CN115329256B - Underwater optical measurement error compensation method based on FPP - Google Patents

Underwater optical measurement error compensation method based on FPP Download PDF

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CN115329256B
CN115329256B CN202211250418.9A CN202211250418A CN115329256B CN 115329256 B CN115329256 B CN 115329256B CN 202211250418 A CN202211250418 A CN 202211250418A CN 115329256 B CN115329256 B CN 115329256B
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韩静
于浩天
郑东亮
吕嫩晴
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Nanjing University of Science and Technology
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Abstract

The invention discloses an underwater optical measurement error compensation method based on FPP, which comprises the following steps: based on a phase-shift sine stripe pattern captured by a camera, a first group of stripe wrapping phases are obtained through calculation by a phase shift algorithm, hilbert Transform (HT) is introduced into the captured stripe pattern, a second group of stripe wrapping phases are obtained through calculation by the phase shift algorithm again, then error compensation is carried out by averaging the two groups of stripe wrapping phases to obtain compensated stripe wrapping phases, finally, a corresponding relation between a camera pixel and a projector pixel is obtained through calculation according to the compensated stripe wrapping phases, and optical reconstruction of an underwater target is achieved. The invention mainly reduces the periodically distributed phase error under the turbid water condition by introducing HT into the FPP, thereby reducing the phase error caused by underwater scattering and effectively improving the optical measurement precision of the underwater FPP.

Description

Underwater optical measurement error compensation method based on FPP
Technical Field
The invention relates to an underwater optical measurement error compensation method based on FPP (focal plane P), belonging to the technical field of optical measurement.
Background
Underwater three-dimensional (3D) measurement plays an important role in ecological protection, archaeological debris, seabed reconstruction and the like. Optical measurement is one of the most promising underwater 3D measurement techniques due to its non-contact and high precision characteristics.
Optical measurements mainly include interferometry, time-of-flight (ToF) techniques and measurements based on optical triangulation. Optical triangulation-based methods can be divided into two categories, passive and active. Passive (i.e., stereo vision) has been successfully used for underwater 3D measurement applications, but suffers from light attenuation due to water scattering and absorption, resulting in inaccurate image correspondence and reduced 3D measurement accuracy. The active mode realizes reliable image correspondence by projecting active light, thereby reconstructing a more accurate 3D shape for the underwater object.
Traditionally, the active light may be a laser stripe or a structured pattern. Laser fringe based measurements can achieve accurate 3D measurements, but are very time consuming. Structured pattern based measurements use various patterns, such as: binary coding, sinusoidal patterns, gray or mixed patterns, etc. In contrast, sinusoidal pattern-based measurement techniques can achieve accurate measurements of thousands of frames per second, and have been widely used in the fields of advanced manufacturing, reverse engineering, and virtual reality.
The sinusoidal fringe based measurement system can be simplified as a projector and a camera. In actual use, the projected sinusoidal pattern varies in the horizontal or vertical direction, looking like stripes, so measurements based on sinusoidal patterns are also referred to as stripe projection profilometry (FPP). FPP establishes image correspondence between the projector and the camera by following phase consistency, i.e. the projected light does not change its phase before reaching the camera sensor.
FPP has been successfully used for 3D measurements in fresh water at present, but under turbid water conditions the background and amplitude of the captured fringe pattern will be greatly reduced, thereby creating phase errors and reducing the measurement accuracy.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides an underwater optical measurement error compensation method based on FPP, which reduces the periodic distribution phase error under the turbid water condition by introducing Hilbert Transform (HT) in the FPP, thereby reducing the influence caused by underwater scattering and effectively improving the optical measurement precision of the underwater FPP.
The technical scheme is as follows: in order to achieve the above object, the present invention provides an underwater optical measurement error compensation method based on FPP, comprising the following steps:
step 1: projecting a group of phase-shifted sinusoidal fringe patterns onto an underwater measured object through a projector, and capturing the phase-shifted sinusoidal fringe patterns reflected from the surface of the measured object through a camera;
and 2, step: calculating a first group of fringe wrapping phases through a phase shift algorithm based on the fringe patterns captured by the camera;
and step 3: introducing Hilbert transform into the captured fringe pattern, and calculating by a phase shift algorithm to obtain a second group of fringe wrapping phases;
and 4, step 4: and averaging the two groups of fringe wrapping phases to perform error compensation to obtain a compensated fringe wrapping phase, so that the corresponding relation between a camera pixel and a projector pixel is obtained, and the three-dimensional optical reconstruction of the underwater target is realized.
