CN112070885A - Three-dimensional reconstruction method and system based on photogrammetric photometric stereo model - Google Patents

Three-dimensional reconstruction method and system based on photogrammetric photometric stereo model Download PDF

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CN112070885A
CN112070885A CN202010895183.3A CN202010895183A CN112070885A CN 112070885 A CN112070885 A CN 112070885A CN 202010895183 A CN202010895183 A CN 202010895183A CN 112070885 A CN112070885 A CN 112070885A
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彭嫚
万文辉
王晔昕
刘召芹
邸凯昌
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Aerospace Information Research Institute of CAS
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Abstract

The invention relates to a three-dimensional reconstruction method and a system based on a photogrammetric photometric stereo model, which comprises the following steps: reading inner orientation posture, outer orientation posture parameters and incident ray vectors of the camera; substituting the parameters into a photogrammetry collinear equation and an error propagation equation to obtain a normal vector of an object space coordinate; according to the normal vector and the incident ray vector, solving a ray incident angle, an emergent angle and a phase angle cosine function; establishing a radiation equation of the image according to the incident angle, the emergent angle and the phase angle of the light; according to a radiation equation of the image, iteratively solving to obtain gradient values of the elevation in the x and y directions of image coordinates; and obtaining the relative elevation value of each point by utilizing least square solution according to the gradient values of the image space coordinates in the x and y directions, thereby obtaining the reconstructed three-dimensional model. The method can effectively break through the limitation that the three postures of the camera in the traditional photometric stereo are all 0 degrees, expand the application range of the photometric stereo in close-range photogrammetry and recover the relative elevation value of an object.

Description

Three-dimensional reconstruction method and system based on photogrammetric photometric stereo model
Technical Field
The invention relates to a three-dimensional reconstruction method and a three-dimensional reconstruction system based on a photogrammetric photometric stereo model, belonging to the technical field of image three-dimensional reconstruction.
Background
In computer vision, the three-dimensional reconstruction technology by using a photometric stereo method is to solve a normal vector of each point on the surface of an object by combining an image radiation equation and utilizing reflection characteristics according to three images obtained by a camera under different illumination conditions at the same position, so that the shape of the object is reconstructed.
The distance obtained by the existing photometric stereo method is usually the relative vertical distance from the lens plane of the camera under the condition of orthoscopic photography. When the terrain is measured by close-range photogrammetry, three angles of a camera are usually not 0 ℃ in practice in order to acquire the terrain within a certain range, so that the existing photometric stereo method is not suitable for three-dimensional reconstruction of a plurality of images in practical situations.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention provides a three-dimensional reconstruction method and system based on a photogrammetric photometric stereo model, which can effectively break through the limitation that the three postures of the camera in the traditional photometric stereo are all 0 °, expand the application range of the photometric stereo in close-range photogrammetry, and recover the relative elevation value of the object.
In order to achieve the above object, the present invention provides a three-dimensional reconstruction method based on photogrammetric photometric stereo model, comprising the following steps: s1, reading the inner orientation posture, the outer orientation posture parameter and the incident ray vector of the camera; s2, substituting the inner orientation attitude and the outer orientation attitude parameters into a photogrammetry collinear equation and an error propagation equation to obtain a normal vector of an object space coordinate; s3, according to the normal vector and the incident ray vector, the incidence angle, the emergence angle and the phase angle cosine function of the ray are obtained; s4, establishing a radiation equation of the image according to the incidence angle, the emergence angle and the phase angle cosine function of the light; s5, according to the radiation equation of the image, iteratively solving to obtain gradient values of the elevation in the x and y directions of the image coordinates; s6, according to the gradient values of the elevation in the x and y directions of the image coordinates, the relative elevation value of each point is obtained by utilizing least square solution, and therefore the reconstructed three-dimensional model is obtained.
