CN112070885B - Three-dimensional reconstruction method and system based on photogrammetry photometric stereo model - Google Patents
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Abstract
The invention relates to a three-dimensional reconstruction method and a system based on a photogrammetry photometric stereo model, comprising the following steps: reading the parameters of the internal azimuth posture and the external azimuth posture of the camera and the incident ray vector; substituting the parameters into a photogrammetry collineation equation and an error propagation equation to obtain a normal vector of the object space coordinate; according to the normal vector and the incident ray vector, obtaining the cosine functions of the incident angle, the emergent angle and the phase angle of the ray; establishing a radiation equation of the image according to the incident angle, the emergent angle and the phase angle of the light; according to the radiation equation of the image, iteratively solving to obtain a gradient value in the x-direction and the y-direction of the Gao Chengzai image space coordinates; and obtaining the relative elevation value of each point by utilizing least square solution according to the gradient values in the x and y directions of the image space coordinates, thereby obtaining the reconstructed three-dimensional model. The three-dimensional camera can effectively break through the limitation that three postures of a 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
Technical Field
The invention relates to a three-dimensional reconstruction method and a three-dimensional reconstruction system based on a photogrammetry photometric stereo model, and belongs to the technical field of three-dimensional reconstruction of images.
Background
In computer vision, the three-dimensional reconstruction technology by utilizing a photometric stereo method is to reconstruct the shape of an object by combining an image radiation equation and solving the normal vector of each point on the surface of the object by utilizing reflection characteristics according to three images obtained by a camera under the same position under different illumination conditions.
The distance found by existing photometric stereo methods is typically the relative perpendicular distance from the camera lens plane under normal photography conditions. When the topography is measured by using close-range photogrammetry, in order to obtain the topography in a certain range, the three angles of the camera are usually not 0 ° in practice, so the existing photometric stereo method is not suitable for three-dimensional reconstruction of multiple images in practical situations.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a three-dimensional reconstruction method and a three-dimensional reconstruction system based on a photogrammetry photometric stereo model, which can effectively break through the limitation that three postures of a 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.
In order to achieve the above object, the present invention provides a three-dimensional reconstruction method based on a photogrammetric stereo model, comprising the steps of: s1, reading the parameters of the internal azimuth posture and the external azimuth posture of a camera and the incident ray vector; s2, substituting the internal azimuth attitude and the external azimuth attitude parameters into a photogrammetric collineation equation and an error propagation equation to obtain a normal vector of an object coordinate; s3, according to the normal vector and the incident light vector, obtaining cosine functions of an incident angle, an emergent angle and a phase angle of the light; s4, establishing a radiation equation of the image according to cosine functions of an incident angle, an emergent angle and a phase angle of the light; s5, according to a radiation equation of the image, iteratively solving to obtain gradient values in x and y directions of Gao Chengzai image space coordinates; s6, obtaining the relative elevation value of each point by utilizing least square solution according to the gradient values of Gao Chengzai in the x and y directions of the image space coordinates, thereby obtaining the reconstructed three-dimensional model.
Further, in step S2, the object method vector is obtained by gradient of the elevation Z in the x, y directions of the image space:
Wherein (x, y) represents the coordinates of an image point in the image plane coordinates; (X, Y, Z) represents coordinate values ;(a1,a2,a3,b1,b2,b3,c1,c2,c3) of the target in the object coordinate system to represent a rotation matrix of the camera; f represents the focal length of the camera; (X S,YS,ZS) represents the three-dimensional coordinates of the principal point of the camera image.
Further, the specific steps of step S3 include: s3.1, obtaining an emergent ray vector V according to the camera position parameter (X s,Ys,Zs) and the three-dimensional coordinates (X, Y, Z) of the target point; and S3.2, multiplying the emergent ray vector V, the ray incidence vector L= (p s,qs, 1) and the normal vector of the object coordinate by two points to obtain the cosine function of the incident angle i, the emergent angle e and the phase angle alpha.
