CN110827362A - Luminosity calibration method based on polynomial camera response function and vignetting effect compensation - Google Patents
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Abstract
The invention discloses a luminosity calibration method based on polynomial camera response function and vignetting effect compensation, which comprises the following steps: collecting Q images with different exposure degrees in the same scene, arranging the Q images from small to large according to the exposure degrees, and sequentially obtaining the exposure ratio R of the initial correction of the adjacent imagesq1Obtaining the exposure ratio matrix of the initial correction, and obtaining the brightness error epsilon of the initial correction of the image1(ii) a Acquiring a primary correction coefficient according to a derivative of the primary corrected brightness error of the image to the primary correction coefficient; obtaining a second corrected exposure ratio matrix according to the first correction coefficient, and obtaining a second corrected brightness error epsilon of the image2(ii) a Acquiring a second correction coefficient according to the derivative of the brightness error of the second correction of the image to the second correction coefficient; sequentially circulating until epsilonk+1≥εkOutputting a k correction coefficient; obtaining a camera pictureAnd acquiring a luminosity calibration function of the camera image after the image response function. The luminosity calibration is more complete and stable, and the imaging is more real and natural.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a luminosity calibration method based on polynomial camera response function and vignetting effect compensation.
Background
The luminosity calibration shows greater advantages along with the development of visual technology, and has great practical value in image modeling and drawing, image splicing and image processing. The common imaging system can hardly reflect the brightness relationship between a real scene and an image due to illumination change, and the relationship becomes complicated due to vignetting effect generated by the influence of an optical lens.
S.man and r.w.picard proposed a camera response function calibration algorithm based on cross histograms in 1995, making standard provisions for the camera response function. The least square-based camera response function calibration algorithm proposed by Debevec and Malik in 1997 is a classic algorithm in the field, has a bad position on the calibration algorithm, and occupies a place as a basis of many calibration algorithms. M.d. grossberg and s.k.nayar in 2002 proposed histogram sampling based camera response function calibration algorithms that obtain camera response equations by fitting the percentiles of histograms, while they created theoretical space for the response functions in 2004 by analyzing the common features of the camera response functions and the constraints that must be met. In 2006, the chapter weixiang et al added an initial constraint of the response function on the basis of the polynomial model proposed by Mitsunaga and Nayar, i.e. in the case of an image luminance of 0, the actual scene luminance should also be 0. However, the iteration condition is not good for the convergence effect of the algorithm.
Disclosure of Invention
The invention designs and develops a luminosity calibration method based on polynomial camera response function and vignetting effect compensation, obtains the correction coefficient of the camera response function through an error function, updates the exposure ratio to carry out algorithm iteration, obtains the optimal camera response function, and combines vignetting effect compensation to carry out luminosity calibration, so that the luminosity calibration is more complete and stable, and the imaging is more real and natural.
The technical scheme provided by the invention is as follows:
a luminosity calibration method based on polynomial camera response function and vignetting effect compensation comprises the following steps:
collecting Q images with different exposure degrees in the same scene, arranging the Q images from small to large according to the exposure degrees, and sequentially obtaining the exposure ratio R of the initial correction of the adjacent imagesq1Obtaining the initial corrected exposure ratio matrixAnd obtaining the first corrected brightness error epsilon of the image1：
In the formula, GqIs the gray value of the q-th image, cn1Is the primary correction coefficient of the nth term, N being the order;
obtaining a primary correction coefficient C based on a derivative of a primary corrected luminance error of the image to the primary correction coefficient1＝[c01,c11,...,cn1,...,cN1]；
Obtaining exposure ratio matrix of the second correction according to the first correction coefficientAnd obtaining a second corrected luminance error epsilon of the image2：
Wherein the content of the first and second substances,
in the formula, Rq2A second corrected exposure ratio for an adjacent image;
obtaining a second correction coefficient C based on a derivative of a second corrected luminance error of the image with respect to the second correction coefficient2＝[c02,c22,...,cn2,...,cN2]；
Sequentially circulating until epsilonk+1≥εkOutputting the k-th correction coefficient Ck＝[c0k,c2k,...,cnk,...,cNk]；
Obtaining a camera image response function:
wherein I is the actual scene luminance, f (G) is the camera image response function, and G is the image gray scale value;
acquiring a luminosity calibration function of a camera image:
G'＝f(G)·S(G)；
wherein G' is the luminosity calibration function of the camera image, and S (G) is the vignetting effect compensation coefficient of the image.
