Approximate geodesic distance tree filter for cost aggregation

Yusheng Jin; Hong Zhao; Penghui Bu; Jiaxing Yan

doi:10.1364/AO.438830

Applied Optics
Vol. 60,
Issue 30,
pp. 9578-9586
(2021)
•https://doi.org/10.1364/AO.438830

Approximate geodesic distance tree filter for cost aggregation

Yusheng Jin, Hong Zhao, Penghui Bu, and Jiaxing Yan

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Yusheng Jin, Hong Zhao, Penghui Bu, and Jiaxing Yan, "Approximate geodesic distance tree filter for cost aggregation," Appl. Opt. 60, 9578-9586 (2021)

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Table of Contents Category
- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: July 26, 2021
- Revised Manuscript: September 10, 2021
- Manuscript Accepted: September 14, 2021
- Published: October 19, 2021

Abstract

The computation of the disparity for the pixels in the weak texture area has always been a difficult task in stereo vision. The non-local method based on a minimum spanning tree (MST) provides a solution to construct content-adaptive support regions to perform cost aggregation. However, it always introduces error disparity in slanted surfaces and is sensitive to noise and highly textural regions. The window-based methods are not effective for information dissemination. To overcome the problem mentioned above, this paper proposes an approximate geodesic distance tree filter, which utilizes geodesic distance as a pixels similarity metric and recursive techniques to perform the filtering process. The filtering process is performed recursively in four directions (namely from top-left, top-right, and vice versa), which make our filter with linear complexity. Our filter has advantages in the sense that: (1) the pixel similarity metric is approximated geodesic distance; (2) the computational complexity is linear to the image pixel. Due to these reasons, the proposed method can properly cope with cost aggregation in the textureless regions and preserve the boundary of disparity maps. We demonstrate the strength of our filter in several applications.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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	GF [1]	NL [19]	ST [22]	SMST