Further, random noise exists due to absorption and scattering of light under underwater conditions, so a multiple sampling method is adopted in step 1 to reduce the influence thereof. In this method, each designed image is projected onto an object and captured several times, and the captured sets of phase shifted sinusoidal fringe patterns are averaged to finally obtain a set of ideal phase shifted sinusoidal fringe patterns.
Further, the stripe pattern captured by the camera in step 2 is set as follows:
Figure 519314DEST_PATH_IMAGE001
，
where a and B are the fringe background and fringe amplitude respectively,
Figure 262886DEST_PATH_IMAGE002
the coordinates of the pixels of the camera are represented,
Figure 839361DEST_PATH_IMAGE003
representing a first set of fringe-wrapped phases, N representing the number of phase-shift steps, and the fringe amplitude is calculated by the following equation:
Figure 296887DEST_PATH_IMAGE004
，
further calculated by a least square algorithm to obtain:
Figure 173576DEST_PATH_IMAGE005
。
further, the fringe pattern after introducing hilbert transform in step 3 is:
Figure 559820DEST_PATH_IMAGE006
，
wherein, the first and the second end of the pipe are connected with each other,
Figure 623591DEST_PATH_IMAGE007
、
Figure 884808DEST_PATH_IMAGE008
the forward scattering component and the backward scattering component after introducing HT are respectively, and the forward scattering component after introducing HT is as follows:
Figure 616004DEST_PATH_IMAGE009
，
the backscattering component after introduction of HT is:
Figure 904640DEST_PATH_IMAGE010
，
wherein the content of the first and second substances,ewhich is a representation of a natural constant of,Qan empirical damping factor related to the turbidity of the water body is shown,Twhich represents an empirical constant of the temperature of the sample,
Figure 455707DEST_PATH_IMAGE011
representing the random noise in Gaussian distribution, and further calculating by a phase shift algorithm to obtain a second group of fringe wrapping phases:
Figure 255036DEST_PATH_IMAGE012
。
further, the fringe wrapping phase compensated in step 4 is:
Figure 575159DEST_PATH_IMAGE013
，
and then unwrapping by a time phase unwrapping algorithm:
Figure 67320DEST_PATH_IMAGE014
，
where K is a coordinate
Figure 872727DEST_PATH_IMAGE015
And finally obtaining a projector pixel corresponding to each camera pixel according to the corresponding fringe level:
1) If the projected stripes are horizontal stripes, then
Figure 944589DEST_PATH_IMAGE016
；
2) If the projected stripes are vertical stripes, then
Figure 650376DEST_PATH_IMAGE017
；
Wherein
Figure 782281DEST_PATH_IMAGE018
The spatial frequency is represented by a representation of,
Figure 72054DEST_PATH_IMAGE019
representing the coordinates of the projector pixels.
Has the beneficial effects that: according to the underwater optical measurement error compensation method based on the FPP, on one hand, the periodic distribution phase error under the turbid water condition is reduced by introducing Hilbert Transform (HT) into the FPP, so that the phase error caused by underwater scattering is reduced, on the other hand, the influence caused by underwater random noise is further reduced by adopting a multi-sampling method, and the optical measurement accuracy of the FPP under the turbid water condition is effectively improved.
Drawings
FIG. 1 is a schematic diagram of an FPP optical measurement system;
FIG. 2 is a schematic diagram of a conventional FPP measurement process;
FIG. 3 is a graph of the effects of sphere reconstruction for conventional FPP and HT-based FPP under four turbidity conditions;
FIG. 4 is a graph of spherical fit error for conventional FPP and HT-based FPP under four turbidity conditions.
Detailed Description
The following description of the embodiments of the present invention with reference to the accompanying drawings will more clearly and completely illustrate the technical solutions of the present invention.
As shown in fig. 1, the FPP is measured using an optical measurement system with a DMD projector and camera. Where the projector can be considered as an inverse of the camera and calibrated in the same way as the camera. When the image correspondence between the projector and camera is established, the desired 3D shape can be reconstructed using typical optical triangulation methods in combination with system calibration parameters.