Further, the cosine function of the incident angle of the light in step S3 is:
Where l= (p s,qs, 1) is the incident ray vector, Is the normal vector of the object space coordinates; the cosine function of the exit angle of the light in step S3 is:
wherein V= (X-X s,Y-Ys,Z-Zs) is the outgoing ray vector, (X, y) represents coordinates of an image point in the image plane coordinates, (x 0,y0) represents coordinates of an image center point in the image plane coordinates; the cosine function of the phase angle of the light in step S3 is:
Further, the radiation equation establishment process in step S4 is as follows: the gray value of each pixel on the image is obtained and divided by a fixed value to obtain a normalized value I (x, y), and a radiation equation is established according to the normalized value I (x, y), the irradiance rho of the image, the incident angle I, the emergence angle e and the cosine value of the phase angle alpha:
Further, the specific process of S5 is: obtaining radiation equations of a plurality of images shot by different light rays at the same position, dividing the radiation equations by each other, simplifying the obtained radiation equations, then setting normalized normal vector X and components N X and N Y in the Y direction as unknowns, and under a limiting condition, carrying out iterative solution on a given initial value, if the solution precision meets the precision requirement, outputting a result, and respectively obtaining gradients of an elevation Z in the X and Y directions of an image space according to N X and N Y.
Further, the limitation conditions are:
further, the gradient of the elevation Z in the x, y direction of the image is:
Wherein:
further, the step S6 specifically includes: establishing a differential matrix Dx in the x direction and a differential matrix Dy in the y direction, and writing a gradient of an elevation Z in the x and y directions of an image side:
Order the The set-up results with respect to the minimization equation are:
min{||g-DZ||2}
the derivative of vector Z is available using least squares:
Z＝(DTD)-1DTg
the Z value is determined and the natural index e Z is taken.
The invention also discloses a three-dimensional reconstruction system based on the photogrammetry photometric stereo model, which comprises: the parameter acquisition module is used for reading the parameters of the internal azimuth posture and the external azimuth posture of the camera and the incident ray vector; the normal vector calculation module is used for substituting the parameters of the internal azimuth posture and the external azimuth posture into a photogrammetric collineation equation and an error propagation equation to calculate the normal vector of the object coordinate; the angle calculation module is used for obtaining cosine functions of an incident angle, an emergent angle and a phase angle of the light according to the normal vector and the incident light vector; the radiation equation building module is used for building a radiation equation of the image according to cosine functions of the incident angle, the emergent angle and the phase angle of the light; the gradient calculation module is used for obtaining gradient values in x and y directions of Gao Chengzai image space coordinates by iterative solution according to a radiation equation of the image; and the output module is used for 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, so as to obtain the 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 photogrammetry, which enables images photographed in any posture under different light rays to be subjected to elevation solution, thereby solving the problem that the traditional photogrammetry limits three angles of a camera to 0 degrees.
2. The invention provides a brand new three-dimensional reconstruction scheme, the object space coordinate system is set as an actual geodetic coordinate system, and the problem that the object space coordinate system in the traditional luminosity three-dimensional system must be parallel to the image plane coordinate system is solved by establishing the relation between the gradient of the elevation in the image plane coordinate and the object space vector and solving the elevation value through least square, so that the method has better applicability, improved precision and better reliability.
Drawings
FIG. 1 is a schematic diagram of a three-dimensional reconstruction method based on a photogrammetric stereo model in an embodiment of the present invention;
FIG. 2 is a schematic diagram of the relationship between an image plane coordinate system and an object space coordinate system according to an embodiment of the present invention;
Fig. 3 is a schematic view of an incident angle, an exit angle and a phase angle of a light ray according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples thereof in order to better understand the technical direction of the present invention by those skilled in the art. It should be understood, however, that the detailed description is presented only to provide a better understanding of the invention, and should not be taken to limit the invention. In the description of the present invention, it is to be understood that the terminology used is for the purpose of description only and is not to be interpreted as indicating or implying relative importance.
Example 1
The embodiment discloses a three-dimensional reconstruction method based on a photogrammetry photometric stereo model, as shown in fig. 1, comprising the following steps:
s1, reading the internal azimuth posture, the external azimuth posture parameters and the incident ray vector of the camera.
And reading the internal azimuth attitude and the external azimuth attitude parameters of the camera, the gray values of the images and the sunlight azimuth angles and the altitude angles of the three images at the same position of the close-range photography. Wherein the internal azimuth pose and the external azimuth pose parameters, as shown in fig. 2, comprise reading coordinates (x, y) of an image point in the coordinates of an image plane; coordinate values (X, Y, Z) of the target in the object coordinate system; three-dimensional coordinates (X s,Ys,Zs) of the principal point of the camera image; the rotation matrix (a1,a2,a3,b1,b2,b3,c1,c2,c3), of the camera the coordinates of the camera image principal point in the image plane coordinate system (x 0,y0) and the focal length f of the camera. And obtaining an incident light vector through the gray value of the image and the sunlight azimuth angle and the altitude angle of the three images.
