CN113379906B - Single-photon three-dimensional image reconstruction method and system based on super-pixel filtering - Google Patents

Single-photon three-dimensional image reconstruction method and system based on super-pixel filtering Download PDF

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CN113379906B
CN113379906B CN202110836863.2A CN202110836863A CN113379906B CN 113379906 B CN113379906 B CN 113379906B CN 202110836863 A CN202110836863 A CN 202110836863A CN 113379906 B CN113379906 B CN 113379906B
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CN113379906A (en
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陈松懋
苏秀琴
郝伟
张振扬
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XiAn Institute of Optics and Precision Mechanics of CAS
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/15—Correlation function computation including computation of convolution operations

Abstract

The invention belongs to the technical field of laser radars, relates to a single photon three-dimensional image reconstruction method and system based on super-pixel filtering, and solves the problems that the existing post-processing algorithm such as UA algorithm has a relatively serious image block effect and the speed is difficult to meet the real-time processing requirement, and the algorithms such as ManiPoP have high requirement on computing resources, are relatively high in cost and cannot meet the requirement of practical application. The invention designs a filtering kernel based on imaging physical parameters, realizes the suppression of noise in echo signals and the effective utilization of signal photons based on a superpixel filtering principle, and realizes the acquisition of real-time target high-precision three-dimensional information with lower calculation cost.

Description

Single-photon three-dimensional image reconstruction method and system based on super-pixel filtering
Technical Field
The invention belongs to the technical field of laser radars, and particularly relates to a single photon three-dimensional image reconstruction method and system based on superpixel filtering.
Background
The single photon imaging technology is the leading-edge field of the modern laser radar technology, has extremely high sensitivity, and makes it possible to acquire three-dimensional information of a target under the condition of extremely weak light, so that the single photon imaging technology can be widely applied to a plurality of application fields such as photoelectric reconnaissance, automatic driving and the like.
However, in practical applications, the technique is very easily interfered by noise due to its extremely low echo energy and extremely high detection sensitivity, and even under extreme conditions, the noise may submerge the target signal, so the noise suppression problem becomes one of the key problems leading to the practical application of the single photon imaging technique.
Noise suppression methods based on imaging systems, such as electronic gating and polarization filtering, are widely applied in the field, but the electronic gating still cannot effectively filter noise in a gating interval, and the polarization filtering reduces the detection probability of signals to a certain extent, so that the reconstruction quality cannot be effectively improved only by means of a hardware system.
The three-dimensional reconstruction performance of the echo signal under noise interference can be effectively improved by the efficient post-processing algorithm, for example, the signal-to-noise ratio is greatly enhanced by the classic UA algorithm through the down-sampling of the echo signal, and the three-dimensional reconstruction with higher quality is realized in the environment that the number of signal photons is less than that of noise photons; however, the image block effect is more serious, and the speed is difficult to meet the requirement of real-time processing. The ManiPoP algorithm and other algorithms have good performance, but the requirement on computing resources is high in cost, and the requirement of practical application cannot be met.
In summary, in the field of single photon imaging technology, a three-dimensional reconstruction algorithm capable of reconstructing target information with high precision under a strong noise condition needs to be explored, and meanwhile, the requirement of real-time performance in practical application needs to be met.
Disclosure of Invention
In order to realize the acquisition of target high-precision three-dimensional information under a noise condition, the invention provides a single photon three-dimensional image reconstruction method and a system based on superpixel filtering, which solve the problems that the existing post processing algorithm such as UA algorithm has more serious image block effect and the speed is difficult to meet the real-time processing requirement, and the algorithms such as ManiPoP have higher requirement cost on computing resources and cannot meet the requirement of practical application. The invention designs a filtering kernel based on imaging physical parameters, realizes the suppression of noise in echo signals and the effective utilization of signal photons based on a superpixel filtering principle, and realizes the acquisition of real-time target high-precision three-dimensional information with lower calculation cost.
