A monte carlo-based polarization three-dimensional reconstruction method for a transmissive medium

Abstract

The application relates to a Monte Carlo-based polarization three-dimensional reconstruction method of a transmissive medium, which comprises the following steps: obtaining the Stokes vector of outgoing light by simulating with a polarization Monte Carlo numerical simulation method, obtaining the Mueller matrix and the backscattering polarization degree of a surface light source in a scattering medium; obtaining the Stokes vector of target object surface reflected light by using the Mueller matrix of the surface light source in the scattering medium, and restoring the polarization information of the target object surface reflected light; calculating the zenith angle and the azimuth angle of the normal vector according to the polarization information of the target object surface reflected light; fusing the backscattering polarization degree and the polarization information of the target object surface reflected light into a scattering formula to obtain the light intensity information of the target object; and correcting the normal vector by using the light intensity information of the target object to perform three-dimensional reconstruction of the target object. The application solves the problem of polarization information distortion of a traditional polarization three-dimensional technology, improves the polarization three-dimensional reconstruction precision, and expands the application range of the three-dimensional reconstruction technology.

Description

Technical Field

[0001] This invention belongs to the technical field of optical imaging, specifically relating to a Monte Carlo-based method for three-dimensional reconstruction of polarization through a medium. Background Technology

[0002] Polarization 3D reconstruction technology can provide depth information that cannot be obtained from 2D images. Through polarization 3D reconstruction technology, complete 3D information such as the structure, texture, and scale of an object can be obtained.

[0003] The scattering environment is influenced by various complex scattering particles (fog, haze, micro-dispersible particles, etc.) that strongly absorb or scatter polarized light. Some of the scattered light propagates towards the detector, forming backscattered light. In scenes with scattering media, the returned signal of polarization-based 3D reconstruction technology is affected by backscattered light, resulting in waveform distortion. During depth calculation, this leads to errors in object distance estimation and distortion of the 3D shape, causing inaccurate information detected by the equipment. Consequently, the results obtained from 3D imaging, detection, and identification of targets in complex environments using polarization information have significant errors and uncertainties. Summary of the Invention

[0004] To address the aforementioned problems in the existing technology, this invention provides a Monte Carlo-based method for three-dimensional reconstruction of polarization through a transparent medium. The technical problem to be solved by this invention is achieved through the following technical solution:

[0005] This invention provides a Monte Carlo-based method for three-dimensional reconstruction of polarization through a medium, comprising the following steps:

[0006] 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;

[0007] S2: The Stokes vector of the outgoing light is obtained by simulating the polarization Monte Carlo numerical simulation method, and the Mueller matrix and backscattering polarization degree of the surface light source in the scattering medium are obtained.

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

[0009] S4: Calculate the zenith angle and azimuth angle of the normal vector based on the polarization information of the light reflected from the surface of the target object;

[0010] S5: The backscattering polarization degree and the polarization information of the light reflected from the surface of the target object are fused into the scattering formula to obtain the light intensity information of the target object;

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

[0012] In one feasible implementation, 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 feasible approach, step S2 includes:

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

[0015] S202: Obtain 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 based on the current scattering direction, azimuth, and scattering angle;

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

[0018] S205: Obtain the Mueller matrix of the point source in the scattering medium based on the Stokes vector of the emitted light, shift and overlap the Mueller matrix of the point source in the scattering medium, and synthesize the Mueller matrix of the surface source in the scattering medium.

[0019] S206: Obtain the backscattering polarization degree based on the Stokes vector of the emitted light.

[0020] In one feasible manner, the expression for the Stokes vector of the emitted light is:

[0021]

[0022] Among them, S sca The Stokes vector representing the emitted light. Let S represent the rotation matrix when the Stokes vector rotates to the meridional plane where the detector plane is located, ∏ represents the product operation, k' represents the number of collisions a photon undergoes, and S i R represents the Stokes vector of the incident light. k (-γ) represents the rotation matrix of the Stokes vector from the scattering plane AOB to the scattering meridional plane COB at the k-th collision, R k (φ) represents the rotation matrix of the Stokes vector from the incident meridional plane COA to the scattering plane AOB at the k-th collision, M k (θ) represents the scattering matrix of the k-th collision.