In the drawings
Figure 213186DEST_PATH_IMAGE020
And
Figure 507901DEST_PATH_IMAGE021
the optical centers of the camera and projector, respectively, the camera optical axis and the intersection point
Figure 341864DEST_PATH_IMAGE022
Perpendicular to the camera image plane, with the projector optical axis at
Figure 823661DEST_PATH_IMAGE023
At a focal length of camera and projector, respectively
Figure 269948DEST_PATH_IMAGE024
And
Figure 950329DEST_PATH_IMAGE025
a given point E on the surface of the object to be measured will be derived from the projector pixel
Figure 689614DEST_PATH_IMAGE026
The emitted light is reflected to the camera pixel
Figure 189866DEST_PATH_IMAGE027
. In the world coordinate system, the coordinate of the E point is recorded as
Figure 194772DEST_PATH_IMAGE028
Can pass through an optical lensThe angle method calculates to obtain:
Figure 464080DEST_PATH_IMAGE029
Figure 639846DEST_PATH_IMAGE030
wherein S is a scale factor and the ratio of S,
Figure 361815DEST_PATH_IMAGE031
and
Figure 382860DEST_PATH_IMAGE032
respectively the camera and projector's internal reference matrices,
Figure 742560DEST_PATH_IMAGE033
and
Figure 89227DEST_PATH_IMAGE034
respectively, the camera and projector's external parameter matrices. As is well known in the art,
Figure 298492DEST_PATH_IMAGE031
and
Figure 123228DEST_PATH_IMAGE032
is that
Figure 101549DEST_PATH_IMAGE035
The matrix is a matrix of a plurality of matrices,
Figure 852074DEST_PATH_IMAGE033
and
Figure 548634DEST_PATH_IMAGE034
is that
Figure 911482DEST_PATH_IMAGE035
And (4) matrix.
From equation (1), three linear equations can be obtained:
Figure 275468DEST_PATH_IMAGE036
，(2)
world coordinates of point E
Figure 167200DEST_PATH_IMAGE037
Can be arranged in
Figure 118101DEST_PATH_IMAGE038
And
Figure 815799DEST_PATH_IMAGE039
uniquely solved when determined, i.e. need to be established
Figure 503132DEST_PATH_IMAGE040
And
Figure 96924DEST_PATH_IMAGE041
the corresponding relation between them.
A. Conventional FPP measurement principle:
in FPP, the projector projects a set of phase-shifted sinusoidal fringe patterns onto the object under test, while the camera captures these patterns reflected from the surface of the object under test, so that each pixel of the camera will correspond to a unique one of the projector pixels with the same phase. The projected fringe pattern is designed to:
Figure 266612DEST_PATH_IMAGE042
，(3)
where N represents the number of phase shift steps,
Figure 502421DEST_PATH_IMAGE043
(i.e. resolution of the projector is
Figure 309840DEST_PATH_IMAGE044
），
Figure 74534DEST_PATH_IMAGE045
And
Figure 734448DEST_PATH_IMAGE046
respectively the background and amplitude of the design stripe pattern,
Figure 508369DEST_PATH_IMAGE047
indicating the phase of the fringes as designed,
Figure 170294DEST_PATH_IMAGE048
representing spatial frequencies. In FPP, only horizontal or vertical stripes are selected for projection, and if vertical stripes are selected, the phase changes
Figure 371468DEST_PATH_IMAGE049
If the horizontal stripe is selected, the phase becomes
Figure 751634DEST_PATH_IMAGE050
。
Let the stripe pattern captured by the camera be
Figure 562202DEST_PATH_IMAGE051
，(4)
Where a and B are the background and amplitude respectively of the captured fringe pattern,
Figure 344213DEST_PATH_IMAGE052
the coordinates of the pixels of the camera are represented,
Figure 716289DEST_PATH_IMAGE003
the fringe-wrapped phase is represented and the fringe amplitude can be calculated by the following equation:
Figure 583751DEST_PATH_IMAGE053
，(5)
the wrapped phase may be calculated by using a least squares algorithm:
Figure 433895DEST_PATH_IMAGE054
，(6)
it is always wrapped in
Figure 837457DEST_PATH_IMAGE055
A phase unwrapping process is required to eliminate these
Figure 114854DEST_PATH_IMAGE056
The phase discontinuity, the required absolute phase is:
Figure 204033DEST_PATH_IMAGE057
，(7)
where K is the fringe order to be determined, and is typically solved using a time-phase unwrapping algorithm. The projector pixel corresponding to each camera pixel can be easily calculated as:
Figure 123447DEST_PATH_IMAGE058
Figure 113007DEST_PATH_IMAGE059
(8)
fig. 2 illustrates a measurement process of a conventional FPP, in which (a) a set of four-step phase-shifted sinusoidal fringe patterns captured by a camera is shown, (b) a wrapping phase calculated from the fringe patterns is shown, (c) an absolute phase obtained by unwrapping the calculated wrapping phase is shown, and (D) a 3D shape obtained by reconstruction of the FPP is shown.
