Image
Data range	(0, $2 π \times N$ ^a)	[0, 255]^b
Data type	Double	Int
Data variation trend	Monotonically increasing	Random
Texture	Blurred	Normal

	Values
Selected Points	Intensity Image	APM Image	APM
(1238, 780)	105	115	197.75
(1238, 797)	242	123	212.8143

		Computational Operation
Matching methods	Matching Process	ADD	Minus	Plus	Divide	ABS	Comparison	Hamming Distance	EXP
SAD	Matching cost computation	0	$N \times N$	0	0	$N \times N$	0	0	0
SAD	Matching cost aggregation	$N \times N$	0	0	0	0	0	0	0
AD-Census	Census transform	0	0	0	0	0	$n \times m$	0	0
	Calculating adaptive support windows	0	0	$4 ({L_{H}}^{2} + {L_{V}}^{2})$	0	$4 ({L_{H}}^{2} + {L_{V}}^{2})$	$4 ({L_{H}}^{2} + {L_{V}}^{2})$	0	0
	Matching cost computation	$(2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	$2 \times (2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	0	$2 \times (2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	$(2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	0	$(2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	$2 \times (2 L_{H} + 1)$ $\times (2 L_{V} + 1)$
	Matching cost aggregation	$(2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	0	$(2 L_{H} + 1)$ $\times (2 L_{V} + 1)$ ^a	0	0	0	0	0
FWA-AD-Census	Census transform	0	0	0	0	0	$n \times m$	0	0
	Calculating adaptive support windows	0	0	0	0	0	0	0	0
	Matching cost computation	$(2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	$2 \times (2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	0	$2 \times (2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	$(2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	0	$(2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	$2 \times (2 L_{H} + 1)$ $\times (2 L_{V} + 1)$
	Matching cost aggregation	$(2 L_{H} + 1)$ $\times (2 L_{V} + 1)$	0	0^a	0	0	0	0	0

Sl.no.	Item	Specifications
Manta G-505B camera	Sensor size	$2542 \times 2056$
	Sensor type	Sony ICX625 progressive scan
	Optical size	Type 2/3° CCD
	Pixel size	$3.45 µ m \times 3.45 µ m$
	Max. frame rate (at full resolution)	15 fps
	A/D	14 bit
	Bit depth	8 bit
Laptop	Operating system	Windows 10 Home Edition
		64-bit operating system
		x64-based processor
	Processor	Intel Core i5-8300H
	Processor speed	2.3 GHz
	System memory (RAM)	8 GB
	Total number of cores	8

PSM Algorithms	RMSE/mm
AD-Census	0.039
FWA-AD-Census	0.046
SAD	0.064

	Deviations Analysis
Matching Algorithms	Maximum Deviation/mm	Average Deviation/mm
AD-Census	+0.072/−0.068	+0.028/−0.028
FWA-AD-Census	+0.075/−0.068	+0.028/−0.028
SAD	+0.131/−0.160	+0.046/−0.046

Method	Parameters		Run Time/s ( $2056 \times 2452 \times 800$ )
AD-Census	$L_{H}$	17	330.992
	$L_{V}$	5
	$τ_{H}$	3
	$τ_{V}$	1
	$n \times m$	$7 \times 7$
FWA-AD-Census	$L_{H}$	17	188.168
	$L_{V}$	5
	$n \times m$	$7 \times 7$
SAD	$N \times N$	$17 \times 17$	32.12

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Applied Optics