In this Letter, we report on high-contrast gradient ghost imaging (GGI) through dynamic and complex scattering media for edge detection. By introducing a reference beam in the designed setup to correct dynamic change of scaling factors induced by dynamic and complex scattering media, the mismatches between illumination patterns and single-pixel intensity measurements can be corrected. Then, edge information of a sample can be obtained through dynamic and complex scattering media with dual single-pixel detections. The proposed scheme can implement direct edge detection without any postprocessing. It is experimentally verified that the proposed method can realize high-contrast GGI of unknown objects through various dynamic and complex scattering media where conventional schemes cannot work. Our experimental results suggest that the proposed method broadens and deepens the GGI, offering a potential for edge detection in diverse applications.

Topics
Optical scattering, Optoelectronic applications, Laser imaging, Lasers, Scattering problem

Ghost imaging has become a strong competitor over some imaging methods, which depend on a pixelated sensor array (e.g., charge-coupled device) in some situations. Owing to characteristics of single-pixel detectors (e.g., large bandwidth and high sensitivity), ghost imaging turns out to be one of the advanced imaging methods.1–5 By using structured illumination and synchronous intensity measurements, ghost imaging can retrieve unknown objects in turbulent or harsh environments.6–8 Ghost imaging has been developed in diverse fields9–13 such as time-resolved imaging and three-dimensional imaging.

Recently, research on edge detection with ghost imaging is being conducted. Edge detection is a fundamental step of human vision perception, which detects peripheries of objects.14,15 Nowadays, edge detection has been widely applied in object recognition, medical diagnosis and safety inspection, etc.16–18 For many edge detection schemes, objects should be retrieved before the differential operators (e.g., Sobel, Canny, and Roberts operators).19–21 Hence, traditional techniques are usually developed based on the premise of clear reconstructions of objects, imposing a limitation on broad applications of edge detection in turbulent or complex scattering environments.22,23 To benefit from ghost imaging for seeing through disturbance, edge detection with ghost imaging has been applied. Liu et al.24 reported that edge information of unknown objects can be detected in a gradient domain using ghost imaging. There is an explosion of ghost imaging-based edge detection schemes such as speckle-shifting ghost imaging, subpixel-speckle-shifting ghost imaging, and joint iteration ghost imaging.25–28 In addition, it has been verified that object edges can be detected in the Fourier domain with differential operators.29 Apart from edge detection of amplitude objects, edge information of phase objects can also be extracted by using single-pixel spiral phase contrast imaging.30 Although progress has been made in ghost imaging-based edge detection, its capability is not sufficient to implement effective edge detection of unknown objects through dynamic and complex scattering media. Since dynamic and complex scattering media lead to dynamic change of scaling factors, it could be impossible for conventional ghost imaging-based edge detection methods to maintain a consistency of illumination patterns and single-pixel intensity measurements. This inconsistency leads to a failure of ghost imaging-based edge detection of unknown objects through dynamic and complex scattering media.

Here, we report a scheme to detect edge information of unknown objects through dynamic and complex scattering media using dual single-pixel detectors. By introducing a reference beam in the designed setup to correct dynamic change of scaling factors, the mismatches between illumination patterns and intensity measurements can be corrected. Then, edge information of unknown objects can be directly detected through dynamic and complex scattering media without any prior information of unknown objects. It is experimentally demonstrated that the proposed method can implement high-contrast edge detection of unknown objects through various dynamic and complex scattering media where conventional ghost imaging-based edge detection methods cannot work. In addition, the number of measurements is not needed to be increased in the proposed method owing to the setup design with dual single-pixel detectors, when edge detection through dynamic and complex scattering media is conducted. This scheme paves a way for edge detection based on ghost imaging through dynamic and complex scattering media.