S2, substituting the parameters of the internal azimuth posture and the external azimuth posture into a photogrammetric collineation equation and an error propagation equation to obtain a normal vector of the object coordinate.
As shown in fig. 2, the relationship between the image plane coordinates and the object space coordinates can be obtained according to the collinearity equation of the photogrammetry:
establishing a full differential equation of the object elevation Z with respect to the object coordinates X and Y according to an error propagation law:
To simplify the derivation process, let:
establishing an error equation according to the collinearity equation and the error propagation law:
The object method vector is obtained by the gradient of the elevation Z in the x, y direction of the image:
To simplify the calculation, set up And/>Substituting the above formula to obtain the object method vector:
S3, according to the normal vector and the incident light vector, the cosine functions of the incident angle, the emergent angle and the phase angle of the light are obtained.
The specific steps of the step S3 include:
s3.1, obtaining an emergent ray vector V according to the camera position parameter (X s,Ys,Zs) and 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:
according to the photogrammetric collinearly equation:
The incident ray vector can be represented using image plane coordinates (x, y)
And S3.2, multiplying the emergent ray vector V, the ray incidence vector L= (p s,qs, 1) and the normal vector of the object coordinate by two points to obtain the cosine function of the incident angle i, the emergent angle e and the phase angle alpha. Wherein the ray incidence vector L is obtained from the solar altitude h and the azimuth angle A, p s represents the component of sunlight in the X direction, and q s represents the component of sunlight in the Y direction
The relationship of 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 in step S3 is:
Where l= (p s,qs, 1) is the incident ray vector, Is the normal vector of the object space coordinates; the cosine function of the exit angle of the light in step S3 is:
wherein V= (X-X s,Y-Ys,Z-Zs) is the outgoing ray vector, (X, y) represents coordinates of an image point in the image plane coordinates, (x 0,y0) represents coordinates of an image center point in the image plane coordinates; the cosine function of the phase angle of the light in step S3 is:
s4, establishing a radiation equation of the image according to cosine functions of the incident angle, the emergent angle and the phase angle of the light.
The radiation equation establishment process in step S4 is as follows: the gray value of each pixel on the image is obtained and divided by a fixed value, in this embodiment, the preferred fixed value is 255, a normalized value I (x, y) is obtained, and a radiation equation is established according to the normalized value I (x, y), the image irradiance ρ, and the cosine values of the incident angle I, the exit angle e, and the phase angle α:
and S5, according to a radiation equation of the image, iteratively solving to obtain gradient values in x and y directions of Gao Chengzai image space coordinates.
S5, the specific process is as follows: acquiring radiation equations of a plurality of images shot by different light rays at the same position, and dividing the radiation equations into two parts:
where i, k is the number of the image, i, k=1, 2,3, i+.k, and N X,NY is the normalized component of the normal vector X, Y.
Thereby obtaining a component V X of the outgoing light vector in the X direction and a component V Y in the Y direction:
simplifying the obtained radiation equation:
Wherein:
is the magnitude of the mode of the exit vector,/> The magnitude of the mode representing the solar incident vector of the kth and ith images,/>The solar light incidence vectors of the kth and ith images are shown.
And then, setting components N X and N Y in the normal vector X and Y directions after normalization as unknowns, and under a limiting condition, carrying out iterative solution on a given initial value, if the solution precision meets the precision requirement, outputting a result, and respectively obtaining gradients of the elevation Z in the directions of the image space X and Y according to N X and N Y. The accuracy requirement is that the difference between the solution of n times and the solution of n-1 times is less than 0.00001.
Wherein, the limiting conditions are as follows:
The gradient of the elevation Z in the x, y direction of the image space is:
Wherein:
S6, obtaining the relative elevation value of each point by utilizing least square solution according to the gradient value of the elevation Z in the x and y directions of the image space coordinates, thereby obtaining the reconstructed three-dimensional model.
The step S6 specifically comprises the following steps: establishing a differential matrix Dx in the x direction and a differential matrix Dy in the y direction, and writing a gradient of an elevation Z in the x and y directions of an image side:
Order the The set-up results with respect to the minimization equation are:
min{||g-DZ||2}
where 2 represents the 2-normal form of the matrix.