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

[0024] In one feasible manner, the backscattering polarization degree P sca The expression is:

[0025]

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

[0027] In one feasible approach, step S3 includes:

[0028] S301: Substitute the Mueller matrix of the surface light source in the scattering medium into the Stokes vector-Mueller matrix mathematical relationship to obtain the Stokes vector of the light reflected from 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] Wherein, the Stokes vector S of the light reflected from the surface of the target object T+P S T S represents the Stokes vector of the target object. B S represents the Stokes vector transmitted to the sensor without passing through the target object. P S represents the Stokes vector emitted after scattering and re-emitting the target object. out This indicates that the sensor receives the total Stokes vector, M. sca S represents the Mueller matrix of a surface light source in a scattering medium. i Let k2 represent the Stokes vector of the incident light, where k2 is a constant;

[0031] S302: Calculate the target polarization degree P based on the Stokes vector of the light reflected from the target object's surface. 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 feasible manner, the target polarization degree P obj The relationship between the zenith angle ω of the normal vector and the normal vector is:

[0035]

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

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

[0038]

[0039] In one feasible approach, the expression for the light intensity information T of the target object is:

[0040]

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

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

[0043] S601: Represent the normal vector using a gradient field based on the zenith angle and azimuth angle of the normal vector:

[0044]

[0045] Where (x,y) are the coordinates of a 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;

[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: Utilizing F x and F y Correction normal vector:

[0048] if make otherwise

[0049] if make otherwise

[0050] S604: Perform 3D reconstruction of the target object based on the corrected normal vector.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] This invention discloses a Monte Carlo-based method for three-dimensional polarization reconstruction through a scattering medium. It utilizes the superposition principle of polarization Monte Carlo numerical simulation to obtain the Mueller matrix of a surface light source in a scattering medium. Based on the principle of the additive nature of Stokes vectors, it effectively removes the influence of backscattering, solves for the Stokes vector of the reflected light from the target object's surface, and effectively recovers the polarization information of the reflected light. Using the simulated backscattering polarization degree and the solved polarization information of the reflected light from the target object's surface, it recalculates the light intensity information of the target object, corrects the normal direction, overcomes the influence of scattering particles, solves the polarization information distortion problem of traditional polarization-based three-dimensional techniques, improves the accuracy of polarization-based three-dimensional reconstruction, and expands the application range of three-dimensional reconstruction technology. Attached Figure Description

[0053] Figure 1 This is a flowchart of the steps of a Monte Carlo-based three-dimensional reconstruction method for polarization through a medium provided in an embodiment of the present invention;

[0054] Figure 2 This is a diagram of the meridional plane analysis during the photon scattering process. Detailed Implementation

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

[0056] Example 1

[0057] Please see Figure 1 , Figure 1 This is a flowchart of a Monte Carlo-based three-dimensional reconstruction method for polarization through a medium, provided in an embodiment of the present invention.

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

[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 under scattering conditions, resulting in four polarization images I0, I10, I20, and I30 of the target object. 45 I 90 I 135By adding and subtracting images with different polarizations (I0 + I... 45 I 45 -I0、I 45 +I 135 -I0-I 90 This yields the I, Q, and U components of the Stokes vector corresponding to each pixel. Furthermore, I0, I... 45 I 90 I 135 The images are polarization images obtained by a polarization camera when the polarizer is positioned at 0°, 45°, 90°, and 135°, respectively.

[0061] S2: The Stokes vector of the outgoing light is obtained by simulating the polarization Monte Carlo numerical simulation method, and the Mueller matrix and backscattering polarization degree of the surface light source in the scattering medium are obtained.