To realize high-contrast edge detection through dynamic and complex scattering media, a schematic experimental setup with dual single-pixel detectors is shown in Fig. 1. A green laser beam (532.0 nm, CrystaLaser CL-2000) with a power of 25.0 mW is expanded and then collimated to illuminate an amplitude-only spatial light modulator (SLM, Holoeye LC-R720, reflective) with a pixel size of 20.0 μm. The illumination patterns and gradient patterns with 128 × 128 pixels are sequentially and alternately embedded into SLM. Then, the laser beam is modulated and reflected by the SLM. To correct dynamic change of scaling factors, the modulated laser beam is divided into two beams (i.e., a reference beam and an object beam) via a beam splitter cube. The object beam illuminates a sample before passing through dynamic and complex scattering media. The reference beam without any interaction with the sample directly passes through dynamic and complex scattering media. The dynamic and complex scattering media are designed by continuously dropping a certain volume of milk into a transparent water tank [dimensions of 10.0 (L) × 30.0 (W) × 30.0 cm3 (H)], which contains 6000 ml pure water. Here, 1000 ml pure water is first placed into a funnel, and then different volumes of full cream milk are directly added into the funnel in each experiment. In addition, a stirrer with a maximum speed of 1200 revolutions per minute (rpm) is applied to generate dynamic and complex scattering media. Then, light intensities of the object and reference beams propagating through dynamic and complex scattering media are collected by single-pixel detectors (Thorlabs, PDA100A2). For synchronous single-pixel intensity measurements, a data acquisition device (Smacq, USB-5210) and a purpose-built Labview program are used to synchronize and control the SLM and single-pixel detectors. Then, dynamic change of scaling factors aroused by dynamic and complex scattering media is corrected. Finally, edge detection of the unknown objects through dynamic and complex scattering media can be effectively and directly implemented with the corrected scaling factors.

FIG. 1.
A schematic experimental setup for the proposed edge detection through dynamic and complex scattering media with dual single-pixel detectors. SLM, spatial light modulator; D1 and D2, single-pixel bucket detectors; BS, beam splitter cube; O, object.
View largeDownload slide

A schematic experimental setup for the proposed edge detection through dynamic and complex scattering media with dual single-pixel detectors. SLM, spatial light modulator; D1 and D2, single-pixel bucket detectors; BS, beam splitter cube; O, object.

FIG. 1.
A schematic experimental setup for the proposed edge detection through dynamic and complex scattering media with dual single-pixel detectors. SLM, spatial light modulator; D1 and D2, single-pixel bucket detectors; BS, beam splitter cube; O, object.
View largeDownload slide

A schematic experimental setup for the proposed edge detection through dynamic and complex scattering media with dual single-pixel detectors. SLM, spatial light modulator; D1 and D2, single-pixel bucket detectors; BS, beam splitter cube; O, object.

Close modal
Figure 2 shows the proposed edge detection through dynamic and complex scattering media. The illumination pattern (Pi) and the corresponding gradient pattern (Pig) are sequentially and alternately embedded into SLM, and the relationship between Pi and Pig is given by25 
P i g ( x m − 1 , y n − 1 ) = P i ( x m , y n ) ,   i = 1 , 2 , 3 , … , 20   000 ,
(1)
where m and n denote an integer ranging from 2 to 128. To detect edge information of unknown object (O) in x and y directions, gradient patterns used in the experimental setup are shifted with one pixel and a gradient vector of 45°. It is worth noting that the gradient vector and the number of shifted pixels can be flexibly selected and designed. Then, the light modulated by Pi or Pig is divided into object and reference beams. When the ith illumination pattern Pi is used, light intensities Bi and Bir recorded by single-pixel detectors in the object and reference beam paths can be, respectively, described by
B i = k ̃ i ∑ ( x , y ) P i O ,
(2)
B i r = k i ∑ ( x , y ) P i ,
(3)
where k ̃ i and k i⁠, respectively, denote scaling factors in the object and reference beam paths when Pi is used. Subsequently, the ith gradient pattern Pig is used, and light intensities Big and Bigr recorded by single-pixel detectors in the object and reference beam paths can be, respectively, described by
B i g = k ̃ i g ∑ P i g O ,
(4)
B igr = k i g ∑ P i g ,
(5)
where k ̃ i g and k i g⁠, respectively, denote scaling factors in the object and reference beam paths when Pig is used. It is found that scaling factors for Pi and Pig are varied when the scattering environment is dynamic and complex. This is the reason why conventional gradient ghost imaging (GGI) is ineffective for edge detection through dynamic and complex scattering media. Hence, it is crucial and necessary to correct scaling factors for each recording using dual single-pixel detectors. In the proposed scheme, there are two reasonable assumptions when the separation distance between two beams is short, respectively, given by
k ̃ i ≈ k i ,
(6)
k ̃ i g ≈ k i g .
(7)
FIG. 2.
A schematic of the proposed edge detection through dynamic and complex scattering media. Pi, the ith illumination pattern; Pig, the ith gradient pattern; DCSM, dynamic and complex scattering media; Bi and Bir, single-pixel intensity values recorded in object and reference beam paths with the ith illumination pattern Pi, respectively; Big and Bigr, single-pixel intensity values recorded in object and reference beam paths with the ith gradient pattern Pig, respectively; Bic and Bigc, corrected single-pixel intensities correspond to the ith illumination pattern Pi and the ith gradient pattern Pig; ∇O, the retrieved edge.
View largeDownload slide