Further, in step S2, the object-side vector is obtained by the gradient of the elevation Z in the x, y direction of the image side:
Figure BDA0002658225700000011
Figure BDA0002658225700000012
wherein (x, y) represents coordinates of an image point in image plane coordinates; (X, Y, Z) represents coordinate values of the object in the object coordinate system; (a)1,a2,a3,b1,b2,b3,c1,c2,c3) Representing a rotation matrix of the camera; f represents the focal length of the camera;
Figure BDA0002658225700000021
Figure BDA0002658225700000022
(XS,YS,ZS) Representing the three-dimensional coordinates of the camera image principal point.
Further, the specific step of step S3 includes: s3.1 according to the Camera position parameter (X)s,Ys,Zs) Obtaining an emergent ray vector V by the three-dimensional coordinates (X, Y, Z) of the target point; s3.2 converting the outgoing ray vector V and the ray incident vector L to (p)s,qsAnd 1) performing point multiplication on the normal vector of the object space coordinate and every two points to obtain a cosine function of the incident angle i, the emergence angle e and the phase angle alpha.
Further, the cosine function of the incident angle of the light ray in step S3 is:
Figure BDA0002658225700000023
wherein, L ═ ps,qsAnd 1) is the vector of the incident light,
Figure BDA0002658225700000024
is a normal vector of the object space coordinates; the cosine function of the exit angle of the light ray in step S3 is:
Figure BDA0002658225700000025
wherein, V ═ X (X-X)s,Y-Ys,Z-Zs) Is the vector of the outgoing light ray,
Figure BDA0002658225700000026
Figure BDA0002658225700000027
(x, y) denotes the coordinates of the image point in the image plane coordinates, (x)0,y0) Coordinates representing an image center point in the image plane coordinates; the cosine function of the phase angle of the light ray in step S3 is:
Figure BDA0002658225700000028
further, the process of establishing the radiation equation in step S4 is: acquiring a gray value of each pixel on an image, dividing the gray value by a fixed value to obtain a normalized value I (x, y), and establishing a radiation equation according to the normalized value I (x, y), the image irradiance rho, the incidence angle I, the emergence angle e and a cosine value of a phase angle alpha:
Figure BDA0002658225700000029
further, the specific process of S5 is: acquiring a radiation equation of a plurality of images shot by different rays at the same position, dividing the radiation equation by two, simplifying the obtained radiation equation, and then normalizing the components N in the X and Y directions of the normal vectorXAnd NYSetting as unknown number, given initial value to carry out iterative solution under limited condition, if the solution precision meets the precision requirement, outputting the result, and according to NXAnd NYRespectively obtaining the elevation Z in the x and y directions of the image spaceAnd (4) gradient.
Further, the limiting conditions are:
Figure BDA0002658225700000031
Figure BDA0002658225700000032
further, the gradient of the elevation Z in the x, y direction of the image is:
Figure BDA0002658225700000033
Figure BDA0002658225700000034
wherein:
Figure BDA0002658225700000035
further, step S6 specifically includes: establishing a difference matrix Dx in the x direction and a difference matrix Dy in the y direction, and writing the gradient of the elevation Z in the x and y directions of the image space:
Figure BDA0002658225700000036
order to
Figure BDA0002658225700000037
The equation for minimization is established as:
min{||g-DZ||2}
derivation of vector Z using least squares can be:
Z＝(DTD)-1DTg
calculating Z value and obtaining natural index eZ。
The invention also discloses a three-dimensional reconstruction system based on the photogrammetric luminosity stereo model, which comprises the following components: the parameter acquisition module is used for reading the inner orientation posture, the outer orientation posture parameters and the incident light ray vector of the camera; the normal vector calculation module is used for substituting the inner orientation attitude and the outer orientation attitude parameters into a photogrammetry collinear equation and an error propagation equation to obtain a normal vector of an object space coordinate; the angle calculation module is used for solving the cosine functions of the incident angle, the emergent angle and the phase angle of the light according to the normal vector and the incident light vector; the radiation equation establishing module is used for establishing a radiation equation of the image according to the incidence angle, the emergence angle and the phase angle cosine function of the light; the gradient calculation module is used for obtaining gradient values of the elevation in the x and y directions of the image coordinates through iterative solution according to the radiation equation of the image; and the output module is used for solving the relative elevation value of each point by using least square according to the gradient values of the image space coordinates in the x and y directions so as to obtain a reconstructed three-dimensional model.