The technical scheme of the invention is to provide a single photon three-dimensional image reconstruction method based on superpixel filtering, which is characterized by comprising the following steps:
step 1, acquiring original three-dimensional echo data;
acquisition of raw three-dimensional echo data by single photon imaging system
Figure 76367DEST_PATH_IMAGE001
And obtaining original three-dimensional echo data
Figure 305092DEST_PATH_IMAGE001
Three-dimensional (D) ofSize of
Figure 84829DEST_PATH_IMAGE002
，
Figure 542355DEST_PATH_IMAGE003
，
Figure 356727DEST_PATH_IMAGE004
In which
Figure 992239DEST_PATH_IMAGE002
The number of rows of pixels is,
Figure 259272DEST_PATH_IMAGE003
the number of the pixel columns is the same as,
Figure 520489DEST_PATH_IMAGE004
is the corresponding grid number in a time-correlated single photon counter (TCSPC) device, i.e., the discrete photon flight time;
step 2, designing a super-pixel filtering kernel based on imaging physical parameters;
step 2.1, acquiring related imaging physical parameters: noise estimation threshold
Figure 189368DEST_PATH_IMAGE005
Width of grid in time-correlated single photon counter
Figure 494316DEST_PATH_IMAGE006
Reference waveform for emitting laser pulses
Figure 248646DEST_PATH_IMAGE007
With full width at half maximum of the emitted laser pulse
Figure 985657DEST_PATH_IMAGE008
(ii) a And from three-dimensional echo data
Figure 571360DEST_PATH_IMAGE001
And its three-dimensional size
Figure 1204DEST_PATH_IMAGE002
，
Figure 55879DEST_PATH_IMAGE003
，
Figure 331002DEST_PATH_IMAGE004
Estimating the average pixel photon number of the echo with the imaging physical parameter
Figure 36790DEST_PATH_IMAGE009
Signal to noise ratio of echo
Figure 371956DEST_PATH_IMAGE010
；
Step 2.2, estimating the super-pixel filtering kernel size according to the formula (5)
Figure 412463DEST_PATH_IMAGE011
；
Figure 491277DEST_PATH_IMAGE012
（5）
Wherein the content of the first and second substances,
Figure 51571DEST_PATH_IMAGE013
it means an operation of taking the maximum value,
Figure 823218DEST_PATH_IMAGE014
it means that the minimum value taking operation is performed,
Figure 586906DEST_PATH_IMAGE015
represents a rounding up operation;
step 2.3, estimating parameters according to the formula (6)
Figure 469411DEST_PATH_IMAGE016
：
Figure DEST_PATH_IMAGE017
（6）
Step 2.4, calculating the response range of the super-pixel filtering kernel according to the formula (7)
Figure 884212DEST_PATH_IMAGE018
Here, the
Figure 826760DEST_PATH_IMAGE018
Is composed of
Figure 373017DEST_PATH_IMAGE019
A matrix of (a);
Figure 528055DEST_PATH_IMAGE020
（7）
wherein the content of the first and second substances, (ii) (i，j) Is shown in (A)i，j) A plurality of pixels, each of which is a pixel,
Figure 625DEST_PATH_IMAGE021
to representi=
Figure 927123DEST_PATH_IMAGE022
，j=
Figure 852354DEST_PATH_IMAGE022
；
Step 2.5, calculate the response of the superpixel Filter Kernel according to equation (8)
Figure DEST_PATH_IMAGE023
Here, the
Figure 138979DEST_PATH_IMAGE023
Is also that
Figure 200476DEST_PATH_IMAGE019
A matrix of (a);
Figure 796411DEST_PATH_IMAGE024
（8）
step 2.6, normalizing the formula (8) by the formula (9):
Figure DEST_PATH_IMAGE025
（9）
3, realizing filtering by utilizing a super-pixel filtering kernel based on a super-pixel filtering principle;
step 3.1, the original three-dimensional echo data
Figure 271255DEST_PATH_IMAGE001
Is divided into on the time axis
Figure 299254DEST_PATH_IMAGE004
Each section is recorded as
Figure 293886DEST_PATH_IMAGE026
；
Step 3.2, according to the formula (10), super-pixel filtering is completed, and the updated distribution of each section is obtained
Figure DEST_PATH_IMAGE027
And then obtaining the three-dimensional echo data after the super-pixel filtration
Figure 545875DEST_PATH_IMAGE028
Wherein
Figure DEST_PATH_IMAGE029
Represents a convolution operation;
Figure 757283DEST_PATH_IMAGE030
（10）
step 3.3, calculating the three-dimensional echo data after the super-pixel filtration according to the formula (15)
Figure 323393DEST_PATH_IMAGE028
Distance information of the object in each pixel
Figure DEST_PATH_IMAGE031
：
Figure DEST_PATH_IMAGE032
（15）
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE033