A schematic of the proposed edge detection through dynamic and complex scattering media. Pi, the ith illumination pattern; Pig, the ith gradient pattern; DCSM, dynamic and complex scattering media; Bi and Bir, single-pixel intensity values recorded in object and reference beam paths with the ith illumination pattern Pi, respectively; Big and Bigr, single-pixel intensity values recorded in object and reference beam paths with the ith gradient pattern Pig, respectively; Bic and Bigc, corrected single-pixel intensities correspond to the ith illumination pattern Pi and the ith gradient pattern Pig; ∇O, the retrieved edge.

FIG. 2.
A schematic of the proposed edge detection through dynamic and complex scattering media. Pi, the ith illumination pattern; Pig, the ith gradient pattern; DCSM, dynamic and complex scattering media; Bi and Bir, single-pixel intensity values recorded in object and reference beam paths with the ith illumination pattern Pi, respectively; Big and Bigr, single-pixel intensity values recorded in object and reference beam paths with the ith gradient pattern Pig, respectively; Bic and Bigc, corrected single-pixel intensities correspond to the ith illumination pattern Pi and the ith gradient pattern Pig; ∇O, the retrieved edge.
View largeDownload slide

A schematic of the proposed edge detection through dynamic and complex scattering media. Pi, the ith illumination pattern; Pig, the ith gradient pattern; DCSM, dynamic and complex scattering media; Bi and Bir, single-pixel intensity values recorded in object and reference beam paths with the ith illumination pattern Pi, respectively; Big and Bigr, single-pixel intensity values recorded in object and reference beam paths with the ith gradient pattern Pig, respectively; Bic and Bigc, corrected single-pixel intensities correspond to the ith illumination pattern Pi and the ith gradient pattern Pig; ∇O, the retrieved edge.

Close modal
By applying Eqs. (6) and (7), corrected single-pixel intensity values (i.e., Bic and Bigc) corresponding to Pi and Pig in the object beam path are, respectively, given by
∑ P i O = B i c = B i B i r ∑ P i ,
(8)
∑ P i g O = B igc = B i g B igr ∑ P i g .
(9)
By subtracting Eqs. (8) and (9), we can have
∇ B i = B i c − B igc = ∑ P i O − ∑ P i g O → ∑ P i O − ∑ P i O g = ∑ P i ∇ O = B i B i r ∑ P i − B i g B igr ∑ P i g ,
(10)
where Og denotes the virtually shifted object and ∇ O denotes edge information. It is worth mentioning that the shift of the illumination pattern from Pi to Pig is equivalent to a shift of the object from O to Og. As can be seen in Eq. (10), edge information ∇ O is related to ∇ B i⁠. Edge detection through dynamic and complex scattering media can be conducted by using a rectified second-order correlation algorithm described by
∇ O = ⟨ P i ∇ B i ⟩ − ⟨ P i ⟩ ⟨ ∇ B i ⟩ = ⟨ P i ( B i B i r ∑ P i − B i g B igr ∑ P i g ) ⟩ − ⟨ P i ⟩ ⟨ B i B i r ∑ P i − B i g B igr ∑ P i g ⟩ ,
(11)
where ⟨ ⋯ ⟩ denotes an ensemble average over the total number of measurements. By introducing a reference beam to correct dynamic change of scaling factors, the mismatches between illumination patterns and single-pixel intensity measurements can be corrected. In this way, edge information of the unknown object can be effectively obtained through dynamic and complex scattering media without any prior information about the object. It is worth noting that Eq. (11) is applicable to detect edge information of unknown objects in various scattering environments.

