Medium-penetrating polarization three-dimensional reconstruction method based on Monte Carlo

Abstract

The invention relates to a Monte Carlo-based transparent medium polarization three-dimensional reconstruction method, which comprises the following steps of: simulating by utilizing a polarization Monte Carlo numerical simulation method to obtain a Stokes vector of emergent light, and obtaining a Mueller matrix and a backscattering polarization degree of an area light source in a scattering medium; acquiring a Stokes vector of reflected light on the surface of the target object by using a Mueller matrix of the area light source in the scattering medium, and recovering polarization information of the reflected light on the surface of the target object; calculating a zenith angle and an azimuth angle of a normal vector according to polarization information of reflected light on the surface of the target object; fusing the backscattering polarization degree and the polarization information of the reflected light on the surface of the target object into a scattering formula to obtain light intensity information of the target object; and correcting the normal vector by using the light intensity information of the target object, and performing three-dimensional reconstruction of the target object. According to the method, the problem of polarization information distortion of the traditional polarization three-dimensional technology is solved, the polarization three-dimensional reconstruction precision is improved, and the application range of the three-dimensional reconstruction technology is expanded.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical imaging, and in particular relates to a Monte Carlo-based three-dimensional reconstruction method of polarization of a transparent medium. Background Art

[0002] Polarization 3D reconstruction technology can provide depth information that cannot be obtained by two-dimensional images. Through polarization 3D reconstruction technology, complete three-dimensional information such as the structure, texture, and scale of an object can be obtained.

[0003] A variety of complex scattering particles (fog, haze, micro-dispersed particles, etc.) in a scattering environment have strong absorption or scattering characteristics on polarized light. Part of the scattered light generated by scattering will propagate toward the detector to form backscattered light. In scenes with scattering media, the return signal of polarization 3D reconstruction technology is affected by the backscattered light, and the waveform is distorted. When performing depth calculation, there will be misestimation of the object distance and distortion of the 3D shape, resulting in distortion of the information detected by the detection equipment. This makes the results of 3D imaging, detection and identification of targets in complex environments using polarization information have large errors and uncertainties. Summary of the invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a method for three-dimensional reconstruction of polarization of a transparent medium based on Monte Carlo. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0005] The present invention provides a Monte Carlo-based three-dimensional reconstruction method of polarization of a transparent medium, comprising the following steps:

[0006] S1: Obtain the Stokes information of each pixel of the target object in the scattering system based on multiple polarization images of the target object;

[0007] S2: Use polarization Monte Carlo numerical simulation method to simulate the Stokes vector of the outgoing light, and obtain the Mueller matrix and backscattering polarization degree of the surface light source in the scattering medium;

[0008] S3: using the Mueller matrix of the surface light source in the scattering medium to obtain the Stokes vector of the reflected light from the surface of the target object, and restore the polarization information of the reflected light from the surface of the target object;

[0009] S4: Calculating the zenith angle and azimuth angle of the normal vector according to the polarization information of the light reflected from the surface of the target object;

[0010] S5: integrating the backscattered polarization degree and the polarization information of the reflected light on the surface of the target object into a scattering formula to obtain the light intensity information of the target object;

[0011] S6: Correcting the normal vector using the light intensity information of the target object to perform three-dimensional reconstruction of the target object.

[0012] In an achievable manner, the plurality of polarization images include polarization image I0, polarization image I 45 , Polarization Image I 90 and polarization image I 135 .

[0013] In one achievable manner, step S2 includes:

[0014] S201: define the initial state of the incident photon;

[0015] S202: Obtaining the coordinates of the incident photon after it collides with the scattering medium;

[0016] S203: Determine the current azimuth and scattering angle of the incident photon, and determine the next scattering direction of the photon according to the current scattering direction, azimuth and scattering angle;

[0017] S204: Analyze the change of polarization state of incident photons during the scattering process using the meridian plane method to determine the Stokes vector of the outgoing light;

[0018] S205: acquiring a Mueller matrix of a point light source in a scattering medium according to the Stokes vector of the emitted light, displacing and overlapping the Mueller matrix of the point light source in the scattering medium, and synthesizing a Mueller matrix of a surface light source in the scattering medium;

[0019] S206: Obtaining a backscattering polarization degree according to the Stokes vector of the outgoing light.