B. FPP underwater error compensation:
first, random noise exists due to absorption and scattering of light under underwater conditions, and thus a multisampling method is employed to reduce the influence thereof. In this method, each designed image is projected onto an object and captured several times, and the captured group images are averaged as an ideal image, so that the standard deviation of the phase error becomes:
Figure 561306DEST_PATH_IMAGE060
，(9)
i.e. standard deviation of the phase error after averaging over M samples
Figure 668939DEST_PATH_IMAGE061
Will be divided by
Figure 860886DEST_PATH_IMAGE062
。
Secondly, under high turbidity conditions, the periodic phase error caused by underwater scattering is the same as the frequency at which the phase is calculated. Therefore, the Hilbert Transform (HT) can be introduced to reduce this error by introducing phase shifts into these ideal phase shift patterns and then by using the phase shift algorithm to compute the spatial phase and hilbert phase twice, the periodically distributed phase error in the muddy water condition will be reduced when the two phases are balanced (i.e., averaged).
When HT is introduced into the underwater captured fringe image, the transformed fringe image becomes:
Figure 471996DEST_PATH_IMAGE063
，(10)
the forward scatter component after the introduction of HT becomes:
Figure 858240DEST_PATH_IMAGE064
，(11)
the backscatter component after introduction of HT becomes:
Figure 922011DEST_PATH_IMAGE065
，(12)
wherein the content of the first and second substances,ethe natural constant is represented by a natural constant,Qan empirical damping factor related to the turbidity of the water body is shown,Tit is shown that the empirical constants are,
Figure 917649DEST_PATH_IMAGE011
random noise in a gaussian distribution is represented, and the wrapped phase after introduction of HT is obtained:
Figure 117686DEST_PATH_IMAGE066
，(13)
the compensated wrapped phase is:
Figure 173367DEST_PATH_IMAGE067
，(14)
and then solving through a time phase expansion algorithm to obtain a compensated absolute phase, and further obtaining a projector pixel corresponding to each camera pixel.
Taking a four-step phase shift (i.e., N = 4) as an example, the forward scattering error of the conventional FPP can be simplified as follows:
Figure 488548DEST_PATH_IMAGE068
(15)
the forward scattering error after introducing error compensation is:
Figure 22298DEST_PATH_IMAGE069
，(16)
it can be seen that the amplitude of the phase error due to forward scattering can be reduced to a value that is based on the error compensation of HT
Figure 342421DEST_PATH_IMAGE070
。
Taking the four-step phase shift (i.e., N = 4) as an example, the compensated backscatter error can be simplified as:
Figure 569003DEST_PATH_IMAGE071
，(17)
it can be seen that the phase error due to backscattering can be reduced to a level where the error compensation based on HT is introduced
Figure 607366DEST_PATH_IMAGE072
Wherein
Figure 711850DEST_PATH_IMAGE073
Representing the backscattering error of a conventional FPP.
Therefore, using HT-based FPP, the phase error due to underwater scattering can be reduced to half of that of conventional FPP.
C. FPP underwater measurement experiment:
the underwater 3D measuring system adopted in the experiment mainly comprises a DLP6500 projector with the resolution of 1920 x 1080, a Basler ACA1920-40um CMOS camera with the resolution of 1920 x 1200 and a camera lens with the focal length of 35 mm. The measured object is placed in a water tank with the size of 0.9m multiplied by 0.4m multiplied by 0.45m, and the measuring system is placed outside the water tank and is about 0.5m away from the object. The water tank is first filled with clear water and then the milk is poured into the water tank to produce cloudy water. Since CMOS cameras cannot image objects in water with turbidity exceeding 20 Nephelometric Turbidity Units (NTU), four different turbidities of water (10, 12, 15 and 19NTU respectively) were used in the experiment.
Figure 3 shows the 3D reconstruction effect of conventional FPP and HT-based FPP on standard spheres at four turbidity conditions: both conventional FPP and HT-based FPP can reconstruct smooth three-dimensional shapes at low turbidity, but only rough three-dimensional shapes at relatively high turbidity. While HT-based FPP significantly improves the accuracy of conventional FPP, it still produces some periodic errors, i.e. speckled errors in the reconstructed 3-D shape under high and very high turbidity conditions.