	(%)	(%)	(%)	[20] (%)	Our (%)
Tsukuba	${2.40}_{1}$	${2.48}_{2}$	${2.95}_{4}$	${3.08}_{5}$	${2.90}_{3}$
Venus	${1.24}_{3}$	${1.37}_{5}$	${1.34}_{4}$	${1.15}_{2}$	${0.89}_{1}$
Teddy	${7.06}_{3}$	${6.85}_{2}$	${8.26}_{5}$	${8.08}_{4}$	${5.73}_{1}$
Cones	${2.45}_{1}$	${4.11}_{4}$	${4.55}_{5}$	${3.98}_{3}$	${2.76}_{2}$
Aloe	${4.48}_{4}$	${4.82}_{5}$	$4 .4 6_{3}$	${3.64}_{1}$	${3.90}_{2}$
Baby1	${3.90}_{1}$	${7.99}_{5}$	$5 .2 3_{3}$	${5.29}_{4}$	${4.38}_{2}$
Baby2	${4.48}_{3}$	${13.48}_{4}$	$14 .5 3_{5}$	${4.04}_{2}$	${3.73}_{1}$
Baby3	${5.45}_{4}$	${5.18}_{2}$	$5 .5 7_{5}$	${5.30}_{3}$	${3.99}_{1}$
Bowling1	${14.78}_{3}$	${18.52}_{5}$	$15 . 8_{4}$	${14.77}_{2}$	${10.91}_{1}$
Bowling2	${6.16}_{2}$	${8.83}_{4}$	$9 .2 6_{5}$	${7.88}_{3}$	${5.25}_{1}$
Cloth1	${0.73}_{5}$	${0.71}_{4}$	$0 .6 9_{3}$	${0.19}_{1}$	${0.49}_{2}$
Cloth2	${2.76}_{3}$	${3.90}_{5}$	$2 .9 0_{4}$	${1.82}_{1}$	${1.91}_{2}$
Cloth3	${1.68}_{2}$	${2.38}_{4}$	$2 .0 9_{3}$	${1.08}_{1}$	${2.09}_{3}$
Cloth4	${1.32}_{2}$	${1.95}_{4}$	$1 .6 1_{3}$	${0.94}_{1}$	${1.32}_{2}$
Flowerpots	${11.56}_{2}$	${14.14}_{5}$	$12 .1 6_{3}$	${12.20}_{4}$	${8.54}_{1}$
Lampshade1	${21.73}_{5}$	${13.69}_{1}$	${22.31}_{4}$	${18.55}_{3}$	${14.07}_{2}$
Lampshade2	${11.91}_{5}$	${9.16}_{2}$	${9.63}_{3}$	${10.24}_{4}$	${7.97}_{1}$
Rocks1	${1.92}_{2}$	$2 .8 8_{5}$	$1 .8 0_{3}$	${1.26}_{1}$	${2.13}_{4}$
Rocks2	${1.11}_{3}$	${1.79}_{5}$	$1 .3 6_{4}$	${0.98}_{1}$	${1.05}_{2}$
Wood1	${3.80}_{2}$	${10.15}_{5}$	${3.92}_{3}$	${4.36}_{4}$	${3.01}_{1}$
Wood2	${2.26}_{1}$	${3.65}_{5}$	$2 .5 0_{2}$	${2.55}_{3}$	${2.59}_{4}$
Art	${8.33}_{2}$	${9.92}_{5}$	${9.03}_{4}$	${8.63}_{3}$	${7.54}_{1}$
Books	${8.58}_{1}$	${11.57}_{5}$	${9.76}_{4}$	${9.33}_{3}$	${9.23}_{2}$
Dolls	${4.21}_{2}$	${5.08}_{5}$	${4.26}_{3}$	${4.36}_{4}$	${3.39}_{1}$
Laundry	${15.26}_{5}$	${12.35}_{1}$	$13 .5 4_{3}$	${13.14}_{2}$	${14.46}_{4}$
Moebius	${8.87}_{5}$	${7.45}_{2}$	${7.92}_{3}$	${8.21}_{4}$	${7.36}_{1}$
Reindeer	${7.01}_{3}$	${10.81}_{5}$	${7.77}_{4}$	${6.89}_{2}$	${6.18}_{1}$
Avg. Error	${5.42}_{2}$	${7.23}_{5}$	${6.87}_{4}$	$5 .6 0_{3}$	${5.10}_{1}$