Preferably, the calibration of the camera image is implemented by calibrating each pixel point on the image:
in the formula (x)p,yp) Is the position of the p-th pixel in the image, GpIs the gray value of the p-th pixel point,
as a function of the response of the p-th pixel,
and compensating the coefficient for the vignetting effect of the p-th pixel point.
Preferably, the first corrected luminance error e of the image is1Comprises the following steps:
wherein P is the number of pixels in the Q-th image, Gp,qAnd the gray value of the p-th pixel point of the q-th image is obtained.
Preferably, the exposure ratio R of the second correction of said adjacent imagesq2Comprises the following steps:
preferably, the exposure ratio R of the initial correction of the adjacent imagesq1Comprises the following steps:
in the formula, tqThe exposure time of the Q-th image.
Preferably, before the Q images are arranged from small to large according to the exposure, the Q images are converted into grayscale images.
Preferably, the method further comprises the following steps:
before the brightness error of the primary correction of the image is obtained, the gray value of the pixel point on the image is normalized, so that Imax＝f(G＝1)；
Wherein, ImaxIs the maximum brightness of the actual scene.
Preferably, the primary correction coefficient C1＝[c01,c11,...,cn1,...,cN1]Is obtained by:
preferably, the vignetting effect compensation coefficient of the p-th pixel point is as follows:
wherein z is the camera focal length.
Preferably, c is01＝c02＝...＝cok＝0。
The invention has the following beneficial effects:
the invention designs and develops a luminosity calibration method based on polynomial camera response function and vignetting effect compensation, obtains the correction coefficient of the camera response function through an error function, updates the exposure ratio, performs algorithm iteration, obtains the optimal camera response function, and performs luminosity calibration by combining vignetting effect compensation, so that the luminosity calibration is more complete and stable, and the imaging is more real and natural.
Drawings
FIG. 1 is a flow chart of calibration of a camera response function according to the present invention.
Fig. 2 is a flow chart of calibrating the vignetting effect compensation coefficient according to the present invention.
FIG. 3 is a flow chart of the calibration of the photometric calibration function according to the present invention.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
Because the range of the irradiation value of the actual scene is as large as one hundred million, and the range of the image brightness value is only 256 brightness levels, the brightness relationship between the actual scene and the image is very complex, most of the brightness relationship is nonlinear, and in order to obtain the image closer to the actual scene, the camera response function needs to be calibrated.
The luminosity calibration experiment needs to use processable picture data, namely a camera can be used for acquiring a plurality of pictures, and the picture data is read and stored in a computer by using a program for a subsequent program to process the picture data;
the image data is generally in a two-dimensional matrix form, each data unit represents the brightness of each pixel point of the image, and the brightness of the pixel point is corrected by the luminosity calibration correction.
The invention provides a luminosity calibration method based on polynomial camera response function and vignetting effect compensation, which comprises the following steps:
establishing a camera response function:
where I is the actual scene luminance, f (G) is the camera image response function, G is the image gray scale value, cnIs a polynomial coefficient and N is a polynomial order.
Collecting Q images with different exposure degrees in the same scene, converting the Q images into gray level images, arranging the Q images from small to large according to the exposure degrees, and sequentially obtaining the exposure ratio R of the initial correction of the adjacent imagesq1Obtaining the initial corrected exposure ratio matrix
Changing the exposure time without changing the camera parameters yields multiple images (with the same parameters, the exposure ratio is obtained by the exposure time ratio), and ordering the images such that the exposure time t isq＜tq+1The exposure ratio is determined so that 0 < Rq1And < 1, Q is the number of images, and P is the number of pixel points of each image (the number of pixel points of each image in Q images is the same as the corresponding position).