finger filtered three-dimensional echo data
Figure 500428DEST_PATH_IMAGE028
The grid position corresponding to each pixel peak value;
step 3.4, calculating the three-dimensional echo data after the super-pixel filtration according to the formula (16)
Figure 861002DEST_PATH_IMAGE028
Reflectivity information of the object in each pixel
Figure 310438DEST_PATH_IMAGE034
：
Figure DEST_PATH_IMAGE035
（16）
Figure 991824DEST_PATH_IMAGE036
Three-dimensional echo data filtered for superpixels
Figure 882420DEST_PATH_IMAGE028
An echo signal of each pixel in (a);
step 3.5, three-dimensional echo data after super-pixel filtering
Figure 741791DEST_PATH_IMAGE028
Distance information of the object in each pixel of
Figure 350627DEST_PATH_IMAGE031
And reflectivity information
Figure 524119DEST_PATH_IMAGE034
Obtaining single photon three-dimensional images
Figure DEST_PATH_IMAGE037
。
Further, in order to obtain a complete image of the boundary region, step 3.5 is followed by step 3.6:
if super pixel filter kernel size
Figure 347850DEST_PATH_IMAGE011
Can be divided by 2 to intercept single photon three-dimensional image
Figure 378123DEST_PATH_IMAGE037
In
Figure 474255DEST_PATH_IMAGE038
And the boundary area is complemented into
Figure DEST_PATH_IMAGE039
Image of (2)
Figure 497443DEST_PATH_IMAGE040
；
If super pixel filter kernel size
Figure 424948DEST_PATH_IMAGE011
If the single photon three-dimensional image can not be divided by 2, the single photon three-dimensional image is intercepted
Figure 563805DEST_PATH_IMAGE037
In
Figure DEST_PATH_IMAGE041
And the boundary area is complemented into
Figure 960283DEST_PATH_IMAGE039
Image of (2)
Figure 209999DEST_PATH_IMAGE040
。
Further, step 2.1 is carried outAverage pixel photon number of wave
Figure 257589DEST_PATH_IMAGE009
Signal to noise ratio of echo
Figure 567348DEST_PATH_IMAGE010
Estimated by the following equation:
estimating the average pixel photon number of the echo according to equation (3)
Figure 949656DEST_PATH_IMAGE009
：
Figure 3063DEST_PATH_IMAGE042
（3）
Estimating the signal-to-noise ratio of the echo according to equation (4)
Figure 905160DEST_PATH_IMAGE010
：
Figure 385820DEST_PATH_IMAGE043
（4）
Wherein the content of the first and second substances,
Figure 678261DEST_PATH_IMAGE044
solving according to equation (1):
Figure 348408DEST_PATH_IMAGE045
（1）
wherein
Figure 42694DEST_PATH_IMAGE046
Indicating the first in the echoi，jIn one pixeltThe number of echo photons at the time;
Figure DEST_PATH_IMAGE047
for each grid echo noise level, estimate according to equation (2):
Figure DEST_PATH_IMAGE048
（2）。
further, in order to simplify the calculation process and improve the calculation efficiency, step 3.2 is to solve the formula (10) by using a fast fourier algorithm, which specifically includes the following steps:
step 3.21, solving two-dimensional discrete Fourier transform of the super-pixel filtering kernel according to the formula (11):
Figure DEST_PATH_IMAGE049
（11）
wherein
Figure 68157DEST_PATH_IMAGE050
Representing a two-dimensional discrete fourier transform;
step 3.22, obtaining each section according to the formula (12)
Figure 175790DEST_PATH_IMAGE026
Conjugation of two-dimensional discrete Fourier transform of echoes
Figure DEST_PATH_IMAGE051
：
Figure 570999DEST_PATH_IMAGE052
（12）
Wherein
Figure DEST_PATH_IMAGE053
Representing the conjugation operation;
and 3.23, solving Fourier transform of the correlation function according to the formula (13):
Figure 932842DEST_PATH_IMAGE054
（13）
step 3.24, for
Figure DEST_PATH_IMAGE055
Performing inverse Fourier transform to obtain each filtered section
Figure 83200DEST_PATH_IMAGE026
Three-dimensional echo data of
Figure 661818DEST_PATH_IMAGE027
(ii) a Further obtaining the three-dimensional echo data after the super-pixel filtration
Figure 860718DEST_PATH_IMAGE028
；
Figure 326335DEST_PATH_IMAGE056
（14）。
The invention also provides a single photon three-dimensional image reconstruction system based on the superpixel filtering, which comprises a processor and a memory, and is characterized in that: the memory has stored therein a computer program which, when run on the processor, performs the above-described method.