Figure 3 shows the retrieved edges of a 3D-printed plastic sample using conventional GGI and the proposed method with the different number of measurements. The dynamic and complex scattering environment is formed by 6-ml full cream milk continuously dropped into water tank and a stirrer at 700 rpm. Without usage of the reference beam, conventional GGI cannot retrieve any effective edge information of unknown object through dynamic and complex scattering media as shown in Figs. 3(a)–3(e) and 3(k)–3(o). Instead, the proposed method can correct scaling factors aroused by dynamic and complex scattering media with dual single-pixel detectors. Then, outline profiles of the object can be effectively revealed as shown in Figs. 3(f)–3(j) and 3(p)–3(t). When the number of intensity measurements by each single-pixel detector increases from 2000 to 20 000 with an interval of 2000, edges of unknown object can be more clearly observed. Hence, it is experimentally verified that corrections of scaling factors play an important role in edge detection of unknown objects through dynamic and complex scattering media.

FIG. 3.
Edges obtained by conventional GGI (without reference beam) and the proposed method through complex scattering media with the different number of measurements (2000–20 000 with an interval of 2000). (a)–(e) and (k)–(o) The retrieved edges by conventional GGI, and (f)–(j) and (p)–(t) the retrieved edges by the proposed method. Scale bar in (t) for 3D-printed samples: 2 mm.
View largeDownload slide

Edges obtained by conventional GGI (without reference beam) and the proposed method through complex scattering media with the different number of measurements (2000–20 000 with an interval of 2000). (a)–(e) and (k)–(o) The retrieved edges by conventional GGI, and (f)–(j) and (p)–(t) the retrieved edges by the proposed method. Scale bar in (t) for 3D-printed samples: 2 mm.

FIG. 3.
Edges obtained by conventional GGI (without reference beam) and the proposed method through complex scattering media with the different number of measurements (2000–20 000 with an interval of 2000). (a)–(e) and (k)–(o) The retrieved edges by conventional GGI, and (f)–(j) and (p)–(t) the retrieved edges by the proposed method. Scale bar in (t) for 3D-printed samples: 2 mm.
View largeDownload slide

Edges obtained by conventional GGI (without reference beam) and the proposed method through complex scattering media with the different number of measurements (2000–20 000 with an interval of 2000). (a)–(e) and (k)–(o) The retrieved edges by conventional GGI, and (f)–(j) and (p)–(t) the retrieved edges by the proposed method. Scale bar in (t) for 3D-printed samples: 2 mm.

Close modal
Figure 4 shows a comparison of quality of the retrieved edges quantified by visibility31,32 as a function of the different number of measurements by each single-pixel detector as given by
visibility = ⟨ I s ⟩ − ⟨ I b ⟩ ⟨ I s ⟩ + ⟨ I b ⟩ ,
(12)
where Is and Ib, respectively, denote intensity distributions in the signal part and the background part. The signal part corresponds to the retrieved edge, and the background part corresponds to a region without effective information about the sample. The average intensity is denoted as ⟨Is⟩ and ⟨Ib⟩. Sharp changes of pixel values in the retrieved edge can be defined and identified for the calculation of visibility. For conventional GGI without the reference beam, when the number of measurements increases from 2000 to 20 000, visibility of the retrieved edges remains steady, i.e., ∼0. Experimental results in Fig. 4 quantitatively demonstrate its serious deficiency in edge detection through dynamic and complex scattering media. For the proposed method, visibility of the retrieved edges is enhanced from 0.1 to ∼0.45 with increased measurements as shown in Fig. 4. Since the influence of scaling factors has been eliminated with the designed optical setup, the proposed method works effectively for edge detection of unknown objects through dynamic and complex scattering media.
FIG. 4.
Influence of the different number of measurements (by each single-pixel detector) on the visibility of edges obtained by using conventional GGI (without reference beam) and the proposed method.
View largeDownload slide

Influence of the different number of measurements (by each single-pixel detector) on the visibility of edges obtained by using conventional GGI (without reference beam) and the proposed method.

FIG. 4.
Influence of the different number of measurements (by each single-pixel detector) on the visibility of edges obtained by using conventional GGI (without reference beam) and the proposed method.
View largeDownload slide

Influence of the different number of measurements (by each single-pixel detector) on the visibility of edges obtained by using conventional GGI (without reference beam) and the proposed method.