And obtaining the first corrected brightness error epsilon of the image1：
In the formula, GqIs the gray value of the q-th image, cn1Is the primary correction system of the nth termNumber, N is order;
further acquiring the brightness error epsilon of the primary correction of the image according to the gray value of each pixel point1：
Wherein P is the number of pixels of the image, Gp,qAnd the gray value of the p-th pixel point of the q-th image is obtained.
Obtaining a primary correction coefficient C based on a derivative of a primary corrected luminance error of the image to the primary correction coefficient1＝[c01,c11,...,cn1,...,cN1](ii) a Namely, it is obtained by the following formula.
Obtaining exposure ratio matrix of the second correction according to the first correction coefficient
Namely:
in the formula, Rq2A second corrected exposure ratio for an adjacent image;
and obtaining a second corrected luminance error epsilon of the image2：
Further acquiring the brightness error epsilon of the second correction of the image according to the gray value of each pixel point2：
Obtaining a second correction coefficient C based on a derivative of a second corrected luminance error of the image with respect to the second correction coefficient2＝[c02,c22,...,cn2,...,cN2](ii) a Namely, it is obtained by the following formula.
In this embodiment, let c01＝c02＝...＝cok＝0。
Obtaining corresponding brightness error epsilon according to corresponding correction coefficient1,ε2And comparing ε1And ε2The magnitude of the value;
sequentially circulating until epsilonk+1≥εkOutputting the k-th correction coefficient Ck＝[c0k,c2k,...,cnk,...,cNk]。
Let the first term coefficient C in the polynomial00 or c01＝c02＝…＝cok0, while improving the algorithm iteration end condition, i.e. epsilonk+1≥εkThe stability of the algorithm is greatly increased, and the response function and the exposure obtained by the method are optimal values.
Obtaining a camera image response function:
where I is the actual scene luminance, f (G) is the camera image response function, and G is the image gray scale value.
And finally, acquiring a luminosity calibration function of the camera image:
G'＝f(G)·S(G)；
wherein G' is the luminosity calibration function of the camera image, and S (G) is the vignetting effect compensation coefficient of the image.
In essence, the calibration of the camera image is realized by calibrating each pixel point on the image, that is:
in the formula (x)p,yp) Is the position of the p-th pixel in the image, GpIs the gray value of the p-th pixel point,
as a function of the response of the p-th pixel,and compensating the coefficient for the vignetting effect of the p-th pixel point.
The vignetting effect is due to the physical size of one or more lenses, with the rear element obscuring the front, resulting in a reduction in the effective incident light off-axis for the front lens, with the result that the intensity of the light gradually diminishes from the center of the image to the periphery.
Through observing image data with vignetting effect, namely taking a standard gray plate as an ideal plane for image acquisition, shooting an image under the condition of uniform brightness, generating image data with vignetting effect for analysis, finding that the center of the image and the edge of the image accord with the cosine value quadratic relation of an off-axis angle, the specific calibration method comprises the following steps:
based on the theoretical basis of pinhole imaging, the image illumination relational formula is as follows:
image illumination E, radiance L of object, and lens areaFourth power cos of off-axis angle cosine value4α all become positiveThe ratio, and the image brightness E is inversely proportional to the distance from the lens center to the image plane (camera focal length) z'.
Since the vignetting effect is related to the position of a pixel point on an image, the irradiation amount H at a certain pixel point can be represented by the following formula:
H＝Et；
where t is the exposure time.
Since vignetting effect generally occurs at the edges of the image and no vignetting effect occurs at the center, the central exposure of the image is defined as the standard exposure
This yields the relationship between the image edge and the central exposure of the image, namely:
where i is the image center pixel point location and c is some pixel point location that is not centered.