The invention also provides a computer readable storage medium, which is characterized in that: a computer program is stored which, when executed, performs the above-described method.
The beneficial effects of the invention are:
1. the invention designs a filtering kernel based on imaging physical parameters, realizes the suppression of noise in echo signals and the effective utilization of signal photons based on a superpixel filtering principle, and realizes the acquisition of real-time target high-precision three-dimensional information with lower calculation cost.
2. Compared with other image processing algorithms, the algorithm has the advantages of simple structure, small calculated amount, capability of parallelizing data processing and full utilization of effective calculation resources, and meanwhile, algorithm parameters are given by physical parameters in a self-adaptive mode, high calculation efficiency and less iteration, so that the processing time is closer to real-time on the premise of ensuring a certain reconstruction signal-to-noise ratio, and the method can be directly applied to engineering practice in the future.
3. Compared with other processing algorithms, the algorithm has the advantages that the main calculated amount is only a plurality of times of independent convolution operation, the solving efficiency of the fast Fourier transform algorithm is extremely high, the requirement on a computer is more practical, the operation complexity of the algorithm is lower, and the algorithm can be completed without depending on a high-performance processor.
Drawings
FIG. 1 is a flow chart of a single photon three-dimensional image reconstruction algorithm based on super-pixel filtering according to the invention;
FIG. 2 is a schematic diagram of the super-pixel filtering process of the present invention; (a) Representing raw three-dimensional echo data
Figure 585278DEST_PATH_IMAGE001
(ii) a (b) To represent
Figure 152656DEST_PATH_IMAGE026
The formation process of (1); (c) Representing a filtering process, i.e.
Figure 889668DEST_PATH_IMAGE026
Through
Figure 475370DEST_PATH_IMAGE057
Is filtered to obtain
Figure 905215DEST_PATH_IMAGE027
The process of (1).
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, specific embodiments accompanied with figures are described in detail below, and it is apparent that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
The invention aims to construct a filtering kernel for different statistical characteristics of signal photons and noise in an echo and realize high-quality image reconstruction in a strong noise environment by a superpixel principle. With reference to fig. 1, the method for reconstructing a single-photon three-dimensional image based on superpixel filtering in this embodiment is as follows:
the method comprises the following steps: acquisition of raw three-dimensional echo data by single photon imaging system
Figure 192845DEST_PATH_IMAGE001
And obtaining original three-dimensional echo data
Figure 733548DEST_PATH_IMAGE001
Three-dimensional size of
Figure 377019DEST_PATH_IMAGE002
，
Figure 774502DEST_PATH_IMAGE003
，
Figure 503424DEST_PATH_IMAGE004
In which
Figure 395288DEST_PATH_IMAGE002
The number of rows of pixels is,
Figure 893265DEST_PATH_IMAGE003
the number of the pixel columns is the same as,
Figure 461650DEST_PATH_IMAGE004
is the corresponding grid number in a time-correlated single photon counter (TCSPC) device, i.e., the discrete photon flight time;
step two: obtaining relevant imaging physical parameters, including noise estimation threshold
Figure 677867DEST_PATH_IMAGE005
