CN109961410B - Optimized image pre-distortion method - Google Patents
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Abstract
The invention discloses an optimized image predistortion method, which comprises the following steps: s1, expressing the nonlinear relation between an original image and a distorted image of a display by utilizing a polynomial transformation equation set between pixel coordinates; s2, under the condition that the number of conversion points between the original image and the distorted image is more than the number of unknowns in the polynomial conversion equation set, solving the polynomial conversion equation set by using a least square algorithm to obtain a conversion coefficient; and S3, obtaining a distorted image by adopting a Lanczos interpolation algorithm according to the transformation coefficient, so as to counteract the distorted image of the optical system of the display. The optimized image predistortion method overcomes the problem of image distortion of a display optical system in the prior art, and realizes the correction of a distorted image.
Description
Technical Field
The present invention relates to image distortion correction, and in particular, to an optimized image pre-distortion method.
Background
Image distortion correction is one of the research hotspots in recent years, and is widely applied to the research fields of aerial photogrammetry, computer graphics, computer vision, helmet display and the like. The image distortion correction includes image distortion and image correction, the image distortion refers to mapping from an original image to a distorted image, and the image correction refers to mapping from the distorted image to the original image. The image distortion includes linear distortion and nonlinear distortion, the former includes perspective distortion and the like, and the latter includes radial distortion and tangential distortion and the like.
The optical system is used as an important component of the helmet-mounted display, the off-axis design is the main design mode of the optical system, and the off-axis optical system has complex distortion problems including radial distortion and tangential distortion, and also including bow distortion and trapezoidal distortion. The distortion caused by the optical system is corrected by two methods, one is a pre-distortion method, the pre-distortion method is to transform a normal original image into a pre-distortion image required by the optical system to offset the image distortion caused by the optical system, and the image is projected to display a distortion-free image; the other method is posterior correction method, which uses polynomial curve to fit each distorted net line in horizontal and vertical directions, then obtains inverse transformation correction function, and uses the correction function to process the distorted image to obtain the image with corrected distortion.
Disclosure of Invention
The invention aims to provide an optimized image predistortion method, which overcomes the problem of image distortion of a display optical system in the prior art and realizes the correction of a distorted image.
In order to achieve the above object, the present invention provides an optimized image predistortion method, including:
s1, expressing the nonlinear relation between an original image and a distorted image of a display by utilizing a polynomial transformation equation set between pixel coordinates;
s2, under the condition that the number of conversion points between the original image and the distorted image is more than the number of unknowns in the polynomial conversion equation set, solving the polynomial conversion equation set by using a least square algorithm to obtain a conversion coefficient;
and S3, obtaining a distorted image by adopting a Lanczos interpolation algorithm according to the transformation coefficient, so as to counteract the distorted image of the optical system of the display.
Preferably, in S1, the method for expressing the non-linear relationship between the original image and the distorted image of the display by using the polynomial transformation equation set between pixel coordinates includes:
u ', v' are coordinate points of the distorted image, x, y are coordinate points of the original image, N is the degree of the undetermined polynomial, a ij And b ij Is the transform coefficient of the pending polynomial.
Preferably, in S2, the method for solving the polynomial transformation equation set to obtain the transformation coefficient by using the least square algorithm includes:
the sum of squared errors after fitting is minimized using the following polynomial:
wherein epsilon x 、ε y Is the sum of squared errors, u 'and v' are coordinate points of the distorted image, x and y are coordinate points of the original image, N is the degree of the polynomial, L is the number of control points, a ij And b ij Transform coefficients that are to-be-determined polynomials.
Preferably, in S2, the least square algorithm is used to solve the polynomial transformation equation system to obtain the transformation coefficient, such that the maximum relative error value is less than 0.5% by the following formula:
wherein E is max Is the maximum relative error value, r model Is coordinate data of a distorted image, r real Is the coordinate data of the original image.
According to the technical scheme, the predistortion method based on the least square algorithm and the Lanczos interpolation algorithm generates distortion effect on a normal image, then the obtained distorted image is used as an input signal of the helmet display to counteract the distortion caused by an optical system in the helmet display, namely the distortion generated by the predistortion method and the distortion generated by the optical system in the helmet display are mutually counteracted, namely the distortion is presented to an observer as a normal original image.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
FIG. 1a is a checkerboard diagram illustrating an original image of a simulation experiment of the present invention;
FIG. 1b is a grid diagram illustrating an original image of a simulation experiment of the present invention;
FIG. 1c is a US army standard resolution panel illustrating the raw images of the simulation experiment of the present invention;
FIG. 2a is a checkerboard plot of a distorted image illustrating a simulation experiment of the present invention;
FIG. 2b is a grid plot of a distorted image illustrating a simulation experiment of the present invention;
FIG. 2c is a Max's standard resolution panel illustrating a distorted image of a simulation experiment of the present invention.
Detailed Description
The following describes in detail embodiments of the present invention with reference to the drawings. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are given by way of illustration and explanation only, not limitation.
The invention provides an optimized image predistortion method, which comprises the following steps:
s1, expressing the nonlinear relation between an original image and a distorted image of a display by utilizing a polynomial transformation equation set between pixel coordinates;
s2, under the condition that the number of conversion points between the original image and the distorted image is more than the number of unknowns in the polynomial conversion equation set, solving the polynomial conversion equation set by using a least square algorithm to obtain a conversion coefficient;
and S3, obtaining a distorted image by adopting a Lanczos interpolation algorithm according to the transformation coefficient, so as to counteract the distorted image of the optical system of the display.