Constructing a function D(x，y)The image is defined as a view field percentage function, and the value range is 0% -100% from the center (0% view field) to the edge (100% view field) of the image. The vignetting effect compensation model function can be obtained as follows:
wherein, x and y are the horizontal and vertical coordinate positions of the pixel points, and z is the focal length of the camera.
Namely, the vignetting effect compensation coefficient of the p-th pixel point is as follows:
examples
The specific implementation flow of the camera response function optimization is shown in fig. 1:
1. using the same camera to change exposure parameters to shoot 8-10 images as an experimental group in the same scene, wherein the number of the images is set as Q;
2. judging whether the image is a gray image or not, and converting the image into a gray image if the image is not the gray image;
3. the image is sorted and stored according to the sequence from dark to light, gray value data G (x, y) of each pixel point on the image is obtained (can be directly generated), the x and the y are positions of the pixel points, and three-order array data with the length and width quantity of the pixel points of the image as one order and the second order and the image sequence number as the first order dimension can be obtained;
4. recording exposure value information of each image, and sequentially dividing to obtain Q-1 exposure ratio information
Taking the first-order array data obtained for the first time as an initial exposure ratio;
5. using the exposure ratio RR1The image brightness error epsilon of the current time and the first time is obtained by the image gray value data G (x, y)1；
6. For image brightness error epsilon1Obtaining a first correction coefficient (coefficient of a polynomial) by obtaining derivatives and limiting each derivative value to be 0;
7. using the established camera response function and obtaining a primary correction coefficient and a gray value G of a pixel point of the imageq(x, y) updating the second image exposure ratio
8. Reuse of the exposure ratio RR2The image brightness error epsilon of the current time and the second time is obtained by the image gray value data G (x, y)2；
9. For image brightness error epsilon2Obtaining a second correction coefficient (coefficient of a polynomial) by obtaining derivatives and limiting each derivative value to be 0;
10. obtaining corresponding brightness error epsilon according to corresponding correction coefficient1,ε2And comparing ε1And ε2Magnitude of value, if ε2＜ε1Then the algorithm is iterated and the exposure ratio is updated to RR3And (4) continuously recalculating according to the steps 5-10 as an exposure initial value of the next iteration until the image error calculated at a certain time is larger than the image error calculated at the last time, stopping iteration, and outputting a correction coefficient corresponding to the image brightness error at the last time to obtain an optimal camera response function.
The specific implementation process of calibration of the vignetting effect compensation function is shown in fig. 2:
1. acquiring a scene image, judging whether the image is a gray image or not, and if not, converting the image into the gray image;
2. recording the positions of all pixel points on the image and the gray values G (x, y) of the pixel points;
3. saving a camera focal length parameter z in the image data information;
4. setting parameters r and c as the maximum values of the length and the width of the image, namely the number of pixel points in rows, columns and columns;
5. setting the initial values of i and j as 1, setting the maximum values as r and c respectively, performing cyclic calculation in a mode of increasing 1 each time, and normalizing the position of each pixel point on the image to a percentage value taking the center of the image as a point 0, namely 0 at the center of the image and 100% at the edge of the image;
6. and (4) solving a vignetting effect compensation coefficient of each pixel point on the image according to the position information (x, y) and the focal length z of each pixel point, wherein the vignetting effect compensation coefficient matrix is formed by the whole coefficient.
After the camera response function and the vignetting effect compensation coefficient are obtained, the two equations can be combined to form a luminosity calibration function, as shown in fig. 3, as shown in the following formula:
by using the method, the luminosity calibration of the image can be completed, and the quality of the picture is improved so as to be closer to a real scene.
The invention designs and develops a luminosity calibration method based on polynomial camera response function and vignetting effect compensation, obtains the correction coefficient of the camera response function through an error function, updates the exposure ratio, performs algorithm iteration, obtains the optimal camera response function, and performs luminosity calibration by combining vignetting effect compensation, so that the luminosity calibration is more complete and stable, and the imaging is more real and natural.