Due to the adoption of the technical scheme, the invention has the following advantages:
1. the invention provides a three-dimensional reconstruction method of a photogrammetric photometric stereo, which enables images shot at any posture under different light rays to be subjected to elevation solution, thereby solving the problem that the traditional photometric stereo has the limitation that three angles of a camera are 0 degree.
2. The invention provides a brand-new three-dimensional reconstruction scheme, an object space coordinate system is set as an actual geodetic coordinate system, the relationship between the gradient of an elevation in an image plane coordinate and an object method vector is established, and the elevation value is solved through least square, so that the problem that the object space coordinate system in the traditional photometric stereo is necessarily parallel to the image plane coordinate system is solved, and the three-dimensional reconstruction method has better applicability, improved precision and better reliability.
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FIG. 1 is a schematic diagram of a photogrammetric photometric stereo model based three-dimensional reconstruction method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the relationship between the image plane coordinate system and the object coordinate system according to an embodiment of the present invention;
FIG. 3 is a schematic illustration of the incident angle, the exit angle and the phase angle of a light ray in an embodiment of the present invention.
Detailed Description
The present invention is described in detail by way of specific embodiments in order to better understand the technical direction of the present invention for those skilled in the art. It should be understood, however, that the detailed description is provided for a better understanding of the invention only and that they should not be taken as limiting the invention. In describing the present invention, it is to be understood that the terminology used is for the purpose of description only and is not intended to be indicative or implied of relative importance.
Example one
The embodiment discloses a three-dimensional reconstruction method based on a photogrammetric photometric stereo model, as shown in fig. 1, comprising the following steps:
s1 reads the inner orientation pose, outer orientation pose parameters and incident ray vector of the camera.
And reading the inner azimuth attitude, the outer azimuth attitude parameters, the gray value of the image and the sunlight azimuth angle and the sunlight altitude angle of the three images of the camera at the same position of close-range photography. The parameters of the inner orientation posture and the outer orientation posture, as shown in fig. 2, include coordinates (x, y) of an image point in the coordinates of the reading image plane; coordinate values (X, Y, Z) of the target in the object coordinate system; three-dimensional coordinates (X) of camera image principal points,Ys,Zs) (ii) a Rotation matrix of camera (a)1,a2,a3,b1,b2,b3,c1,c2,c3) Coordinates (x) of camera image principal point in image plane coordinate system0,y0) And the focal length f of the camera. And obtaining an incident light vector through the gray value of the image and the azimuth angle and the altitude angle of the sunlight of the three images.
S2, substituting the inner orientation attitude and the outer orientation attitude parameters into the photogrammetry collinear equation and the error propagation equation to obtain the normal vector of the object space coordinate.
As shown in fig. 2, the relationship between the image plane coordinate and the object coordinate can be obtained according to the collinear equation of photogrammetry as follows:
Figure BDA0002658225700000041
Figure BDA0002658225700000042
establishing a full differential equation of an object space elevation Z relative to object space coordinates X and Y according to an error propagation law:
Figure BDA0002658225700000051
Figure BDA0002658225700000052
to simplify the derivation process, let:
Figure BDA0002658225700000053
Figure BDA0002658225700000054
Figure BDA0002658225700000055
Figure BDA0002658225700000056
Figure BDA0002658225700000057
establishing an error equation according to a collinearity equation and an error propagation law:
Figure BDA0002658225700000058
Figure BDA0002658225700000059
Figure BDA00026582257000000510
Figure BDA00026582257000000511
the object-side normal vector is obtained by the gradient of the elevation Z in the x, y direction of the image:
Figure BDA00026582257000000512
Figure BDA00026582257000000513
to simplify the calculation, let
Figure BDA00026582257000000514
And
Figure BDA00026582257000000515
substituting the formula to obtain an object normal vector:
Figure BDA00026582257000000516
Figure BDA0002658225700000061
s3, according to the normal vector and the incident ray vector, the cosine function of the incident angle, the emergent angle and the phase angle of the ray is obtained.