Close modal

We also apply the proposed method for testing other samples, e.g., samples in Fig. 5. In addition, Group –1, Group 0, and Group 1 of USAF 1951 resolution target (Thorlabs, R3L3S1N) have been tested. Without corrections of scaling factors induced by dynamic and complex scattering media, conventional GGI cannot retrieve edge information about the samples as shown in Figs. 5(a)–5(e) and 5(k)–5(o). For the proposed method, outlines of unknown objects can be clearly recognized as shown in Figs. 5(f)–5(j) and 5(p)–5(t). It is also found that edges of the bars in the resolution target can be distinguished as shown in Figs. 5(r)–5(t), and the finest structure that can be identified in the retrieved edges of the resolution target is Element 4 of Group 1 (176.78 μm) in Fig. 5(t). Hence, it is experimentally verified that the proposed method manifests good performance in high-contrast edge detection through various dynamic and complex scattering media where conventional methods cannot work. Owing to dual single-pixel detections used in the proposed method, influence of dynamic changes of scaling factors is eliminated.

FIG. 5.
Edges of the samples retrieved by conventional GGI and the proposed method through dynamic and complex scattering media. The dynamic and complex scattering media for these samples are, respectively, formed by dropping different volumes of full cream milk (i.e., 6, 5, 6, 4, 3, 4, 6, 6, 5, and 4 ml) into water tank and the stirrer at different speeds (i.e., 800, 700, 800, 700, 600, 600, 800, 600, 800, and 700 rpm). (a)–(e) and (k)–(o) The edges retrieved by conventional GGI, and (f)–(j) and (p)–(t) edges retrieved by the proposed method. Here, the number of measurements in each detector is 20 000.
View largeDownload slide

Edges of the samples retrieved by conventional GGI and the proposed method through dynamic and complex scattering media. The dynamic and complex scattering media for these samples are, respectively, formed by dropping different volumes of full cream milk (i.e., 6, 5, 6, 4, 3, 4, 6, 6, 5, and 4 ml) into water tank and the stirrer at different speeds (i.e., 800, 700, 800, 700, 600, 600, 800, 600, 800, and 700 rpm). (a)–(e) and (k)–(o) The edges retrieved by conventional GGI, and (f)–(j) and (p)–(t) edges retrieved by the proposed method. Here, the number of measurements in each detector is 20 000.

FIG. 5.
Edges of the samples retrieved by conventional GGI and the proposed method through dynamic and complex scattering media. The dynamic and complex scattering media for these samples are, respectively, formed by dropping different volumes of full cream milk (i.e., 6, 5, 6, 4, 3, 4, 6, 6, 5, and 4 ml) into water tank and the stirrer at different speeds (i.e., 800, 700, 800, 700, 600, 600, 800, 600, 800, and 700 rpm). (a)–(e) and (k)–(o) The edges retrieved by conventional GGI, and (f)–(j) and (p)–(t) edges retrieved by the proposed method. Here, the number of measurements in each detector is 20 000.
View largeDownload slide

Edges of the samples retrieved by conventional GGI and the proposed method through dynamic and complex scattering media. The dynamic and complex scattering media for these samples are, respectively, formed by dropping different volumes of full cream milk (i.e., 6, 5, 6, 4, 3, 4, 6, 6, 5, and 4 ml) into water tank and the stirrer at different speeds (i.e., 800, 700, 800, 700, 600, 600, 800, 600, 800, and 700 rpm). (a)–(e) and (k)–(o) The edges retrieved by conventional GGI, and (f)–(j) and (p)–(t) edges retrieved by the proposed method. Here, the number of measurements in each detector is 20 000.

Close modal

In conclusion, we have reported a scheme for high-contrast edge detection through dynamic and complex scattering media in ghost imaging. By using dual single-pixel detectors, the influence of dynamic scaling factors induced by dynamic and complex scattering media is eliminated. Then, high-contrast edge detection can be implemented by using the proposed method through dynamic and complex scattering media where conventional GGI cannot work. Furthermore, the proposed method allows direct edge detection of unknown objects without any postprocessing. This scheme is expected to pave a way for directly detecting the edges of unknown objects through dynamic and complex scattering media. Our scheme provides a significant step for the GGI and also remains an exciting avenue for the further research. In terms of imaging efficiency, we can refine the method to realize efficient edge detection by optimizing the number of realizations.33 The positions of the sample and scattering media in the optical channel can also be investigated in the future study.

This work was supported by the Hong Kong Research Grants Council (Nos. C5011-19G, 15224921, and 15223522) and the Hong Kong Polytechnic University (Nos. 1-BD4Q, 1-W167, and 1-W19E).

The authors have no conflicts to disclose.