[0020] In one possible implementation, the Stokes vector of the outgoing light is expressed as:

[0021]

[0022] Among them, S sca represents the Stokes vector of the outgoing light, represents the rotation matrix when the Stokes vector rotates to the meridian plane where the detection surface is located, ∏ represents the quadrature operation, k' represents the number of collisions of a photon, S i represents the Stokes vector of the incident light, R k (-γ) represents the rotation matrix of the Stokes vector from the scattering plane AOB to the scattering meridian plane COB during the kth collision, R k (φ) represents the rotation matrix of the Stokes vector from the incident meridian plane COA to the scattering plane AOB during the kth collision, M k (θ) represents the scattering matrix of the kth collision.

[0023] In one achievable manner, the initial state of the incident photon includes: the initial position coordinates of the incident photon, the motion direction coordinates, the energy weight threshold, and light of four different Stokes vectors.

[0024] In one possible implementation, the backscattered polarization degree P sca The expression is:

[0025]

[0026] Among them, I sca , Q sca , U sca is the Stokes vector S of the outgoing light sca The amount.

[0027] In one achievable manner, step S3 includes:

[0028] S301: Substitute the Mueller matrix of the surface light source in the scattering medium into the mathematical relationship between the Stokes vector and the Mueller matrix to obtain the Stokes vector of the reflected light on the surface of the target object:

[0029] S T+P =S T +S P =S out -S B =S out -k2M sca S i ;

[0030] Among them, the Stokes vector S of the reflected light on the surface of the target object T+P , S T Represents the Stokes vector of the target object, S B represents the Stokes vector transmitted to the sensor without passing through the target object, S P It represents the Stokes vector radiated by the target object after scattering, S out Represents the total Stokes vector received by the sensor, M sca represents the Mueller matrix of a surface light source in a scattering medium, S i represents the Stokes vector of the incident light, k2 is a constant;

[0031] S302: Calculate the target polarization degree P according to the Stokes vector of the reflected light on the surface of the target object obj and target polarization angle AOP obj :

[0032]

[0033] Among them, I T+P , U T+P and QT+P For S T+P The amount.

[0034] In one possible implementation, the target polarization degree P obj The relationship between the zenith angle ω and the normal vector is:

[0035]

[0036] Where n represents the refractive index of the target object surface;

[0037] Azimuth of the normal vector and target polarization angle AOP obj The relationship is:

[0038]

[0039] In one achievable manner, the expression of the light intensity information T of the target object is:

[0040]

[0041] Among them, I max and I min They represent a pair of images of the brightest and darkest scenes produced by the rotating analyzer, P sca is the backscattered polarization degree, P obj is the target polarization degree.

[0042] In one achievable manner, step S6 includes:

[0043] S601: According to the zenith angle and azimuth angle of the normal vector, the normal vector is represented by a gradient field:

[0044]

[0045] Where (x, y) is the point coordinate, Z(x, y) represents the height function on the three-dimensional surface, p represents the gradient in the x direction, and q represents the gradient in the y direction;

[0046] S602: Obtain the partial derivative F of the light intensity information T of the target object in the x direction x and the partial derivative F in the y direction y ;

[0047] S603: Using F x and F y Corrected normal vector:

[0048] if make otherwise

[0049] if make otherwise

[0050] S604: Perform three-dimensional reconstruction of the target object according to the corrected normal vector.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] The present invention discloses a polarization 3D reconstruction method for a transparent medium based on Monte Carlo. The method utilizes the superposition principle of a polarization Monte Carlo numerical simulation method to simulate and obtain the Mueller matrix of a surface light source in a scattering medium. Based on the principle that Stokes vectors are additive, the influence of backscattering is effectively removed. The Stokes vector of the light reflected from the surface of a target object is obtained by solving and the polarization information of the light reflected from the surface of the target object is effectively restored. The light intensity information of the target object is recalculated by using the backscattering polarization degree obtained by simulation and the polarization information of the light reflected from the surface of the target object obtained by solving and the normal direction is corrected. The influence of scattering particles is overcome, the problem of polarization information distortion of traditional polarization 3D technology is solved, the accuracy of polarization 3D reconstruction is improved, and the application scope of the 3D reconstruction technology is expanded. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flowchart of a method for three-dimensional reconstruction of polarization of a transparent medium based on Monte Carlo provided by an embodiment of the present invention;

[0054] Figure 2 It is a meridian plane analysis diagram during the photon scattering process. DETAILED DESCRIPTION

[0055] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0056] Embodiment 1

[0057] See also Figure 1 , Figure 1 It is a flowchart of the steps of a Monte Carlo-based three-dimensional reconstruction method of polarization of a transparent medium provided by an embodiment of the present invention.

[0058] This embodiment provides a Monte Carlo-based three-dimensional reconstruction method for polarization of a transparent medium, including:

[0059] S1: Based on multiple polarization images of the target object, obtain the Stokes information of each pixel of the target object in the scattering system.

[0060] Specifically, a polarization camera is used to collect reflected light from the target surface in a scattering environment to obtain four polarization images I0, I 45 ,I 90 ,I 135By adding and subtracting different polarization images (I0+I 45 ,I 45 -I0、I 45 +I 135 -I0-I 90 ) obtains the I component, Q component and U component of the Stokes vector corresponding to each pixel. Further, I0, I 45 ,I 90 ,I 135 These are the polarization images obtained by the polarization camera when the polarizer is at positions of 0°, 45°, 90°, and 135° respectively.

[0061] S2: Use the polarization Monte Carlo numerical simulation method to simulate the Stokes vector of the outgoing light, and obtain the Mueller matrix and backscattering polarization degree of the surface light source in the scattering medium.

[0062] The polarization Monte Carlo model is constructed by using the polarization Monte Carlo numerical simulation method. First, the simulation object is determined in the polarization Monte Carlo model, that is, several important physical parameters of the medium environment: the effective radius of the medium (r), the wavelength of the incident light wave (λ), the asymmetry factor (g), the effective relative refractive index of the dispersed system (m), the particle number density (ρ), the transmission distance (L), the scattering coefficient (u s ), absorption coefficient (u a ), extinction coefficient (u t ), by emitting a large number of photons in the constructed polarization Monte Carlo model, simulating the process of photons acting in the scattering medium, and processing the photons arriving at the receiving end, the Stokes vector of the outgoing light is determined, and finally the Mueller matrix of the point light source in the transmission medium is obtained. The Mueller matrix of the point light source in the scattering medium is displaced and overlapped to synthesize the Mueller matrix of the surface light source in the scattering medium, and the backscattering polarization is obtained according to the Stokes vector of the outgoing light.

[0063] In this embodiment, step S2 includes:

[0064] S201: Define the initial state of the incident photon.

[0065] Specifically, the initial state of the incident photon includes: the initial position coordinates (0, 0, 0) of the incident photon, the motion direction coordinates (0, 0, 1), the polarization state weight threshold, and light of four different Stokes vectors.

[0066] Furthermore, the four lights with different Stokes vectors include: natural light S=[1 0 0 0], horizontal linear polarized light S=[1 1 0 0], 45° linear polarized light S=[1 0 1 0], and right circularly polarized light S=[1 0 0 1].

[0067] S202: Obtain the coordinates of the incident photon after it collides with the scattering medium.

[0068] Furthermore, the path length Δs that the photon travels between two collision events with the scattering medium is based on a random number, and Δs is obtained according to the following formula:

[0069]

[0070] Among them, ζ is a random number between (0, 1], u t =u a +u s , where u s is the scattering coefficient, u a is the absorption coefficient, u t is the extinction coefficient.