The specific steps of step S3 include:
s3.1 according to the Camera position parameter (X)s,Ys,Zs) And obtaining the emergent ray vector V by the three-dimensional coordinates (X, Y, Z) of the target point.
V＝(X-XS,Y-YS,Z-ZS)
The emergent vector obtained after normalization processing is as follows:
Figure BDA0002658225700000062
according to the photogrammetric collinearity equation:
Figure BDA0002658225700000063
incident ray vector can be represented using image plane coordinates (x, y)
Figure BDA0002658225700000064
S3.2 converting the outgoing ray vector V and the ray incident vector L to (p)s,qsAnd 1) performing point multiplication on the normal vector of the object space coordinate and every two points to obtain a cosine function of the incident angle i, the emergence angle e and the phase angle alpha. Wherein the light ray incidence vector L is obtained according to the solar altitude angle h and the azimuth angle A, psRepresenting the component of sunlight in the X direction, qsRepresenting the component of sunlight in the Y direction
Figure BDA0002658225700000065
Figure BDA0002658225700000066
The relationship between the incident angle i, the exit angle e and the phase angle α is shown in fig. 3.
The cosine function of the incident angle of the light ray in step S3 is:
Figure BDA0002658225700000071
wherein, L ═ ps,qsAnd 1) is the vector of the incident light,
Figure BDA0002658225700000072
is a normal vector of the object space coordinates; the cosine function of the exit angle of the light ray in step S3 is:
Figure BDA0002658225700000073
wherein, V ═ X (X-X)s,Y-Ys,Z-Zs) Is the vector of the outgoing light ray,
Figure BDA0002658225700000074
Figure BDA0002658225700000075
(x, y) denotes the coordinates of the image point in the image plane coordinates, (x)0,y0) Coordinates representing an image center point in the image plane coordinates; the cosine function of the phase angle of the light ray in step S3 is:
Figure BDA0002658225700000076
s4, establishing a radiation equation of the image according to the incidence angle, the emergence angle and the cosine function of the phase angle of the light.
The process of establishing the radiation equation in step S4 is: acquiring a gray value of each pixel on the image, dividing the gray value by a fixed value, preferably 255 in this embodiment, to obtain a normalized value I (x, y), and establishing a radiation equation according to the normalized value I (x, y), the image irradiance ρ, the cosine values of the incident angle I, the emergent angle e, and the phase angle α:
Figure BDA0002658225700000077
and S5, according to the radiation equation of the image, iteratively solving to obtain gradient values of the elevation in the x and y directions of the image coordinates.
The specific process of S5 is as follows: acquiring a radiation equation of a plurality of images shot by different rays at the same position, and dividing the radiation equation by two:
Figure BDA0002658225700000078
where i, k are the serial numbers of the images, i, k is 1,2,3, i ≠ k, NX,NYIs the normalized component of the normal vector X and Y directions.
Figure BDA0002658225700000081
Figure BDA0002658225700000082
Thereby obtaining the component V of the emergent ray vector in the X directionXAnd a component V in the Y directionY：
Figure BDA0002658225700000083
Figure BDA0002658225700000084
The resulting radiation equation is simplified:
Figure BDA0002658225700000085
wherein:
Figure BDA0002658225700000086
Figure BDA0002658225700000087
Figure BDA0002658225700000088
Figure BDA0002658225700000089
Figure BDA00026582257000000810
Figure BDA00026582257000000811
Figure BDA00026582257000000812
is the magnitude of the mode of the exit vector,
Figure BDA00026582257000000813
showing the magnitude of the mode of the sunlight incidence vector of the k-th and i-th images,
Figure BDA00026582257000000814
the sunlight incidence vectors of the k-th and i-th images are shown.
Then, the normalized component N in the X and Y directions of the normal vectorXAnd NYSetting as unknown number, given initial value to carry out iterative solution under limited condition, if the solution precision meets the precision requirement, outputting the result, and according to NXAnd NYThe gradients of the elevation Z in the x and y directions of the image are obtained respectively. The precision requirement is that the difference between the n-time solution and the n-1-time solution result is less than 0.00001.