Width of grid in TCSPC device
Figure 871957DEST_PATH_IMAGE058
Emitting a reference waveform of laser pulses
Figure 224441DEST_PATH_IMAGE007
And full width at half maximum thereof
Figure 229306DEST_PATH_IMAGE008
Here, the
Figure 667241DEST_PATH_IMAGE008
The grid number corresponding to the actual pulse width of the emitted laser in the TCSPC device can be recorded and obtained in the calibration step;
Figure 87858DEST_PATH_IMAGE005
selecting according to system design parameters and actual scenes;
step three: according to the formula (1) pair
Figure 373477DEST_PATH_IMAGE001
And (3) summing:
Figure 221347DEST_PATH_IMAGE045
（1）
wherein
Figure 208895DEST_PATH_IMAGE046
Indicating the first in the echoi，jIn one pixeltThe number of echo photons at the time;
step four: estimating echo noise level of each grid according to equation (2)
Figure 433203DEST_PATH_IMAGE047
：
Figure 71863DEST_PATH_IMAGE048
（2）
Step five: estimating the average pixel photon number of the echo according to equation (3)
Figure 356214DEST_PATH_IMAGE009
：
Figure 831058DEST_PATH_IMAGE042
（3）
Step six: estimating the signal-to-noise ratio of the echo according to equation (4)
Figure DEST_PATH_IMAGE059
：
Figure 593477DEST_PATH_IMAGE060
（4）
Step seven: estimation of superpixel filter kernel size according to equation (5)
Figure 588109DEST_PATH_IMAGE011
：
Figure DEST_PATH_IMAGE061
（5）
Wherein
Figure DEST_PATH_IMAGE062
It is indicated that the maximum value operation is taken,
Figure 105678DEST_PATH_IMAGE014
it means that the minimum value taking operation is performed,
Figure 317086DEST_PATH_IMAGE015
represents a rounding up operation;
step eight: estimating parameters according to equation (6)
Figure 883196DEST_PATH_IMAGE016
：
Figure 981602DEST_PATH_IMAGE063
（6）
Step nine: computing superpixel filter kernel response range according to equation (7)
Figure 607756DEST_PATH_IMAGE018
Here, the
Figure 994875DEST_PATH_IMAGE018
Is composed of
Figure 912146DEST_PATH_IMAGE019
A matrix of (a);
Figure 68321DEST_PATH_IMAGE020
（7）
wherein the content of the first and second substances, (ii) (i，j) Is shown in (A)i，j) A plurality of pixels, each of which is a pixel,
Figure 927693DEST_PATH_IMAGE021
to representi=
Figure 536529DEST_PATH_IMAGE022
，j=
Figure 857543DEST_PATH_IMAGE022
；
Step ten: computing the response of a superpixel filter kernel according to equation (8)
Figure 868224DEST_PATH_IMAGE023
Here, the
Figure 898497DEST_PATH_IMAGE023
Is also that
Figure 994629DEST_PATH_IMAGE019
A matrix of (a);
Figure DEST_PATH_IMAGE064
（8）
step eleven: normalization of equation (8) by equation (9):
Figure 253703DEST_PATH_IMAGE025
（9）
step twelve: as shown in FIG. 2 (a) and (b), the original three-dimensional echo data is processed
Figure 384470DEST_PATH_IMAGE001
Is divided into on the time axis
Figure 585645DEST_PATH_IMAGE004
Each section is recorded as
Figure 169073DEST_PATH_IMAGE026
；
Step thirteen: as shown in FIG. 2 (c), the superpixel filtering is performed according to equation (10), and the updated distribution of each cross section is obtained
Figure 730373DEST_PATH_IMAGE027
And then obtaining the three-dimensional echo data after the super-pixel filtration
Figure 715646DEST_PATH_IMAGE028
Wherein
Figure 87722DEST_PATH_IMAGE065
Represents a convolution operation;
Figure DEST_PATH_IMAGE066
（10）
the equation (10) can be solved using a fast fourier algorithm:
first, the two-dimensional discrete fourier transform of the superpixel filter kernel is found according to equation (11):
Figure 971495DEST_PATH_IMAGE049
（11）
wherein
Figure 24902DEST_PATH_IMAGE050
Representing a two-dimensional discrete fourier transform.