[0071] The coordinates [x', y', z'] of the photon after colliding with the scattering medium satisfy the following equation:

[0072]

[0073] Among them, [u x ,u y ,u z ] represents the scattering direction before the photon collides with the scattering medium, and [x, y, z] represents the position coordinates of the photon when it last collided with the scattering medium. It should be understood that the position coordinates of the incident photon when it first collides with the scattering medium are the initial position coordinates of the photon (0, 0, 0), and the scattering direction is the moving direction coordinates of the incident photon (0, 0, 1).

[0074] Specifically, after a photon collides, it is determined whether the energy of the photon is less than a threshold. The weight of a photon after a collision can be obtained by the following formula:

[0075]

[0076] Among them, w' represents the weight of the photon after colliding with the scattering medium, and w represents the weight of the photon before colliding with the scattering medium.

[0077] If the weight of the photon after colliding with the medium is less than the preset threshold, the photon is considered dead and tracking is stopped.

[0078] S203: Determine the current azimuth and scattering angle of the incident photon, and determine the next scattering direction of the photon according to the current scattering direction, azimuth and scattering angle.

[0079] Specifically, the scattering angle θ of the scattered light is obtained according to the HG (Henyey-Greenstein) scattering phase function. The expression of the HG scattering phase function is:

[0080]

[0081] Sampling the HG scattering phase function yields the scattering angle θ:

[0082]

[0083] The azimuth angle φ=2πks2, wherein ks1 and ks2 are pseudo-random numbers uniformly distributed in the range of 0 to 1, and g is an asymmetric factor.

[0084] The next scattered direction of the photon [u' x ,u' y ,u' z ] is the scattering direction [u x ,u y ,u z ], azimuth angle φ, scattering angle θ and scattering coefficient σ of the medium are determined according to the formula:

[0085] When|u z |<0.9999:

[0086]

[0087] When|u z |≥0.9999:

[0088]

[0089] S204: Analyze the change in polarization state of incident photons during the scattering process using the meridian plane method to determine the Stokes vector of the outgoing light.

[0090] Taking the Stokes information of each pixel of the target object in the scattering system obtained in step S1 as the initial value, the change of the polarization state of the incident photon during the scattering process is analyzed according to the meridian plane method. Figure 2 , Figure 2 This is a meridian plane analysis diagram during the photon scattering process. Among them, D1 is the direction of the photon before colliding with the medium, D2 is the direction of the photon after colliding with the medium, D1 and the z-axis constitute the meridian plane (incident meridian plane) COA before scattering, D2 and the z-axis constitute the meridian plane (scattering meridian plane) COB after scattering, and the scattering plane is AOB. First, the Stokes vector is rotated from the incident meridian plane COA to the scattering plane AOB, and then scattered. After scattering, the Stokes vector is rotated from the scattering plane AOB to the scattering meridian plane COB.

[0091] The Stokes change after scattering can be expressed as the following formula:

[0092] S new =R(-γ)M(θ)R(φ)S

[0093] Among them, S new represents the new Stokes vector after scattering, S represents the Stokes vector before scattering, R(-γ) represents the rotation matrix of the Stokes vector from the scattering plane AOB to the scattering meridian plane COB, R(β) represents the rotation matrix of the Stokes vector from the incident meridian plane COA to the scattering plane AOB, γ represents the angle between the scattering plane AOB and the scattering meridian plane COB, β represents the angle between the incident meridian plane COA and the scattering plane AOB, θ is the scattering angle, and M(θ) is the scattering matrix. At the first scattering, the Stokes vector S before scattering is the Stokes information of each pixel of the target object in the scattering system obtained in step S1.

[0094] Specifically, M(θ) can be expressed as:

[0095]

[0096] m 11 (θ) and m 12 (θ) represents the parameters related to linear polarized light, indicating the change in light intensity and polarization state, m 33 (θ) and m 34 (θ) represents the parameter related to circular polarization, m 33 (θ) represents how the intensity of light is maintained or reduced, and is related to the transmission / reflection properties of the polarizer or material, m 34 (θ) represents the coupling between polarization states of light, especially the conversion between linearly polarized light and circularly polarized light, m 11 (θ), m 12 (θ), m 33 (θ), m 34 (θ) can be obtained from the scattering amplitudes S1 and S2; S1 and S2 are obtained from Mie theory, and their sizes are related to the photon radius and the effective relative refractive index.