According to the technical scheme, the predistortion method based on the least square algorithm and the Lanczos interpolation algorithm generates distortion effect on a normal image, then the obtained distorted image is used as an input signal of the helmet display to counteract the distortion caused by an optical system in the helmet display, namely the distortion generated by the predistortion method and the distortion generated by the optical system in the helmet display are mutually counteracted, namely the distortion is presented to an observer as a normal original image.
In one embodiment of the present invention, in S1, a method for expressing a non-linear relationship between an original image and a distorted image of a display by using a polynomial transformation equation set between pixel coordinates includes:
u ', v' are coordinate points of the distorted image, x, y are coordinate points of the original image, N is the degree of the undetermined polynomial, a ij And b ij Is the transform coefficient of the pending polynomial.
In one embodiment of the invention, if the number of corresponding points between the original image and the distorted image is the same as the number of unknowns in the system of equations, the system of equations can be solved directly, but to obtain a higher accuracy, the number of transformed points between the original image and the distorted image is always greater than the number of unknowns in the system of equations, so that the resulting system of equations is an overdetermined system of equations. It is assumed that for L control points, a least squares algorithm is used to solve the over-determined system of equations, i.e. the sum of squared errors after polynomial fitting is minimized.
In S2, the method for solving the polynomial transformation equation set to obtain the transformation coefficient using the least square algorithm may include:
the sum of squared errors after fitting is minimized using the following polynomial:
wherein epsilon x 、ε y Is the sum of squared errors, u 'and v' are coordinate points of the distorted image, x and y are coordinate points of the original image, N is the degree of the polynomial, L is the number of control points, a ij And b ij Transform coefficients that are to-be-determined polynomials.
In an embodiment of the present invention, in S2, a least square algorithm is used to solve the polynomial transformation equation system to obtain the transformation coefficient, and the maximum relative error value is less than 0.5% by the following formula:
wherein E is max Is the maximum relative error value, r model Is coordinate data of a distorted image, r real Is the coordinate data of the original image.
The distortion correction precision is related to a polynomial degree N, and the polynomial degree N and the correction precision are in a direct proportion relation. The least square algorithm can provide an optimal approximate solution on the premise that the fitting polynomial degree is not very high, and through relevant data investigation and simulation experiments, the transformation coefficient between an original image and a distorted image is solved by using a cubic polynomial, and meanwhile, the maximum relative error value is calculated.
The software platform of the patent uses Qt + OpenCV as experimental programming software to realize a predistortion method based on a least square algorithm and a Lanczos interpolation algorithm, the hardware platform uses an Intel Core i3-3240CPU @3.40GHz quad-Core, the memory is 4G, and the operating system is 32-bit Windows 7. The checkerboard graph and the grid graph US military standard resolution board graph are used as simulation experiment graphs, and the resolution is 1400 x 1050, as shown in FIG. 1a, FIG. 1b and FIG. 1 c.
The predistortion software inputs two parts, namely the mapping parameters of the optical system and the simulation experiment chart, the predistortion software calculates the conversion matrix according to the mapping parameters of the optical system, then the simulation experiment chart is led in, the distorted image is obtained by utilizing the conversion matrix, and finally the obtained distorted image is used as the input signal of the helmet display, as shown in fig. 2a, 2b and 2 c.
The preferred embodiments of the present invention have been described in detail with reference to the accompanying drawings, however, the present invention is not limited to the specific details of the above embodiments, and various simple modifications may be made to the technical solution of the present invention within the technical idea of the present invention, and these simple modifications all fall within the protection scope of the present invention.
It should be noted that the various technical features described in the above embodiments can be combined in any suitable manner without contradiction, and the invention is not described in any way for the possible combinations in order to avoid unnecessary repetition.
In addition, any combination of the various embodiments of the present invention can be made, and the same should be considered as the disclosure of the present invention as long as the idea of the present invention is not violated.
Claims (1)
1. An optimized image predistortion method, characterized in that the optimized image predistortion method comprises:
s1, expressing the nonlinear relation between an original image and a distorted image of a display by utilizing a polynomial transformation equation set between pixel coordinates;
s2, under the condition that the number of transformation points between the original image and the distorted image is more than the number of unknowns in the polynomial transformation equation set, solving the polynomial transformation equation set by using a least square algorithm to obtain a transformation coefficient;
s3, obtaining a distorted image by adopting a Lanczos interpolation algorithm according to the transformation coefficient, so as to counteract the distorted image of the optical system of the display;
in S1, a method of expressing a nonlinear relationship between an original image and a distorted image of a display using a polynomial transformation equation set between pixel coordinates includes:
u ', v' are coordinate points of the distorted image, x, y are coordinate points of the original image, N is the degree of the undetermined polynomial, a ij And b ij Transform coefficients that are to-be-determined polynomials;
in S2, the method for solving the polynomial transformation equation set using the least square algorithm to obtain the transformation coefficient includes:
the sum of squared errors after fitting is minimized using the following polynomial:
wherein epsilon x 、ε y Is the sum of squared errors, u 'and v' are coordinate points of the distorted image, x and y are coordinate points of the original image, N is the degree of the polynomial, L is the number of control points, a ij And b ij Transform coefficients that are a to-be-determined polynomial;
in S2, a least square algorithm is used to solve the polynomial transformation equation set to obtain a transformation coefficient, such that the maximum relative error value is less than 0.5% by the following formula:
wherein E is max Is the maximum relative error value, r model Is coordinate data of a distorted image, r real Is the coordinate data of the original image.
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