Then, each cross section is obtained from the equation (12)
Figure 864682DEST_PATH_IMAGE026
Conjugation of two-dimensional discrete Fourier transform of echoes
Figure 407659DEST_PATH_IMAGE051
：
Figure 700100DEST_PATH_IMAGE052
（12）
Wherein
Figure 868782DEST_PATH_IMAGE053
Representing a conjugate taking operation;
next, the fourier transform of the correlation function is found according to equation (13):
Figure 563069DEST_PATH_IMAGE054
（13）
finally, to
Figure DEST_PATH_IMAGE067
Performing inverse Fourier transform to obtain each filtered section
Figure 276947DEST_PATH_IMAGE026
Three-dimensional echo data of
Figure 135312DEST_PATH_IMAGE027
(ii) a Further obtaining the three-dimensional echo data after the super-pixel filtration
Figure 530522DEST_PATH_IMAGE028
；
Figure DEST_PATH_IMAGE068
（14）。
Fourteen steps: obtaining filtered three-dimensional echo data
Figure 141632DEST_PATH_IMAGE028
At the grid position corresponding to each pixel peak
Figure DEST_PATH_IMAGE069
And calculating superpixel-filtered three-dimensional echo data according to equation (15)
Figure 541258DEST_PATH_IMAGE028
Distance information of the object in each pixel
Figure DEST_PATH_IMAGE070
：
Figure DEST_PATH_IMAGE071
（15）
Step fifteen: estimating superpixel filtered three-dimensional echo data according to equation (16)
Figure 870608DEST_PATH_IMAGE028
Reflectivity information of the object in each pixel
Figure 616978DEST_PATH_IMAGE034
：
Figure 285857DEST_PATH_IMAGE035
（16）
Figure DEST_PATH_IMAGE072
Three-dimensional echo data filtered for superpixels
Figure 607117DEST_PATH_IMAGE028
An echo signal of each pixel in (1);
the sheet can be obtained by the stepsPhotonic three-dimensional images
Figure 95867DEST_PATH_IMAGE037
. Sixthly, the single photon three-dimensional image can be processed
Figure 410043DEST_PATH_IMAGE037
And (5) completing the boundary area:
sixthly, the steps are as follows: if super pixel filter kernel size
Figure 933428DEST_PATH_IMAGE011
Can be divided by 2 to intercept single photon three-dimensional image
Figure 160010DEST_PATH_IMAGE037
In
Figure 401635DEST_PATH_IMAGE038
And the boundary area is complemented into
Figure 755387DEST_PATH_IMAGE039
Image of (2)
Figure 133279DEST_PATH_IMAGE040
(ii) a Otherwise go to step seventeen.
Seventeen steps: if super pixel filter kernel size
Figure 796342DEST_PATH_IMAGE011
If the single photon three-dimensional image can not be divided by 2, the single photon three-dimensional image is intercepted
Figure 259684DEST_PATH_IMAGE037
In (1)
Figure 604078DEST_PATH_IMAGE041
And the boundary area is complemented into
Figure 413639DEST_PATH_IMAGE039
Image of (2)
Figure 919707DEST_PATH_IMAGE040
。
The invention also provides a single photon three-dimensional image reconstruction system based on the super-pixel filtering, which comprises a processor and a memory, wherein the memory stores a computer program, and the computer program executes the single photon three-dimensional image reconstruction method based on the super-pixel filtering when running in the processor.
The invention also provides a computer readable storage medium for storing a program which when executed implements the steps of a single photon three-dimensional image reconstruction method based on superpixel filtering. In some possible embodiments, the invention may also be implemented in the form of a program product comprising program code means for causing a terminal device to carry out the steps according to various exemplary embodiments of the invention described in the method part of the description above, when said program product is run on the terminal device.
A program product for implementing the above method, which may employ a portable compact disc read only memory (CD-ROM) and include program code, may be run on a terminal device, such as a personal computer. However, the program product of the present invention is not limited thereto, and in the present invention, the computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
The program product may employ any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples (a non-exhaustive list) of the readable storage medium include: an electrical connection having one or more wires, a portable disk, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

Claims (5)

1. A single photon three-dimensional image reconstruction method based on superpixel filtering is characterized by comprising the following steps:
step 1, acquiring original three-dimensional echo data;
acquiring original three-dimensional echo data Y through a single-photon imaging system, and acquiring three-dimensional sizes r, c and T of the original three-dimensional echo data Y, wherein r is the number of pixel lines, c is the number of pixel columns, and T is the number of corresponding grids in a time-dependent single-photon counter;
step 2, designing a super-pixel filtering kernel based on imaging physical parameters;
step 2.1, acquiring related imaging physical parameters: noise estimation threshold gamma, width t of grid in time-dependent single photon counter bin Emitting a reference waveform lambda of the laser pulse and emitting a full width at half maximum eta of the laser pulse; estimating the average pixel photon number theta of the echo and the signal-to-noise ratio phi of the echo according to the three-dimensional echo data Y and the three-dimensional sizes r, c and T thereof and the imaging physical parameters;
the average pixel photon number Θ of the echo is estimated according to equation (3):