Lina Zhou: Conceptualization (lead); Investigation (lead); Writing – original draft (lead). Yin Xiao: Investigation (supporting). Wen Chen: Conceptualization (lead); Methodology (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
N.
Horiuchi
,
Nat. Photonics
7
,
943
(
2013
).
https://doi.org/10.1038/nphoton.2013.325
Crossref
Search ADS
 
2.
S.
Li
,
F.
Cropp
,
K.
Kabra
,
T. J.
Lane
,
G.
Wetzstein
,
P.
Musumeci
, and
D.
Ratner
,
Phys. Rev. Lett.
121
,
114801
(
2018
).
https://doi.org/10.1103/PhysRevLett.121.114801
Crossref
Search ADS
PubMed
 
3.
M.
Sun
,
M. P.
Edgar
,
G. M.
Gibson
,
B.
Sun
,
N.
Radwell
,
R.
Lamb
, and
M. J.
Padgett
,
Nat. Commun.
7
,
12010
(
2016
).
https://doi.org/10.1038/ncomms12010
Crossref
Search ADS
PubMed
 
4.
D.
Pelliccia
,
A.
Rack
,
M.
Scheel
,
V.
Cantelli
, and
D. M.
Paganin
,
Phys. Rev. Lett.
117
,
113902
(
2016
).
https://doi.org/10.1103/PhysRevLett.117.113902
Crossref
Search ADS
PubMed
 
5.
Y.
Bromberg
,
O.
Katz
, and
Y.
Silberberg
,
Phys. Rev. A
79
,
053840
(
2009
).
https://doi.org/10.1103/PhysRevA.79.053840
Crossref
Search ADS
 
6.
J. H.
Shapiro
,
Phys. Rev. A
78
,
061802
(
2008
).
https://doi.org/10.1103/PhysRevA.78.061802
Crossref
Search ADS
 
7.
N. D.
Hardy
 and
J. H.
Shapiro
,
Phys. Rev. A
84
,
063824
(
2011
).
https://doi.org/10.1103/PhysRevA.84.063824
Crossref
Search ADS
 
8.
Y.
Xiao
,
L.
Zhou
, and
W.
Chen
,
Opt. Lett.
47
,
3692
(
2022
).
https://doi.org/10.1364/OL.463897
Crossref
Search ADS
PubMed
 
9.
N.
Radwell
,
K. J.
Mitchell
,
G. M.
Gibson
,
M. P.
Edgar
,
R.
Bowman
, and
M. J.
Padgett
,
Optica
1
,
285
(
2014
).
https://doi.org/10.1364/OPTICA.1.000285
Crossref
Search ADS
 
10.
R. I.
Stantchev
,
X.
Yu
,
T.
Blu
, and
E.
Pickwell-MacPherson
,
Nat. Commun.
11
,
2535
(
2020
).
https://doi.org/10.1038/s41467-020-16370-x
Crossref
Search ADS
PubMed
 
11.
V.
Cecconi
,
V.
Kumar
,
A.
Pasquazi
,
J. S.
Totero Gongora
, and
M.
Peccianti
,
Open Res. Europe
2
,
32
(
2023
).
https://doi.org/10.12688/openreseurope.14508.3
Crossref
Search ADS
 
12.
B.
Sun
,
M. P.
Edgar
,
R.
Bowman
,
L. E.
Vittert
,
S.
Welsh
,
A.
Bowman
, and
M. J.
Padgett
,
Science
340
,
844
(
2013
).
https://doi.org/10.1126/science.1234454
Crossref
Search ADS
PubMed
 
13.
I. M.
Vellekoop
 and
A. P.
Mosk
,
Opt. Lett.
32
,
2309
(
2007
).
https://doi.org/10.1364/OL.32.002309
Crossref
Search ADS
PubMed
 
14.
M.
Kmiec
 and
A.
Glowacz
,
Pattern Recognit. Lett.
52
,
72
(
2015
).
https://doi.org/10.1016/j.patrec.2014.09.018
Crossref
Search ADS
 
15.
D. H.
Hubel
 and
T. N.
Wiesel
,
J. Physiol.
160
,
106
(
1962
).
https://doi.org/10.1113/jphysiol.1962.sp006837
Crossref
Search ADS
PubMed
 
16.
X.
Li
,
S.
Zhang
,
X.
Pan
,
P.
Dale
, and
R.
Cropp
,
Int. J. Remote Sens.
31
,
5041
(
2010
).
https://doi.org/10.1080/01431160903283835
Crossref
Search ADS
 