[0097] Because the reference surface of the Mueller matrix is ​​the scattering surface of this scattering process, the reference surface needs to be adjusted twice during each photon collision. Here, the rotation matrix is ​​used to implement this process. The rotation matrix is ​​expressed as:

[0098]

[0099] The rotation angle γ of the Stokes vector from the scattering plane AOB to the scattering meridian plane COB can be obtained by the following expression:

[0100]

[0101] Specifically, after repeating the scattering process for many times, the photon finally stops transmitting and is received by the detection surface. Before the photon is finally received by the detection surface, its Stokes vector needs to be rotated to the meridian plane where the detection surface is located for correction. The rotation angle of the photon when it reaches the detection surface is

[0102]

[0103] Because the Stokes vector is additive, in the polarization Monte Carlo imaging method, for the scattering process of a point light source, the Stokes vector of the outgoing light of the point light source can be obtained by accumulating and superimposing all photons at the corresponding positions. The Stokes vector of the outgoing light can be expressed as:

[0104]

[0105] Among them, S sca represents the Stokes vector of the outgoing light, represents the rotation matrix when the Stokes vector rotates to the meridian plane where the detection surface is located, k' represents the number of photon collisions, S i represents the Stokes vector of the incident light, R k (-γ) represents the rotation matrix of the Stokes vector from the scattering plane AOB to the scattering meridian plane COB during the kth collision, R k (φ) represents the rotation matrix of the Stokes vector from the incident meridian plane COA to the scattering plane AOB during the kth collision, M k (θ) represents the scattering matrix of the kth collision. It should be understood that S i This can be achieved by simulating or adjusting the light source used.

[0106] S205: Obtain the Mueller matrix of the point light source in the scattering medium according to the Stokes vector of the emitted light, displace and overlap the Mueller matrix of the point light source in the scattering medium, and synthesize the Mueller matrix of the surface light source.

[0107] Specifically, it is assumed that the effective Mueller matrix M of the scattering medium under study (the Mueller matrix of a point light source in the scattering medium) is:

[0108]

[0109] Stokes vector S of the outgoing light sca The Stokes vector S of the incident light i The Mueller matrix M of the scattering system is expressed as:

[0110]

[0111] Among them, I i , Q i , Ui 、V i The Stokes vector S represents the incident light i The amount.

[0112] Through the expression, it is found that since the Mueller matrix is ​​a 4x4 matrix, solving the matrix elements of the scattering system requires establishing a set of equations to determine 16 of the elements. For isotropic media, these elements are usually related to the geometric structure of the scattering system and the optical properties of the medium. The coefficients in these equations can be determined by appropriate optical simulation, so as to solve the Mueller matrix of the scattering system and understand the influence of the medium on the polarization properties of light. Therefore, by incident several unrelated polarized lights to obtain 16 equations, the value of each element can be obtained. In this embodiment, four Stokes vectors of natural light S = [1 0 0 0], horizontal linear polarized light S = [1 1 0 0], 45° linear polarized light S = [1 0 1 0], and right-handed circularly polarized light S = [1 0 0 1] are incident on the scattering medium environment. The Mueller matrix for the scattering medium can be expressed as:

[0113]

[0114] Among them, I1, Q1, U1, and V1 represent the components of the Stokes vector of natural light output light, I2, Q2, U2, and V2 represent the components of the Stokes vector of horizontal linear polarized light output light, I3, Q3, U3, and V3 represent the components of the Stokes vector of 45° linear polarized light output light, and I4, Q4, U4, and V4 represent the components of the Stokes vector of right-handed circularly polarized light output light.