While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in various fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.
Claims (10)
1. A luminosity calibration method based on polynomial camera response function and vignetting effect compensation is characterized by comprising the following steps:
collecting Q images with different exposure degrees in the same scene, arranging the Q images from small to large according to the exposure degrees, and sequentially obtaining the exposure ratio R of the initial correction of the adjacent imagesq1Obtaining the initial corrected exposure ratio matrix
And obtaining the first corrected brightness error epsilon of the image1：
In the formula, GqIs the gray value of the q-th image, cn1Is the primary correction coefficient of the nth term, N being the order;
obtaining a primary correction coefficient C based on a derivative of a primary corrected luminance error of the image to the primary correction coefficient1＝[c01,c11,...,cn1,...,cN1]；
Based on the primary correction coefficientObtaining a second corrected exposure ratio matrix RR2＝[R12,R22,...,Rq2,...R(Q-1)2]And obtaining a second corrected luminance error epsilon of the image2：
Wherein the content of the first and second substances,
in the formula, Rq2A second corrected exposure ratio for an adjacent image;
obtaining a second correction coefficient C based on a derivative of a second corrected luminance error of the image with respect to the second correction coefficient2＝[c02,c22,…,cn2,…,cN2]；
Sequentially circulating until epsilonk+1≥εkOutputting the k-th correction coefficient Ck＝[c0k,c2k,...,cnk,...,cNk]；
Obtaining a camera image response function:
wherein I is the actual scene luminance, f (G) is the camera image response function, and G is the image gray scale value;
acquiring a luminosity calibration function of a camera image:
G'＝f(G)·S(G)；
wherein G' is the luminosity calibration function of the camera image, and S (G) is the vignetting effect compensation coefficient of the image.
2. The photometric calibration method based on polynomial camera response function and vignetting effect compensation as claimed in claim 1 wherein the calibration of the camera image is performed by calibrating each pixel point on the image:
in the formula (x)p,yp) Is the position of the p-th pixel in the image, GpIs the gray value of the p-th pixel point,
as a function of the response of the p-th pixel,and compensating the coefficient for the vignetting effect of the p-th pixel point.
3. The method for photometric calibration based on polynomial camera response function and vignetting effect compensation of claim 2 wherein the first corrected luminance error of the image is e1Comprises the following steps:
wherein P is the number of pixels of the image, Gp,qAnd the gray value of the p-th pixel point of the q-th image is obtained.
4. The method for photometric calibration based on polynomial camera response function and vignetting effect compensation of claim 3 wherein the exposure ratio R of the second correction of the neighboring imageq2Comprises the following steps:
5. the polynomial-based camera system of claim 4Photometric calibration method with compensation for the vignetting effect and the function, characterized in that the initial corrected exposure ratio R of said adjacent imagesq1Comprises the following steps:
in the formula, tqThe exposure time of the Q-th image.
6. The method for photometric calibration based on polynomial camera response function and vignetting effect compensation according to any of the claims 1-5 wherein said Q images are converted to grayscale images before being arranged from small to large in exposure.
7. The method for photometric calibration based on polynomial camera response function and vignetting effect compensation of claim 2, 3, 4 or 5 further comprising:
before the brightness error of the primary correction of the image is obtained, the gray value of the pixel point on the image is normalized, so that Imax＝f(G＝1)；
Wherein, ImaxIs the maximum brightness of the actual scene.
8. The method for photometric calibration based on polynomial camera response function and vignetting effect compensation of claim 7 wherein said primary correction factor C1＝[c01,c11,...,cn1,…,cN1]Is obtained by:
9. the photometric calibration method based on polynomial camera response function and vignetting effect compensation of claim 8 wherein the vignetting effect compensation coefficient of said p-th pixel point is:
wherein z is the camera focal length.
10. The method for photometric calibration based on polynomial camera response function and vignetting effect compensation of claim 9 wherein c is01＝c02＝...＝cok＝0。
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