CN108362226B - Double four-step phase shift method for improving phase measurement precision of image overexposure area - Google Patents
Double four-step phase shift method for improving phase measurement precision of image overexposure area Download PDFInfo
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Abstract
The invention providesA dual-four-step phase shift method for improving the phase measurement accuracy of an overexposed region of an image is used for obtaining the phase value of a pixel point (x, y) on a sine stripe image by the four-step phase shift method twice
And
the initial phase of each step in the second four-step phase shift is more than pi/4 of that of the first four-step phase shift; calculating the final phase value according to the phase value obtained by two times of four-step phase shifts
If the first four-step phase shift is over-exposed and the second one is not over-exposed, then
Get
(ii) a If the first four-step phase shift is not over-exposed and the second time is over-exposed, then
Get
(ii) a If both overexposure times or neither overexposure time occurs, then
The average of the two phases is taken. The invention can effectively improve the phase measurement precision of the image overexposure area and reduce the calculation expense.
Description
Technical Field
The invention relates to an image-based optical three-dimensional measurement technology-phase profilometry, in particular to a method for improving the phase measurement precision of an image overexposure area in the phase profilometry.
Background
The core of the optical three-dimensional measurement based on the image is to recover the height information on the image, so as to recover the three-dimensional profile of an object, and the optical three-dimensional measurement based on the image has wide application in a plurality of fields such as reverse engineering, cultural relic replication, industrial automatic detection, biomedicine, human body detection and the like, and the phase measurement profilometry is the optical three-dimensional measurement technology based on the image.
In phase profilometry, a sinusoidal grating projection is performed on the surface of an object, and a sinusoidal fringe image projected onto the surface of the object is acquired. For each reference plane, four sinusoidal stripe images with different initial phases are obtained through four-step phase-shift sinusoidal grating projection, and the phase value of the sinusoidal stripe is obtained through calculation according to the sinusoidal variation law of the gray value of the four sinusoidal stripe images; and then, calculating to obtain a phase height mapping relation by using the phase values of the sine stripes of the plurality of reference planes with different heights. And similarly, performing four-step phase shift sinusoidal grating projection on the surface of the measured object to obtain a phase value of a sinusoidal stripe on the surface of the measured object, and substituting the phase value into the phase height mapping relation to obtain a height value of the measured object. When calculating the phase height mapping relation, at least 5 reference planes are usually required, and 20 images are needed in total. The accuracy of the measurement of the phase values of the sinusoidal stripes in this method directly affects the accuracy of the measurement of the height. When the sinusoidal stripe image projected to the surface of an object is collected, the phenomenon of image overexposure can occur in an area where the surface of the object to be measured is smooth and mirror reflection occurs due to the influence of the material of the surface of the object to be measured and nonlinear response when the industrial camera collects the image. In the image overexposure area, the gray value of the image does not change in a sine rule, so that the phase value measured in the area is inaccurate, and the measurement precision of the height of the area is reduced finally.
The method for solving the problem of image overexposure in the phase profilometry at present is mainly based on a high-dynamic phase profilometry technology, and the technology can be classified into the following three types: a multi-exposure based method, a method based on adjusting the intensity of the projected light and a method based on polarizing filters. The method based on multiple exposures is characterized in that a series of sine stripe images under different exposure conditions are shot, a phase value under each exposure is obtained through calculation, then a measurement value under the optimal exposure is selected for each measurement point of an object, and finally the measurement values are combined to obtain a final measurement value. The method can improve the phase measurement precision of the image overexposure area, but the number of processed images is too large, at least 20 sinusoidal fringe images are needed for one-time four-step phase shift measurement of a group of reference planes, the calculation cost is high, and the time is very long. The position information of the strip image overexposure area is obtained by shooting based on the method for adjusting the projection light intensity, the projection light intensity of the sinusoidal grating at the position corresponding to the overexposure area is adjusted by combining with the structural model of the measuring system, and the process is repeated, so that the overexposure phenomenon disappears finally. The method can also effectively solve the problem of overexposure and improve the precision, but the method consumes much time due to the need of iteration. The method based on the polarization filter lens enables projection to penetrate through the linear polarization filter, effectively reduces specular reflection by adjusting the polarization angle, and reduces the occurrence of an overexposure phenomenon, but the polarization angle is difficult to accurately control, and the complexity of a hardware system is increased.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a double four-step phase shift method. The method can effectively improve the phase measurement precision of the image overexposure area, and compared with a phase profile measurement technology based on high dynamics, the number of the sine stripe images can be reduced from 20 to 8, and the calculation cost is greatly reduced.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step one, carrying out four-step phase shift for the first time to obtain four sinusoidal stripe images with initial phases of 0, pi/2, pi and 3 pi/2 respectively, wherein gray values of the four sinusoidal stripe images at (x, y) are as follows:
solving the phase value at pixel point (x, y) in the first four-step phase shift
Step two, carrying out second four-step phase shift, wherein the initial phase of each step in the second four-step phase shift is pi/4 more than that of the first four-step phase shift, and the gray values of the four acquired sinusoidal fringe images are as follows:
obtaining the phase value at the pixel point (x, y) in the second four-step phase shift
Step three, calculating a final phase value according to the phase value obtained by the two-time four-step phase shift and the phase value obtained by the two-time four-step phase shift
If the pixel point (x, y) is overexposed during the first four-step phase shift and is not overexposed during the second four-step phase shift, then
Get
If no overexposure occurs during the first four-step phase shift and overexposure occurs during the second four-step phase shift, then
Get
If the overexposure appears or does not appear in the two-time four-step phase shift, then
Get
And
average value of (a).