[0115] In the actual imaging process, the light source used in this embodiment is a surface light source. In order to more accurately reproduce the imaging scene in reality and achieve a more balanced lighting effect, the surface light source is simulated. In order to improve the calculation speed, since linear systems all obey the superposition principle, the Mueller matrix of a single point light source can be displaced and overlapped to synthesize the Mueller matrix of the surface light source in the scattering medium. Therefore, the Mueller matrix M of the surface light source in the scattering medium sca The expression is:

[0116]

[0117] Among them, M sca is the Mueller matrix of the surface light source, M (i,j) is the Mueller matrix of the point light source, H and G are the values ​​of the maximum position of the incident light in the x and y directions respectively.

[0118] S206: According to the Stokes vector S of the outgoing light sca Get the backscattered polarization degree P sca, the formula is as follows:

[0119]

[0120] Among them, I sca , Q sca , U sca is the Stokes vector S of the outgoing light sca The amount.

[0121] S3: Using the Mueller matrix of the surface light source in the scattering medium, the Stokes vector of the reflected light on the surface of the target object is obtained, and the polarization information of the surface of the target object is restored;

[0122] S301: According to the mathematical relationship between the Stokes vector and the Mueller matrix, the Stokes vector of the reflected light on the target surface is obtained.

[0123] For polarization imaging in a scattering environment, the sensor receives the total Stokes vector S out for:

[0124] S out =S T +S B +S P =M total S i =(k1M obj +k2M sca +k3M sca M obj )S i ;

[0125] Among them, S T represents the Stokes vector of the target, S B represents the Stokes vector transmitted to the sensor without passing through the target, S P represents the Stokes vector radiated by the target after scattering, M obj Represents the Mueller matrix of the target, M sca represents the Mueller matrix of a surface light source in a scattering medium, S i represents the Stokes vector of the incident light, k1, k2, and k3 are constants. The sensor receives the total Stokes vector S out It is obtained by the I component, Q component and U component of the Stokes vector corresponding to each pixel in step S1.

[0126] Therefore, according to the Mueller matrix of the surface light source in the scattering medium accurately obtained in advance, based on the principle that the Stokes vector has additive properties, the mathematical relationship between the Stokes vector and the Mueller matrix can be used to remove the influence of backscattering on the polarization information, thereby maximizing the acquisition of the Stokes vector S of the reflected light on the target surface. T+P .

[0127]

[0128] Among them, S T+P =S T +S P , I out ', Q out '、U out '、V out 'For S out The weight, is the rotation angle of the photon when it reaches the detection surface, I is the intensity of the incident light, and P is the polarization degree of the incident light.

[0129] S302: Based on the Stokes vector S of the reflected light from the target surface T+P Calculate the target polarization degree P obj and target polarization angle AOP obj .

[0130]

[0131] Among them, I T+P , U T+P and Q T+P For S T+P The amount.

[0132] S4: Calculate the zenith angle and azimuth angle of the normal vector according to the polarization information of the light reflected from the surface of the target object.

[0133] Specifically, the target polarization degree P obj The relationship between the zenith angle ω and the normal vector is as follows:

[0134]

[0135] Where n represents the refractive index of the target object surface;

[0136] Target polarization angle AOP obj and the azimuth of the normal vector The relationship is as follows:

[0137]

[0138] Specifically, when the linear polarization light and the normal vector are in the same direction, the target polarization angle AOP obj and the azimuth of the normal vector When the linear polarized light and the normal vector are opposite, 180° needs to be added to correct the azimuth angle.

[0139] S5: The backscattered polarization degree of the target object and the polarization information of the surface of the target object are integrated into the scattering formula to obtain the light intensity information of the target object.

[0140] The formula for the light intensity information T of the target object in a scattering environment is:

[0141]

[0142] Among them, I max and I min They represent a pair of images of the brightest and darkest scenes produced by the rotating analyzer, P sca is the backscattered polarization degree.

[0143] S6: Correct the normal vector using the light intensity information of the target object to perform three-dimensional reconstruction of the target object.