Wherein the limiting conditions are as follows:
Figure BDA0002658225700000091
Figure BDA0002658225700000092
the gradient of the elevation Z in the x, y direction of the image space is:
Figure BDA0002658225700000093
Figure BDA0002658225700000094
wherein:
Figure BDA0002658225700000095
s6, according to the gradient values of the elevation Z in the x and y directions of the image coordinates, obtaining the relative elevation value of each point by using least square solution, thereby obtaining the reconstructed three-dimensional model.
Step S6 specifically includes: establishing a difference matrix Dx in the x direction and a difference matrix Dy in the y direction, and writing the gradient of the elevation Z in the x and y directions of the image space:
Figure BDA0002658225700000096
order to
Figure BDA0002658225700000097
The equation for minimization is established as:
min{||g-DZ||2}
wherein | | | purple hair2Representing a 2-normal form of the matrix.
Derivation of vector Z using least squares can be:
Z＝(DTD)-1DTg
calculating Z value, because the elevation is logarithmized and then elevation gradient is calculated in the derivation of p and q, finally, natural index e is calculated for each pixel Z valueZ。
Example two
Based on the same inventive concept, the embodiment also discloses a three-dimensional reconstruction system based on the photogrammetric photometric stereo model, which comprises:
the parameter acquisition module is used for reading the inner orientation posture, the outer orientation posture parameters and the incident light ray vector of the camera;
the normal vector calculation module is used for substituting the inner orientation attitude and the outer orientation attitude parameters into a photogrammetry collinear equation and an error propagation equation to obtain a normal vector of an object space coordinate;
the angle calculation module is used for solving the cosine functions of the incident angle, the emergent angle and the phase angle of the light according to the normal vector and the incident light vector;
the radiation equation establishing module is used for establishing a radiation equation of the image according to the incidence angle, the emergence angle and the phase angle cosine function of the light;
the gradient calculation module is used for obtaining gradient values of the elevation in the x and y directions of the image coordinates through iterative solution according to the radiation equation of the image;
and the output module is used for solving the relative elevation value of each point by using least square according to the gradient values of the image space coordinates in the x and y directions so as to obtain a reconstructed three-dimensional model.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims. The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application. Therefore, the protection scope of the present application should be defined by the claims.

Claims (10)

1. A three-dimensional reconstruction method based on a photogrammetric photometric stereo model is characterized by comprising the following steps:
s1, reading the inner orientation posture, the outer orientation posture parameter and the incident ray vector of the camera;
s2, substituting the inner orientation attitude and the outer orientation attitude parameters into a photogrammetry collinear equation and an error propagation equation to obtain a normal vector of an object space coordinate;
s3, according to the normal vector and the incident ray vector, obtaining an incident angle, an emergent angle and a phase angle cosine function of the ray;
s4, establishing a radiation equation of the image according to the incidence angle, the emergence angle and the phase angle cosine function of the light;
s5, according to the radiation equation of the image, iteratively solving to obtain gradient values of the elevation in the x and y directions of the image coordinates;
s6, according to the gradient values of the image space coordinates in the x and y directions, obtaining the relative elevation value of each point by using least square solution, thereby obtaining the reconstructed three-dimensional model.
2. The photogrammetric photometric stereo model-based three-dimensional reconstruction method according to claim 1, wherein the object-side vector in the step S1 is obtained by gradient of elevation Z in x, y direction of the image side:
Figure FDA0002658225690000011
Figure FDA0002658225690000012
wherein (x, y) represents coordinates of an image point in image plane coordinates;(X, Y, Z) represents coordinate values of the object in the object coordinate system; (a)1,a2,a3,b1,b2,b3,c1,c2,c3) Representing a rotation matrix of the camera; f represents the focal length of the camera;
Figure FDA0002658225690000013
(XS,YS,ZS) Representing the three-dimensional coordinates of the camera image principal point.
3. The photogrammetric photometric stereo model based three-dimensional reconstruction method according to claim 1 or 2, wherein the specific steps of the step S3 include:
s3.1 according to the Camera position parameter (X)s,Ys,Zs) Obtaining an emergent ray vector V by the three-dimensional coordinates (X, Y, Z) of the target point;
s3.2 sets the outgoing ray vector V and the ray incident vector L to (p)s,qsAnd 1) performing point multiplication on the normal vector of the object space coordinate and every two points to obtain a cosine function of the incident angle i, the emergence angle e and the phase angle alpha.