The derivative of vector Z is available using least squares:
Z＝(DTD)-1DTg
Since the elevation is logarithmically further raised Cheng Tidu in the derivation of p and q to obtain the Z value, the natural index e Z is finally obtained for each pixel Z value obtained.
Example two
Based on the same inventive concept, the embodiment also discloses a three-dimensional reconstruction system based on a photogrammetric stereo model, comprising:
the parameter acquisition module is used for reading the parameters of the internal azimuth posture and the external azimuth posture of the camera and the incident ray vector;
the normal vector calculation module is used for substituting the parameters of the internal azimuth posture and the external azimuth posture into a photogrammetric collineation equation and an error propagation equation to calculate the normal vector of the object coordinate;
The angle calculation module is used for obtaining cosine functions of an incident angle, an emergent angle and a phase angle of the light according to the normal vector and the incident light vector;
the radiation equation building module is used for building a radiation equation of the image according to cosine functions of the incident angle, the emergent angle and the phase angle of the light;
The gradient calculation module is used for obtaining gradient values in x and y directions of Gao Chengzai image space coordinates by iterative solution according to a radiation equation of the image;
And the output module is used for 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, so as to obtain the reconstructed three-dimensional model.
Finally, it should be noted that: the above embodiments are only for illustrating the technical aspects of the present application and not for limiting the same, and although the present application has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the application without departing from the spirit and scope of the application, which is intended to be covered by the claims. The foregoing is merely illustrative of the present application, and the present application is not limited thereto, and any person skilled in the art will readily appreciate variations or alternatives within the scope of the present application. Therefore, the protection scope of the application should be as defined in the claims.
Claims (4)
1. The three-dimensional reconstruction method based on the photogrammetry photometric stereo model is characterized by comprising the following steps of:
S1, reading the parameters of the internal azimuth posture and the external azimuth posture of a camera and the incident ray vector;
S2, substituting the internal azimuth posture and the external azimuth posture parameters into a photogrammetric collineation equation and an error propagation equation to obtain a normal vector of an object coordinate;
S3, according to the normal vector and the incident light vector, obtaining cosine functions of an incident angle, an emergent angle and a phase angle of the light;
S4, establishing a radiation equation of the image according to cosine functions of the incidence angle, the emergence angle and the phase angle of the light;
s5, according to a radiation equation of the image, iteratively solving to obtain a gradient value in the x-y direction of Gao Chengzai image space coordinates;
S6, obtaining a 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, so as to obtain a reconstructed three-dimensional model;
In the step S1, the object method vector is obtained by gradient of the elevation Z in the x, y direction of the image space:
Wherein (x, y) represents the coordinates of an image point in the image plane coordinates; (X, Y, Z) represents coordinate values ;(a1,a2,a3,b1,b2,b3,c1,c2,c3) of the target in the object coordinate system to represent a rotation matrix of the camera; f represents the focal length of the camera;
(X S,YS,ZS) represents the three-dimensional coordinates of the principal point of the camera image;
The specific steps of the step S3 include:
s3.1, obtaining an emergent ray vector V according to the camera position parameter (X s,Ys,Zs) and the three-dimensional coordinates (X, Y, Z) of the target point;
S3.2, multiplying the emergent ray vector V, the ray incidence vector L= (p s,qs, 1) and the normal vector of the object coordinate by two points to obtain cosine functions of an incident angle i, an emergent angle e and a phase angle alpha;
the cosine function of the incident angle of the light in step S3 is:
Where l= (p s,qs, 1) is the incident ray vector, Is the normal vector of the object space coordinates;
The cosine function of the exit angle of the light in step S3 is:
wherein V= (X-X s,Y-Ys,Z-Zs) is the outgoing ray vector, (X, y) represents coordinates of an image point in the image plane coordinates, (x 0,y0) represents coordinates of an image center point in the image plane coordinates;
the cosine function of the azimuth angle of the light in the step S3 is as follows:
the radiation equation establishing process in the step S4 is as follows: the gray value of each pixel on the image is obtained and divided by a fixed value to obtain a normalized value I (x, y), and a radiation equation is established according to the normalized value I (x, y), the image irradiance rho and cosine values of an incident angle I, an exit angle e and a phase angle alpha:
The specific process of S5 is as follows: acquiring radiation equations of a plurality of images shot by different light rays at the same position, dividing the radiation equations by each other, simplifying the acquired radiation equations, then setting components N X and N Y in the normal vector X and Y directions after normalization as unknowns, and under a limiting condition, carrying out iterative solution on a given initial value, if the solution precision meets the precision requirement, outputting a result, and respectively acquiring gradients of an elevation Z in the X and Y directions according to the N X and the N Y;
The limiting conditions are as follows:
2. The three-dimensional reconstruction method based on a photogrammetric stereoscopic model according to claim 1, wherein the gradient of the elevation Z in the x, y direction of the image space is:
Wherein:
3. the three-dimensional reconstruction method based on a photogrammetric stereoscopic model according to claim 2, wherein the step S6 specifically comprises: establishing a differential matrix Dx in the x direction and a differential matrix Dy in the y direction, and writing gradients of the elevation Z in the x and y directions of an image side:
Order the The set-up results with respect to the minimization equation are:
min{||g-DZ||2}
the derivative of vector Z is available using least squares:
Z＝(DTD)-1DTg
the Z value is determined and the natural index e Z is taken.