[0062] A polarization Monte Carlo model is constructed using the polarization Monte Carlo numerical simulation method. First, the simulation object, namely the medium environment, is defined in the polarization Monte Carlo model, including several important physical parameters: the effective radius of the medium (r), the incident light wavelength (λ), the asymmetry factor (g), the effective relative refractive index of the dispersed system (m), the particle number density (ρ), the propagation distance (L), and the scattering coefficient (u). s ), absorption coefficient (u) a ), extinction coefficient (u) t By emitting a large number of photons in a constructed polarization Monte Carlo model, the process of photons interacting in a scattering medium is simulated. The photons arriving at the receiver are processed to determine the Stokes vector of the outgoing light, ultimately obtaining the Mueller matrix of the point source in the transmission medium. The Mueller matrix of the point source in the scattering medium is then shifted and superimposed to synthesize the Mueller matrix of the surface source in the scattering medium. Finally, the backscattering polarization is obtained based on the Stokes vector of the outgoing light.

[0063] In this embodiment, step S2 includes:

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

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

[0066] Furthermore, the four different Stokes vectors of light include: natural light S = [1 0 0 0], horizontally linearly polarized light S = [1 1 0 0], 45° linearly polarized light S = [1 0 1 0], and right-hand 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 between two collisions between a photon and the scattering medium is based on a random number, and Δs is obtained according to the following formula:

[0069]

[0070] Where ζ is a random number between (0, 1], u t =u a +u s , where u s U is the scattering coefficient. a U is the absorption coefficient. t The extinction coefficient is denoted as .

[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 [x, y, z] represents the scattering direction of the photon before it collides with the scattering medium, and [x, y, z] represents the position coordinates of the photon when it first collides 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 coordinates of the incident photon's direction of motion (0, 0, 1).

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

[0075]

[0076] Where w' represents the weight after the photon collides with the scattering medium, and w represents the weight before the photon collides with the scattering medium.

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

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

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

[0080]

[0081] The scattering angle θ is obtained by sampling the HG scattering phase function:

[0082]

[0083] The azimuth angle φ = 2πks2, where 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 scattering direction of the photon [u' x ,u' y ,u' z From the current scattering direction [u] x ,u y ,u z The azimuth angle φ, scattering angle θ, and scattering coefficient σ of the medium are determined according to the formula:

[0085] when|u z When |<0.9999:

[0086]

[0087] when|u z When |≥0.9999:

[0088]

[0089] S204: The Stokes vector of the outgoing light is determined by analyzing the polarization state change of the incident photon during scattering using the meridional plane method.

[0090] Using the Stokes information of each pixel of the target object in the scattering system obtained in step S1 as the initial value, the polarization state change of the incident photon during scattering is analyzed according to the meridional plane method. Please refer to [link to relevant documentation]. Figure 2 , Figure 2 This is a diagram analyzing the meridional plane during photon scattering. D1 represents the direction of the photon before collision with the medium, and D2 represents the direction after collision. D1 and the z-axis form the pre-scattering meridional plane (incident meridional plane) COA, and D2 and the z-axis form the post-scattering meridional plane (scattering meridional plane) COB. The scattering plane is AOB. First, the Stokes vector is rotated from the incident meridional plane COA to the scattering plane AOB, then scattering occurs, and after scattering, the Stokes vector is rotated again from the scattering plane AOB to the scattering meridional plane COB.

[0091] The Stokes variation after scattering can be expressed by the following formula:

[0092] S new =R(-γ)M(θ)R(φ)S

[0093] Among them, S new Let S represent the Stokes vector after scattering, S represent the Stokes vector before scattering, R(-γ) represent the rotation matrix of the Stokes vector from the scattering plane AOB to the scattering meridional plane COB, R(β) represent the rotation matrix of the Stokes vector from the incident meridional plane COA to the scattering plane AOB, γ represent the angle between the scattering plane AOB and the scattering meridional plane COB, β represent the angle between the incident meridional plane COA and the scattering plane AOB, θ represent the scattering angle, and M(θ) represent the scattering matrix. During 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 a parameter associated with linearly polarized light, indicating changes in light intensity and polarization state, m 33 (θ) and m 34 (θ) represents a parameter related to circularly polarized light, 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. 34 (θ) represents the coupling between the 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 magnitudes are related to the photon radius and the effective relative refractive index.