FIG. 4 shows the spherical fit error (RMSE) of conventional FPP and HT-based FPP under four turbidity conditions: for turbidity of 10NTU and 12NTU, the sphere fit error for HT-based FPP is around 0.1mm, whereas for turbidity of 15NTU and 19NTU, the sphere fit error for conventional FPP is 0.468 mm and 1.915 mm. Thus, HT-based FPP has better accuracy at low, medium and high turbidity, while still producing periodic errors at very high turbidity.
In conclusion, the invention establishes an error model of the underwater FPP: at that time, the phase error of the underwater FPP is a random noise, otherwise the phase error becomes a spatial correlation error having the same frequency as the calculated phase. In order to compensate for the phase error caused by underwater scattering, the present invention proposes HT-based FPP, whereby the phase error can be reduced to half of the conventional FPP.
The above detailed description merely describes preferred embodiments of the present invention and does not limit the scope of the invention. Without departing from the spirit and scope of the present invention, it should be understood that various changes, substitutions and alterations can be made herein by those skilled in the art from the following detailed description and drawings.

Claims (3)

1. An underwater optical measurement error compensation method based on FPP is characterized by comprising the following steps:
step 1: projecting the phase-shifted sinusoidal fringe pattern onto an underwater object to be measured by a projector, and capturing the fringe pattern reflected from the surface of the object to be measured by a camera;
step 2: calculating a first group of fringe wrapping phases through a phase shift algorithm based on the fringe patterns captured by the camera;
and step 3: introducing Hilbert transform into the captured fringe pattern, and calculating by a phase shift algorithm to obtain a second group of fringe wrapping phases;
and 4, step 4: error compensation is carried out by averaging the two groups of fringe-wrapped phases to obtain compensated fringe-wrapped phases, so that the corresponding relation between the camera pixels and the projector pixels is obtained, and the three-dimensional optical reconstruction of the underwater target is realized;
in the step 2, the stripe pattern captured by the camera is set as follows:
Figure DEST_PATH_IMAGE002
，
where a and B are the background and amplitude respectively of the captured fringe pattern,
Figure DEST_PATH_IMAGE004
the coordinates of the pixels of the camera are represented,
Figure DEST_PATH_IMAGE006
representing a first set of fringe-wrapped phases, N represents the number of phase-shift steps, and the fringe amplitude is calculated by the following equation:
Figure DEST_PATH_IMAGE008
，
further calculated by a least square algorithm to obtain:
Figure DEST_PATH_IMAGE010
；
the fringe pattern after introducing hilbert transform in step 3 is:
Figure DEST_PATH_IMAGE012
，
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE014
、
Figure DEST_PATH_IMAGE016
the forward scattering component and the backward scattering component after introducing HT are respectively, and the forward scattering component after introducing HT is as follows:
Figure DEST_PATH_IMAGE018
，
the backscattering components after introduction of HT are:
Figure DEST_PATH_IMAGE020
，
wherein, the first and the second end of the pipe are connected with each other,ewhich is a representation of a natural constant of,Qan empirical damping factor related to the turbidity of the water body is shown,Tit is shown that the empirical constants are,
Figure DEST_PATH_IMAGE022
representing the random noise in Gaussian distribution, and further calculating by a phase shift algorithm to obtain a second group of fringe wrapping phases:
Figure DEST_PATH_IMAGE024
。
2. the method for compensating the underwater optical measurement error based on the FPP of claim 1, wherein the multiple sampling method is adopted for the fringe capture in step 1, that is: and capturing the phase-shifted sinusoidal fringe patterns reflected by the surface of the measured object for M times through a camera, and averaging the captured M groups of phase-shifted sinusoidal fringe patterns to finally obtain a group of ideal phase-shifted sinusoidal fringe patterns.
3. The method of claim 1, wherein the fringe-wrapped phase compensated in step 4 is:
Figure DEST_PATH_IMAGE026
，
and then unwrapping by a time phase unwrapping algorithm:
Figure DEST_PATH_IMAGE028
，
wherein K is a coordinate
Figure DEST_PATH_IMAGE030
And finally obtaining a projector pixel corresponding to each camera pixel according to the corresponding fringe level:
1) If the projected stripes are horizontal stripes, then
Figure DEST_PATH_IMAGE032
；
2) If the projected stripes are vertical stripes, then
Figure DEST_PATH_IMAGE034
；
Wherein
Figure DEST_PATH_IMAGE035
The spatial frequency is represented by a representation of,
Figure DEST_PATH_IMAGE037
representing the coordinates of the projector pixels.
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