4. A three-dimensional reconstruction system based on a photogrammetric volumetric model, comprising:
the parameter acquisition module is used for reading the parameters of the internal azimuth posture and the external azimuth posture of the camera and the incident ray vector;
The normal vector calculation module is used for substituting the internal azimuth attitude and the external azimuth attitude parameters into a photogrammetry collineation equation and an error propagation equation to obtain a normal vector of the object space coordinate;
The angle calculation module is used for obtaining cosine functions of an incident angle, an emergent angle and a phase angle of the light according to the normal vector and the incident light vector;
The radiation equation building module is used for building a radiation equation of an image according to cosine functions of the incidence angle, the emergence angle and the phase angle of the light;
The gradient calculation module is used for obtaining gradient values in x and y directions of Gao Chengzai image space coordinates by iterative solution according to a radiation equation of the image;
The output module is used for 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, so as to obtain a reconstructed three-dimensional model;
the object method vector in the step parameter acquisition module is obtained through gradient of the elevation Z in the x and y directions of the image side:
Wherein (x, y) represents the coordinates of an image point in the image plane coordinates; (X, Y, Z) represents coordinate values ;(a1,a2,a3,b1,b2,b3,c1,c2,c3) of the target in the object coordinate system to represent a rotation matrix of the camera; f represents the focal length of the camera;
(X S,YS,ZS) represents the three-dimensional coordinates of the principal point of the camera image;
the specific steps of the angle calculation module comprise:
s3.1, obtaining an emergent ray vector V according to the camera position parameter (X s,Ys,Zs) and the three-dimensional coordinates (X, Y, Z) of the target point;
S3.2, multiplying the emergent ray vector V, the ray incidence vector L= (p s,qs, 1) and the normal vector of the object coordinate by two points to obtain cosine functions of an incident angle i, an emergent angle e and a phase angle alpha;
The cosine function of the incident angle of the light in the angle calculation module is as follows:
Where l= (p s,qs, 1) is the incident ray vector, Is the normal vector of the object space coordinates;
the cosine function of the emergence angle of the light ray in the angle calculation module is as follows:
wherein V= (X-X s,Y-Ys,Z-Zs) is the outgoing ray vector, (X, y) represents coordinates of an image point in the image plane coordinates, (x 0,y0) represents coordinates of an image center point in the image plane coordinates;
the cosine function of the azimuth angle of the light in the angle calculation module is as follows:
The radiation equation establishment process in the radiation equation establishment module is as follows: the gray value of each pixel on the image is obtained and divided by a fixed value to obtain a normalized value I (x, y), and a radiation equation is established according to the normalized value I (x, y), the image irradiance rho and cosine values of an incident angle I, an exit angle e and a phase angle alpha:
The specific process of the gradient calculation module is as follows: acquiring radiation equations of a plurality of images shot by different light rays at the same position, dividing the radiation equations by each other, simplifying the acquired radiation equations, then setting components N X and N Y in the normal vector X and Y directions after normalization as unknowns, and under a limiting condition, carrying out iterative solution on a given initial value, if the solution precision meets the precision requirement, outputting a result, and respectively acquiring gradients of an elevation Z in the X and Y directions according to the N X and the N Y;
The limiting conditions are as follows:
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