4. The photogrammetric photometric stereo model-based three-dimensional reconstruction method according to claim 3, wherein the cosine function of the incident angle of the light ray in the step S3 is:
Figure FDA0002658225690000014
wherein, L ═ ps,qsAnd 1) is the vector of the incident light,
Figure FDA0002658225690000021
is a normal vector of the object space coordinates;
the cosine function of the exit angle of the light ray in the step S3 is:
Figure FDA0002658225690000022
wherein, V ═ X (X-X)s,Y-Ys,Z-Zs) Is the vector of the outgoing light ray,
Figure FDA0002658225690000023
(x, y) denotes the coordinates of the image point in the image plane coordinates, (x)0,y0) Coordinates representing an image center point in the image plane coordinates;
the cosine function of the azimuth angle of the light ray in the step S3 is:
Figure FDA0002658225690000024
5. the photogrammetric photometric stereo model-based three-dimensional reconstruction method according to claim 4, wherein the radiation equation is established in the step S4 by: acquiring a gray value of each pixel on an image, dividing the gray value by a fixed value to obtain a normalized value I (x, y), and establishing a radiation equation according to the normalized value I (x, y), the image irradiance rho, the incidence angle I, the emergence angle e and a cosine value of a phase angle alpha:
Figure FDA0002658225690000025
6. the photogrammetric photometric stereo model-based three-dimensional reconstruction method according to claim 5, wherein the specific process of S5 is: acquiring a radiation equation of a plurality of images shot by different rays at the same position, dividing the radiation equation in pairs, simplifying the obtained radiation equation, and then normalizing the components N in the X and Y directions of the normal vectorXAnd NYSetting as unknown number, and given initial value to carry out iterative solution under limited condition, such as solution refinementIf the degree meets the precision requirement, outputting a result according to the NXAnd NYThe gradients of the elevation Z in the x and y directions of the image are obtained respectively.
7. The photogrammetric photometric stereo model based three-dimensional reconstruction method according to claim 6, characterized in that the defining conditions are:
Figure FDA0002658225690000026
Figure FDA0002658225690000027
8. the photogrammetric photometric stereo model based three-dimensional reconstruction method according to claim 7, characterized in that the gradient of the elevation Z in the x, y direction of the image space is:
Figure FDA0002658225690000031
Figure FDA0002658225690000032
wherein:
Figure FDA0002658225690000033
9. the photogrammetric photometric stereo model-based three-dimensional reconstruction method according to claim 8, wherein the step S6 specifically comprises: establishing a difference matrix Dx in the x direction and a difference matrix Dy in the y direction, and writing the gradient of the elevation Z in the x and y directions of an image space:
Figure FDA0002658225690000034
order to
Figure FDA0002658225690000035
The equation for minimization is established as:
min{||g-DZ||2}
derivation of vector Z using least squares can be:
Z＝(DTD)-1DTg
calculating Z value and obtaining natural index eZ。
10. A photogrammetric photometric stereo model based three-dimensional reconstruction system comprising:
the parameter acquisition module is used for reading the inner orientation posture, the outer orientation posture parameters and the incident light ray vector of the camera;
the normal vector calculation module is used for substituting the inner orientation attitude and the outer orientation attitude parameters into a photogrammetry collinear equation and an error propagation equation to obtain a normal vector of an object space coordinate;
the angle calculation module is used for solving the cosine functions of the incident angle, the emergent angle and the phase angle of the light according to the normal vector and the incident light vector;
the radiation equation establishing module is used for establishing a radiation equation of the image according to the incidence angle, the emergence angle and the phase angle cosine function of the light;
the gradient calculation module is used for obtaining gradient values of the elevation in the x and y directions of the image coordinates through iterative solution according to the radiation equation of the image;
and the output module is used for solving by utilizing least square according to the gradient values of the image space coordinates in the x and y directions to obtain the relative elevation value of each point, so that a reconstructed three-dimensional model is obtained.
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