17.
C. M.
Kao
,
X.
Pan
,
E.
Hiller
, and
C. T.
Chen
,
IEEE Trans. Nucl. Sci.
45
,
3089
(
1998
).
https://doi.org/10.1109/23.737669
Crossref
Search ADS
 
18.
B.
Ramamurthy
 and
K. R.
Chandran
,
Int. J. Comput. Appl.
17
,
32
(
2011
).
https://doi.org/10.5120/2222-2831
Crossref
Search ADS
 
19.
J.
Canny
,
IEEE Trans. Pattern Anal. Mach. Intell.
PAMI-8
,
679
(
1986
).
https://doi.org/10.1109/TPAMI.1986.4767851
Crossref
Search ADS
 
20.
I.
Sobel
, “Camera models and machine perception,” Technical Report (Computer Science Department, Technion, Israel, 1972).
21.
I. E.
Abdou
 and
W. K.
Pratt
,
Proc. IEEE
67
,
753
(
1979
).
https://doi.org/10.1109/PROC.1979.11325
Crossref
Search ADS
 
22.
P.
Bao
,
L.
Zhang
, and
X.
Wu
,
IEEE Trans. Pattern Anal. Mach. Intell.
27
,
1485
(
2005
).
https://doi.org/10.1109/TPAMI.2005.173
Crossref
Search ADS
PubMed
 
23.
S.
Yi
,
D.
Labate
,
G. R.
Easley
, and
H.
Krim
,
IEEE Trans. Image Process.
18
,
929
(
2009
).
https://doi.org/10.1109/TIP.2009.2013082
Crossref
Search ADS
PubMed
 
24.
X.
Liu
,
X.
Yao
,
R.
Lan
,
C.
Wang
, and
G.
Zhai
,
Opt. Express
23
,
33802
(
2015
).
https://doi.org/10.1364/OE.23.033802
Crossref
Search ADS
PubMed
 
25.
T.
Mao
,
Q.
Chen
,
W.
He
,
Y.
Zou
,
H.
Dai
, and
G.
Gu
,
IEEE Photonics J.
8
,
6900810
(
2016
).
https://doi.org/10.1109/JPHOT.2016.2578934
Crossref
Search ADS
 
26.
W.
Yang
,
W.
Meng
,
D.
Shi
,
L.
Zha
,
Y.
Chen
,
J.
Huang
, and
Y.
Wang
,
Opt. Commun.
529
,
129064
(
2023
).
https://doi.org/10.1016/j.optcom.2022.129064
Crossref
Search ADS
 
27.
S.
Yuan
,
D.
Xiang
,
X.
Liu
,
X.
Zhou
, and
P.
Bing
,
Opt. Commun.
410
,
350
(
2018
).
https://doi.org/10.1016/j.optcom.2017.10.016
Crossref
Search ADS
 
28.
C.
Zhou
,
G.
Wang
,
H.
Huang
,
L.
Song
, and
K.
Xue
,
Opt. Express
27
,
27295
(
2019
).
https://doi.org/10.1364/OE.27.027295
Crossref
Search ADS
PubMed
 
29.
H.
Ren
,
S.
Zhao
, and
J.
Gruska
,
Opt. Express
26
,
5501
(
2018
).
https://doi.org/10.1364/OE.26.005501
Crossref
Search ADS
PubMed
 
30.
Y.
Liu
,
P.
Yu
,
X.
Hu
,
Z.
Wang
,
Y.
Li
, and
L.
Gong
,
Opt. Lett.
45
,
4028
(
2020
).
https://doi.org/10.1364/OL.396903
Crossref
Search ADS
PubMed
 
31.
L.
Zhou
,
Y.
Xiao
,
Z.
Pan
,
Y.
Cao
, and
W.
Chen
,
Opt. Express
29
,
25675
(
2021
).
https://doi.org/10.1364/OE.428564
Crossref
Search ADS
PubMed
 
32.
R. I.
Khakimov
,
B. M.
Henson
,
D. K.
Shin
,
S. S.
Hodgman
,
R. G.
Dall
,
K. G. H.
Baldwin
, and
A. G.
Truscott
,
Nature
540
,
100
(
2016
).
https://doi.org/10.1038/nature20154
Crossref
Search ADS
PubMed
 
33.
Z.
Ye
,
J.
Xiong
, and
H. C.
Liu
,
Phys. Rev. Appl.
15
,
034035
(
2021
).
https://doi.org/10.1103/PhysRevApplied.15.034035
Crossref
Search ADS
 
© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)