[0097] Because the reference plane of the Mueller matrix is ​​the scattering plane in this scattering process, the reference plane needs to be adjusted twice during each photon collision. This process is implemented using a rotation matrix. The rotation matrix is ​​represented as:

[0098]

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

[0100]

[0101] Specifically, after repeated scattering processes, the photon's propagation eventually terminates, and it is received by the detector surface. Before being finally received by the detector surface, the photon's Stokes vector needs to be rotated to the meridional plane where the detector surface is located for correction. The rotation angle when the photon reaches the detector surface is...

[0102]

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

[0104]

[0105] Among them, S sca The Stokes vector representing the emitted light. S represents the rotation matrix when the Stokes vector rotates to the meridional plane where the detector plane is located, k' represents the number of photon collisions, and S i R represents the Stokes vector of the incident light. k (-γ) represents the rotation matrix of the Stokes vector from the scattering plane AOB to the scattering meridional plane COB at the k-th collision, R k (φ) represents the rotation matrix of the Stokes vector from the incident meridional plane COA to the scattering plane AOB at the k-th collision, M k (θ) represents the scattering matrix of the k-th 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 source in the scattering medium based on the Stokes vector of the emitted light. Shift and overlap the Mueller matrix of the point source in the scattering medium to synthesize the Mueller matrix of the surface source.

[0107] Specifically, let's assume the effective Mueller matrix (the Mueller matrix of the point source in the scattering medium) M of the scattering medium under study is:

[0108]

[0109] Stokes vector S of the emitted light sca Using 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 representing the incident light i The amount.

[0112] The expression reveals that, since the Mueller matrix is ​​a 4x4 matrix, solving for the matrix elements of the scattering system requires establishing a set of equations to determine 16 elements. For isotropic media, these elements are typically related to the geometry of the scattering system and the optical properties of the medium. Appropriate optical simulations can determine the coefficients in these equations, thereby solving for the Mueller matrix of the scattering system and understanding the influence of the medium on the polarization properties of light. Therefore, by incident several uncorrelated polarized lights, the 16 equations are obtained, and the value of each element can be determined. In this embodiment, natural light S = [1 0 0 0], horizontally linearly polarized light S = [1 1 0 0], 45° linearly polarized light S = [1 0 1 0], and right-hand circularly polarized light S = [1 0 0 1] with four Stokes vectors are incident on the scattering medium environment. The Mueller matrix of the scattering medium can then be expressed as:

[0113]

[0114] Wherein, I1, Q1, U1, and V1 represent the components of the Stokes vector of the naturally emitted light, I2, Q2, U2, and V2 represent the components of the Stokes vector of the horizontally linearly polarized light emitted, I3, Q3, U3, and V3 represent the components of the Stokes vector of the 45° linearly polarized light emitted, and I4, Q4, U4, and V4 represent the components of the Stokes vector of the right-hand circularly polarized light emitted.

[0115] In the actual imaging process, the light source used in this embodiment is a surface light source. To more accurately reproduce the imaging scene under real conditions and achieve a more balanced lighting effect, the surface light source is simulated. To improve the computing speed, since linear systems all obey the superposition principle, the Mueller matrix of the surface light source in the scattering medium can be synthesized by shifting and overlapping the Mueller matrix of a single point light source. Therefore, the Mueller matrix M of the surface light source in the scattering medium is... sca The expression is:

[0116]

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

[0118] S206: Based on the Stokes vector S of the emitted light sca Obtain the backscattering polarization degree P scaThe formula is as follows:

[0119]

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

[0121] S3: Use 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 recover the polarization information of the target object surface;

[0122] S301: Obtain the Stokes vector of the light reflected from the target surface based on the mathematical relationship between the Stokes vector and the Mueller matrix.

[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 S represents the Stokes vector of the target. B S represents the Stokes vector that has not been transmitted to the sensor via the target. P M represents the Stokes vector emitted after scattering and re-emitting from the target. obj M represents the Mueller matrix of the target. sca S represents the Mueller matrix of a surface light source in a scattering medium. i Let S represent the Stokes vector of the incident light, where k1, k2, and k3 are constants. The sensor receives the total Stokes vector S. out It is obtained by taking the I, Q and U components of the Stokes vector corresponding to each pixel in step S1.