	Initial Disparity		Final Disparity
Method	Noc (%)	All (%)	Noc (%)	All (%)
GF [1]	5.42	17.09	5.07	11.05
NL [19]	7.23	17.99	6.89	12.08
ST [22]	6.87	17.16	6.08	11.90
SMST [20]	5.60	17.71	5.60	11.59
Our	5.10	17.32	4.77	10.75

	Initial Disparity		Final Disparity
Method	Noc (%)	All (%)	Noc (%)	All (%)
GF [1]	17.18	27.54	15.87	24.60
NL [19]	19.55	28.83	17.46	26.02
ST [22]	15.82	26.50	13.57	21.97
SMST [20]	15.39	25.84	12.95	21.50
Our	13.60	24.62	12.07	20.60

	GF [1]	NL [19]	ST [22]	SMST
	(%)	(%)	(%)	[20] (%)	Our (%)
Tsukuba	${2.40}_{1}$	${2.48}_{2}$	${2.95}_{4}$	${3.08}_{5}$	${2.90}_{3}$
Venus	${1.24}_{3}$	${1.37}_{5}$	${1.34}_{4}$	${1.15}_{2}$	${0.89}_{1}$
Teddy	${7.06}_{3}$	${6.85}_{2}$	${8.26}_{5}$	${8.08}_{4}$	${5.73}_{1}$
Cones	${2.45}_{1}$	${4.11}_{4}$	${4.55}_{5}$	${3.98}_{3}$	${2.76}_{2}$
Aloe	${4.48}_{4}$	${4.82}_{5}$	$4 .4 6_{3}$	${3.64}_{1}$	${3.90}_{2}$
Baby1	${3.90}_{1}$	${7.99}_{5}$	$5 .2 3_{3}$	${5.29}_{4}$	${4.38}_{2}$
Baby2	${4.48}_{3}$	${13.48}_{4}$	$14 .5 3_{5}$	${4.04}_{2}$	${3.73}_{1}$
Baby3	${5.45}_{4}$	${5.18}_{2}$	$5 .5 7_{5}$	${5.30}_{3}$	${3.99}_{1}$
Bowling1	${14.78}_{3}$	${18.52}_{5}$	$15 . 8_{4}$	${14.77}_{2}$	${10.91}_{1}$
Bowling2	${6.16}_{2}$	${8.83}_{4}$	$9 .2 6_{5}$	${7.88}_{3}$	${5.25}_{1}$
Cloth1	${0.73}_{5}$	${0.71}_{4}$	$0 .6 9_{3}$	${0.19}_{1}$	${0.49}_{2}$
Cloth2	${2.76}_{3}$	${3.90}_{5}$	$2 .9 0_{4}$	${1.82}_{1}$	${1.91}_{2}$
Cloth3	${1.68}_{2}$	${2.38}_{4}$	$2 .0 9_{3}$	${1.08}_{1}$	${2.09}_{3}$
Cloth4	${1.32}_{2}$	${1.95}_{4}$	$1 .6 1_{3}$	${0.94}_{1}$	${1.32}_{2}$
Flowerpots	${11.56}_{2}$	${14.14}_{5}$	$12 .1 6_{3}$	${12.20}_{4}$	${8.54}_{1}$
Lampshade1	${21.73}_{5}$	${13.69}_{1}$	${22.31}_{4}$	${18.55}_{3}$	${14.07}_{2}$
Lampshade2	${11.91}_{5}$	${9.16}_{2}$	${9.63}_{3}$	${10.24}_{4}$	${7.97}_{1}$
Rocks1	${1.92}_{2}$	$2 .8 8_{5}$	$1 .8 0_{3}$	${1.26}_{1}$	${2.13}_{4}$
Rocks2	${1.11}_{3}$	${1.79}_{5}$	$1 .3 6_{4}$	${0.98}_{1}$	${1.05}_{2}$
Wood1	${3.80}_{2}$	${10.15}_{5}$	${3.92}_{3}$	${4.36}_{4}$	${3.01}_{1}$
Wood2	${2.26}_{1}$	${3.65}_{5}$	$2 .5 0_{2}$	${2.55}_{3}$	${2.59}_{4}$
Art	${8.33}_{2}$	${9.92}_{5}$	${9.03}_{4}$	${8.63}_{3}$	${7.54}_{1}$
Books	${8.58}_{1}$	${11.57}_{5}$	${9.76}_{4}$	${9.33}_{3}$	${9.23}_{2}$
Dolls	${4.21}_{2}$	${5.08}_{5}$	${4.26}_{3}$	${4.36}_{4}$	${3.39}_{1}$
Laundry	${15.26}_{5}$	${12.35}_{1}$	$13 .5 4_{3}$	${13.14}_{2}$	${14.46}_{4}$
Moebius	${8.87}_{5}$	${7.45}_{2}$	${7.92}_{3}$	${8.21}_{4}$	${7.36}_{1}$
Reindeer	${7.01}_{3}$	${10.81}_{5}$	${7.77}_{4}$	${6.89}_{2}$	${6.18}_{1}$
Avg. Error	${5.42}_{2}$	${7.23}_{5}$	${6.87}_{4}$	$5 .6 0_{3}$	${5.10}_{1}$

	Initial Disparity		Final Disparity
Method	Noc (%)	All (%)	Noc (%)	All (%)
GF [1]	5.42	17.09	5.07	11.05
NL [19]	7.23	17.99	6.89	12.08
ST [22]	6.87	17.16	6.08	11.90
SMST [20]	5.60	17.71	5.60	11.59
Our	5.10	17.32	4.77	10.75

Abstract

Data Availability

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Figures (7)

Tables (4)

Equations (17)

Applied Optics