[0144] Specifically, step S6 includes:

[0145] S601: According to the zenith angle and azimuth angle of the normal vector, the normal vector is represented by a gradient field:

[0146]

[0147] Among them, (x, y) is the coordinate of the point, Z(x, y) represents the height function on the three-dimensional surface, p represents the gradient in the x direction, and q represents the gradient in the y direction.

[0148] S602: Obtain the partial derivative F of the light intensity information T of the target object in the x direction x and the partial derivative F in the y direction y ;

[0149] Specifically, based on the knowledge of advanced mathematics, the continuous integrable function surface z = z(x, y) is transformed into an equation: F(x, y, z) = Z(x, y)-z;

[0150] Taking partial derivatives of the function gives the normal vector (F x ,F y ,-1).

[0151] in, is the partial derivative of the function z=z(x,y) in the x direction; is the partial derivative of the function z=z(x,y) in the y direction.

[0152] Since the light intensity information T of the target after descattering is a three-dimensional surface, we can use the light intensity information of the target to correct the normal vector according to the above principle.

[0153] S603: Using F x and F y Corrected normal vector:

[0154] The partial derivative of the light intensity information F x and F yThe zenith angle ω and the azimuth angle of the normal vector obtained are For comparison, correct the normal vector:

[0155] if make otherwise

[0156] if make otherwise

[0157] S604: Perform three-dimensional reconstruction of the target object according to the corrected normal vector.

[0158] Specifically, the three-dimensional information of the real target object can be obtained by integrating the surface of the object according to the corrected normal vector.

[0159] The present embodiment provides a Monte Carlo-based polarization 3D reconstruction method for a transparent medium. The method utilizes the superposition principle of the polarization Monte Carlo numerical simulation method to simulate the Mueller matrix of a surface light source in a scattering medium, and based on the principle that the Stokes vector has the additivity, effectively removes the influence of backscattering, obtains the Stokes vector of the light reflected from the surface of the target object, effectively restores the polarization information of the light reflected from the surface of the target object, recalculates the light intensity information of the target object using the simulated backscattering polarization degree and the solved polarization information of the light reflected from the surface of the target object, corrects the normal direction, overcomes the influence of scattering particles, solves the problem of polarization information distortion of traditional polarization 3D technology, improves the accuracy of polarization 3D reconstruction, and expands the application scope of 3D reconstruction technology.

[0160] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A Monte Carlo-based three-dimensional reconstruction method for polarization of transparent media, characterized in that: The following steps are involved: S1: Obtain the Stokes information of each pixel of the target object in the scattering system based on multiple polarization images of the target object; S2: Use polarization Monte Carlo numerical simulation method to simulate the Stokes vector of the outgoing light, and obtain the Mueller matrix and backscattering polarization degree of the surface light source in the scattering medium; S3: using the Mueller matrix of the surface light source in the scattering medium to obtain the Stokes vector of the reflected light from the surface of the target object, and restore the polarization information of the reflected light from the surface of the target object; S4: Calculating the zenith angle and azimuth angle of the normal vector according to the polarization information of the light reflected from the surface of the target object; S5: integrating the backscattered polarization degree and the polarization information of the reflected light on the surface of the target object into a scattering formula to obtain the light intensity information of the target object; S6: Correcting the normal vector using the light intensity information of the target object to perform three-dimensional reconstruction of the target object.

2. The Monte Carlo-based three-dimensional reconstruction method of polarization of a transparent medium according to claim 1, characterized in that: The plurality of polarization images include polarization image I0, polarization image I 45 , Polarization Image I 90 and polarization image I 135 .

3. The Monte Carlo-based three-dimensional reconstruction method of polarization of transparent media according to claim 1, characterized in that: Step S2 includes: S201: define the initial state of the incident photon; S202: Obtaining the coordinates of the incident photon after it collides with the scattering medium; S203: Determine the current azimuth and scattering angle of the incident photon, and determine the next scattering direction of the photon according to the current scattering direction, azimuth and scattering angle; S204: Analyze the change of polarization state of incident photons during the scattering process using the meridian plane method to determine the Stokes vector of the outgoing light; S205: acquiring a Mueller matrix of a point light source in a scattering medium according to the Stokes vector of the emitted light, displacing and overlapping the Mueller matrix of the point light source in the scattering medium, and synthesizing a Mueller matrix of a surface light source in the scattering medium; S206: Obtaining a backscattering polarization degree according to the Stokes vector of the outgoing light.