[0126] Therefore, based on the accurately obtained Mueller matrix of the surface light source in the scattering medium, and leveraging the principle of the additive nature of Stokes vectors, the influence of backscattering on polarization information can be eliminated by utilizing the mathematical relationship between the Stokes vector and the Mueller matrix, thereby maximizing the acquisition of the Stokes vector S of the light reflected from 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 amount, Let θ be the rotation angle when the photon reaches the detector surface, I be the intensity of the incident light, and P be the degree of polarization of the incident light.

[0129] S302: Based on the Stokes vector S of the light reflected 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 based on 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 of the normal vector and the zenith angle ω is shown below:

[0134]

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

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

[0137]

[0138] Specifically, when the linearly polarized light and the normal vector are in the same direction, the target polarization angle AOP obj azimuth angle of the normal vector They are equal; however, when the linearly polarized light and the normal vector are in opposite directions, an additional 180° is needed to correct the azimuth angle.

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

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

[0141]

[0142] Among them, I max and I min P represents a pair of images of the brightest and darkest scenes produced by the rotating analyzer. sca This represents the backscattering polarization degree.

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

[0144] Specifically, step S6 includes:

[0145] S601: Represent the normal vector using a gradient field based on the zenith angle and azimuth angle of the normal vector:

[0146]

[0147] Where (x,y) are the coordinates of a 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 continuously integrable function surface z = z(x,y) is transformed into the equation: F(x,y,z) = Z(x,y) - z;

[0150] Taking the partial derivative of the function yields the normal vector (F) at any point on the surface. x ,F y ,-1).

[0151] in, Let z be the partial derivative of the function z = z(x,y) in the x-direction; Let z = z(x,y) be 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: Utilizing F x and F y Correction normal vector:

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

[0155] if make otherwise

[0156] if make otherwise

[0157] S604: Perform 3D reconstruction of the target object based on the corrected normal vector.

[0158] Specifically, the true three-dimensional information of the target object can be obtained by integrating the surface of the object based on the corrected normal vector.

[0159] This embodiment provides a Monte Carlo-based method for three-dimensional polarization reconstruction through a scattering medium. It utilizes the superposition principle of polarization Monte Carlo numerical simulation to obtain the Mueller matrix of the surface light source in the scattering medium. Based on the principle that Stokes vectors are additive, it effectively removes the influence of backscattering, solves for the Stokes vector of the reflected light from the target object's surface, and effectively recovers the polarization information of the reflected light. Using the simulated backscattering polarization degree and the solved polarization information of the reflected light from the target object's surface, it recalculates the light intensity information of the target object, corrects the normal direction, overcomes the influence of scattering particles, solves the polarization information distortion problem of traditional polarization-based three-dimensional techniques, improves the accuracy of polarization-based three-dimensional reconstruction, and expands the application scope of three-dimensional reconstruction technology.

[0160] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A Monte Carlo-based method for three-dimensional reconstruction of polarization through a medium, characterized in that, Includes the following steps: 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; S2: The Stokes vector of the outgoing light is obtained by simulating the polarization Monte Carlo numerical simulation method, and the Mueller matrix and backscattering polarization degree of the surface light source in the scattering medium are obtained. S3: Use the Mueller matrix of the surface light source in the scattering medium to obtain the Stokes vector of the light reflected from the surface of the target object, and recover the polarization information of the light reflected from the surface of the target object. S4: Calculate the zenith angle and azimuth angle of the normal vector based on the polarization information of the light reflected from the surface of the target object; S5: The backscattering polarization degree and the polarization information of the light reflected from the surface of the target object are fused into the scattering formula to obtain the light intensity information of the target object; S6: Use the light intensity information of the target object to correct the normal vector and perform three-dimensional reconstruction of the target object; Step S3 includes: S301: Substitute the Mueller matrix of the surface light source in the scattering medium into the Stokes vector-Mueller matrix mathematical relationship to obtain the Stokes vector of the light reflected from the surface of the target object: ； Among them, the Stokes vector of the light reflected from the surface of the target object , The Stokes vector representing the target object. This represents the Stokes vector that is transmitted to the sensor without passing through the target object. This represents the Stokes vector emitted after scattering and re-emitting from the target object. This indicates that the sensor receives the total Stokes vector. This represents the Mueller matrix of a surface light source in a scattering medium. The Stokes vector representing the incident light. It is a constant; S302: Calculate the polarization degree of the target based on the Stokes vector of the light reflected from the surface of the target object. and target polarization angle : ； ； in, , and for The amount.