Figure FDA0003946122150000011
estimating the signal-to-noise ratio Φ of the echo according to equation (4):
Figure FDA0003946122150000012
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003946122150000013
solving according to equation (1):
Figure FDA0003946122150000014
wherein Y is i,j,t Representing the number of echo photons at the t moment in the ith and j th pixels in the echo;
Figure FDA0003946122150000015
for each grid echo noise level, estimate according to equation (2):
Figure FDA0003946122150000021
2.2, estimating the size delta of the super-pixel filtering kernel according to the formula (5);
Figure FDA0003946122150000022
wherein max (.) represents the maximum value taking operation, min (.) represents the minimum value taking operation,
Figure FDA0003946122150000027
represents a rounding up operation;
step 2.3, estimating a parameter sigma according to the formula (6):
Figure FDA0003946122150000023
step 2.4, calculating a response range omega of the super-pixel filtering kernel according to the formula (7), wherein omega is a matrix of delta multiplied by delta;
Figure FDA0003946122150000024
wherein, (i, j) represents the (i, j) th pixel, (i, j) ∈ [1 … δ ] represents i = [1 … δ ], j = [1 … δ ];
step 2.5, calculating the response gamma of the super-pixel filtering kernel according to the formula (8), wherein gamma is a matrix of delta multiplied by delta;
Figure FDA0003946122150000025
step 2.6, normalizing formula (8) by formula (9):
Figure FDA0003946122150000026
3, realizing filtering by utilizing a super-pixel filtering kernel based on a super-pixel filtering principle;
step 3.1, dividing the original three-dimensional echo data Y into T sections on a time axis, and recording each section as X t ；
Step 3.2, according to the formula (10), super-pixel filtering is completed, and the updated distribution Z of each section is obtained t And further obtaining superpixel-filtered three-dimensional echo data Z, wherein
Figure FDA0003946122150000031
Represents a convolution operation;
Figure FDA0003946122150000032
step 3.3, calculating the distance information D of the target in each pixel in the three-dimensional echo data Z after the super-pixel filtration according to the formula (15) i,j ：
Figure FDA0003946122150000033
Wherein, tau ij The grid position corresponding to each pixel peak value in the three-dimensional echo data Z after filtering is indicated;
step 3.4, calculating the reflectivity information of the target in each pixel in the three-dimensional echo data Z after the super-pixel filtration according to the formula (16)
Figure FDA0003946122150000034
Figure FDA0003946122150000035
Z i,j Echo signals of each pixel in the three-dimensional echo data Z after the super-pixel filtration;
step 3.5, according to the distance information D of the target in each pixel of the three-dimensional echo data Z after the super-pixel filtration i,j And reflectivity information
Figure FDA0003946122150000036
Obtaining a single-photon three-dimensional image->
Figure FDA0003946122150000037
2. The single photon three-dimensional image reconstruction method based on the superpixel filtering according to claim 1, characterized in that step 3.5 is followed by step 3.6:
if the super-pixel filtering kernel size delta can be divided by 2, intercepting the single-photon three-dimensional image
Figure FDA0003946122150000038
Is/is>
Figure FDA0003946122150000039
Figure FDA00039461221500000310
The boundary area is complemented into an R multiplied by c image R by adopting a mirror surface filling mode;
if the super-pixel filtering kernel size delta cannot be divided by 2, intercepting the single-photon three-dimensional image
Figure FDA00039461221500000311
In
Figure FDA00039461221500000312
The boundary area is complemented into an R multiplied by c image R by adopting a mirror filling mode; c is the number of pixel columns.
3. The single photon three-dimensional image reconstruction method based on superpixel filtering according to claim 2, characterized in that step 3.2 uses fast fourier algorithm to solve formula (10), comprising the following steps:
step 3.21, solving the two-dimensional discrete Fourier transform of the super-pixel filtering kernel according to the formula (11):
Λ＝FFT(Γ＇) (11)
wherein FFT (.) represents a two-dimensional fast fourier transform;
step 3.22, each section X is obtained according to the formula (12) t Conjugate omega of two-dimensional discrete Fourier transform of echo t ：
ω t ＝[FFT(X t )] * (12)
Wherein [.] * Representing the conjugation operation;
and 3.23, solving Fourier transform of the correlation function according to the formula (13):
Ψ＝Λ×ω t (13)
step 3.24, carrying out inverse Fourier transform on psi to obtain each filtered section X t Three-dimensional echo data Z t (ii) a Further obtaining three-dimensional echo data Z after superpixel filtering;
Z t ＝IFFT(Ψ) (14)；
where IFFT (·) denotes an inverse fourier transform.
4. A single photon three-dimensional image reconstruction system based on superpixel filtering comprises a processor and a memory, and is characterized in that: the memory has stored therein a computer program which, when run on the processor, performs the method of any of claims 1 to 3.
5. A computer-readable storage medium characterized by: a computer program is stored which, when executed, implements the method of any one of claims 1 to 3.
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