4. The Monte Carlo-based three-dimensional reconstruction method of polarization of a transparent medium according to claim 1, characterized in that: The expression of the Stokes vector of the outgoing light is: Among them, S sca represents the Stokes vector of the outgoing light, represents the rotation matrix when the Stokes vector rotates to the meridian plane where the detection surface is located, ∏ represents the quadrature operation, k' represents the number of collisions of a photon, S i represents the Stokes vector of the incident light, R k (-γ) represents the rotation matrix of the Stokes vector from the scattering plane AOB to the scattering meridian plane COB during the kth collision, R k (φ) represents the rotation matrix of the Stokes vector from the incident meridian plane COA to the scattering plane AOB during the kth collision, M k (θ) represents the scattering matrix of the kth collision.

5. The method for 3D reconstruction of polarization of transparent media based on Monte Carlo according to claim 4, characterized in that: The initial state of the incident photon includes: the initial position coordinates of the incident photon, the motion direction coordinates, the energy weight threshold, and the light of four different Stokes vectors.

6. The method for 3D reconstruction of polarization of transparent media based on Monte Carlo according to claim 4, characterized in that: Backscattered polarization degree P sca The expression is: Among them, I sca , Q sca , U sca is the Stokes vector S of the outgoing light sca The amount.

7. The method for 3D reconstruction of polarization of transparent media based on Monte Carlo according to claim 1, characterized in that: Step S3 includes: S301: Substitute the Mueller matrix of the surface light source in the scattering medium into the mathematical relationship between the Stokes vector and the Mueller matrix to obtain the Stokes vector of the reflected light on the surface of the target object: S T+P =S T +S P =S out -S B =S out -k2M sca S i ; Among them, the Stokes vector S of the reflected light on the surface of the target object T+P , S T Represents the Stokes vector of the target object, S B represents the Stokes vector transmitted to the sensor without passing through the target object, S P It represents the Stokes vector radiated by the target object after scattering, S out Represents the total Stokes vector received by the sensor, M sca represents the Mueller matrix of a surface light source in a scattering medium, S i represents the Stokes vector of the incident light, k2 is a constant; S302: Calculate the target polarization degree P according to the Stokes vector of the reflected light on the surface of the target object obj and target polarization angle AOP obj : Among them, I T+P , U T+P and Q T+P For S T+P The amount.

8. The Monte Carlo-based three-dimensional reconstruction method of polarization of transparent media according to claim 1, characterized in that: Target polarization degree P obj The relationship between the zenith angle ω and the normal vector is: Where n represents the refractive index of the target object surface; Azimuth of the normal vector and target polarization angle AOP obj The relationship is:

9. The Monte Carlo-based three-dimensional reconstruction method of polarization of transparent media according to claim 1, characterized in that: The expression of the light intensity information T of the target object is: Among them, I max and I min They represent a pair of images of the brightest and darkest scenes produced by the rotating analyzer, P sca is the backscattered polarization degree, P obj is the target polarization degree.

10. The Monte Carlo-based three-dimensional reconstruction method of polarization of transparent media according to claim 1, characterized in that: Step S6 includes: S601: According to the zenith angle and azimuth angle of the normal vector, the normal vector is represented by a gradient field: Where (x, y) is the point coordinate, Z(x, y) represents the height function on the three-dimensional surface, p represents the gradient in the x direction, and q represents the gradient in the y direction; S602: Obtain the partial derivative F of the light intensity information T of the target object in the x direction x and the partial derivative F in the y direction y ; S603: Using F x and F y Corrected normal vector: if make otherwise if make otherwise S604: Perform three-dimensional reconstruction of the target object according to the corrected normal vector.

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