2. The Monte Carlo-based three-dimensional reconstruction method for polarization through a medium according to claim 1, characterized in that, The multiple polarization images include polarization images. Polarization image Polarization image and polarization image .

3. The Monte Carlo-based three-dimensional reconstruction method for polarization through a medium according to claim 1, characterized in that, Step S2 includes: S201: Defines the initial state of the incident photon; S202: Obtain 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 based on the current scattering direction, azimuth, and scattering angle; S204: Analyze the polarization state change of the incident photon during scattering using the meridional plane method to determine the Stokes vector of the outgoing light; S205: Obtain the Mueller matrix of the point source in the scattering medium based on the Stokes vector of the emitted light, shift and overlap the Mueller matrix of the point source in the scattering medium, and synthesize the Mueller matrix of the surface source in the scattering medium. S206: Obtain the backscattering polarization degree based on the Stokes vector of the emitted light.

4. The Monte Carlo-based three-dimensional reconstruction method for polarization through a medium according to claim 1, characterized in that, The expression for the Stokes vector of the emitted light is: ； in, The Stokes vector representing the emitted light. This represents the rotation matrix when the Stokes vector rotates to the meridional plane where the probe surface is located. This represents the product operation. This represents the number of collisions a photon undergoes. The Stokes vector representing the incident light. This represents the rotation matrix that rotates the Stokes vector from the scattering plane AOB to the scattering meridional plane COB during the k-th collision. This represents the rotation matrix that rotates the Stokes vector from the incident meridional plane COA to the scattering plane AOB during the k-th collision. Indicates the first k The scattering matrix of the second collision.

5. The Monte Carlo-based three-dimensional reconstruction method for polarization through a medium according to claim 4, characterized in that, The initial state of the incident photon includes: the initial position coordinates of the incident photon, the direction coordinates of motion, the energy weight threshold, and the light of four different Stokes vectors.

6. The Monte Carlo-based three-dimensional reconstruction method for polarization through a medium according to claim 4, characterized in that, Backscattering polarization degree The expression is: ； in, , , Stokes vector of the emitted light The amount.

7. The Monte Carlo-based three-dimensional reconstruction method for polarization through a medium according to claim 1, characterized in that, Target polarization degree Zenith angle with the normal vector The relation is: ； in, n Represents the refractive index of the target object's surface; azimuth of the normal vector and target polarization angle The relation is: 。 8. The Monte Carlo-based three-dimensional reconstruction method for polarization through a medium according to claim 1, characterized in that, Light intensity information of the target object The expression is: ； in, and These represent a pair of images showing the brightest and darkest scenes produced by the rotating analyzer. This refers to the backscattering polarization degree. The target polarization degree.

9. The Monte Carlo-based three-dimensional reconstruction method for polarization through a medium according to claim 1, characterized in that, Step S6 includes: S601: Represent the normal vector using a gradient field based on the zenith angle and azimuth angle of the normal vector: ； in, Let Z be the coordinates of the point. Represents the height function on a three-dimensional surface. This represents the gradient in the x-direction. This represents the gradient in the y-direction; S602: Obtain the light intensity information of the target object. exist partial derivatives of direction and in partial derivatives of direction ; S603: Exploit and Correction normal vector: if ,make ,otherwise ; if ,make ,otherwise ; S604: Perform 3D reconstruction of the target object based on the corrected normal vector.

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