The invention has the beneficial effects that: for the traditional phase measurement profilometry using a single four-step phase shift method, the phase measurement of an image overexposure area is inaccurate, and a large error exists, so that the final height measurement precision is reduced. For the case that only one time of four-step phase shift is shifted out and overexposure is performed, directly using the phase value of the non-overexposed one time of four-step phase shift as the final phase value; and for the situation that overexposure occurs in both the two four-step phase shifts, according to the periodic characteristics of the phase error of the overexposure area, the error of the second four-step phase shift is shifted by half a period relative to the error of the first four-step phase shift, and the phase errors can be effectively reduced by adding the two four-step phase shift error with different signs at the same point. The method obviously improves the height measurement precision of the image overexposure area, and the effect of reducing the phase error in the double four-step phase shift method is more obvious when the overexposure degree is larger and the phase error in the single four-step phase shift method is larger. Compared with the phase profile measurement technology based on high dynamic, the double four-step phase shift method can reduce the number of processed sine stripe images from 20 to 8, thereby greatly reducing the calculation cost.
Drawings
FIG. 1 is a graph of the change in pixel gray level in the middle row of two sinusoidal cycles in an overexposed sinusoidal fringe image;
FIG. 2 is a spectral plot of the gray scale of a pixel in the middle row of a sinusoidal fringe image with overexposure;
FIG. 3 is a schematic diagram of ideal phase values and phase values where an overexposure condition occurs;
FIG. 4 is a schematic phase diagram of example 1, wherein (a) is a single four-step phase shift method in which pixels are overexposed only in one image, (b) is a phase error of two four-step phase shifts in a two-four-step phase shift method, (c) is a phase error comparison of the two four-step phase shift method and the single four-step phase shift method, and (d) is a phase value comparison of the two four-step phase shift method and the one-time four-step phase shift method with an ideal phase value;
FIG. 5 is a schematic phase diagram of example 2, wherein (a) is a single four-step phase shift method, and pixel points are overexposed in one image and overexposed in two images, (b) is a phase error of two four-step phase shifts in a double four-step phase shift method, (c) is a phase error comparison of the double four-step phase shift method and one four-step phase shift method, and (d) is a phase value comparison of the double four-step phase shift method and one four-step phase shift method with an ideal phase value;
FIG. 6 is a schematic phase diagram of example 3, wherein (a) is a single four-step phase shift method, where pixels are over-exposed and neither over-exposed in one image, (b) is a phase error of two four-step phase shifts in a double four-step phase shift method, (c) is a phase error comparison of the double four-step phase shift method and one four-step phase shift method, and (d) is a phase value comparison of the double four-step phase shift method and one four-step phase shift method with an ideal phase value;
fig. 7 is a flow chart of a two four-step phase shifting method.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
And setting the origin of the image coordinate system at the upper left corner of the image, the X axis horizontally faces to the right, and the Y axis vertically faces downwards. The coordinates of a certain point a on the sinusoidal fringe image are (x, y), and the gray value model of the point a is as follows:
wherein Ib(x, y) is background light intensity, Im(x, y) is the intensity of the grating modulation light,
for the phase of the sinusoidal fringe of the three-dimensional object surface to be solved at point a, s is the initial phase. The initial phase is respectively 0, pi/2, pi and 3 pi/2, four sine stripe images can be obtained, and the phase is obtained by calculation
The method is a four-step phase shift method. For the sake of distinction, it is referred to herein as "single four-step phase shift method". When the sinusoidal grating is projected to a smooth plane, a sinusoidal stripe image with an overexposure phenomenon can be acquired, the pixel gray values in two sinusoidal stripe periods in the middle line of the sinusoidal stripe image are discussed without losing generality, and the gray change curve is shown in fig. 1. The fourier transform is performed, as shown in fig. 2, it can be seen that there are integral multiple harmonic components, which is because the nonlinear response of the image collected by the camera causes the image overexposure in the specular reflection area, and the gray value of the image no longer changes sinusoidally. The nonlinear response mathematical model of the camera is represented by the following polynomialThe following steps:
wherein
Is the gray value of A point in the actually acquired fringe image, IA(x, y) is the intensity of light at point A of the projected sinusoidal grating, and f (-) is the nonlinear response map. The gray value model of actually collecting the A point of the fringe image is as follows:
actual phase
And ideal phase
There is some error as shown in fig. 3. Calculating the actual phase value according to a single four-step phase shift method
And calculating to obtain the phase error between the actual phase value and the ideal phase value of the overexposed region of the image generated by the nonlinear response
Where C is an unknown coefficient, related to the coefficients of the polynomial. The phase error is known as the period error of the quadruple frequency.
In order to reduce the phase error of an overexposed region of an image, the invention provides a double four-step phase shift method, which carries out two four-step phase shifts according to the periodic characteristics of the phase error of the overexposed region, wherein in the second four-step phase shift, the initial phase of each step is more than pi/4 of that of the first four-step phase shift. The technical scheme is as follows:
performing four-step phase shift for the first time, and calculating the phase value of pixel point (x, y) on the sine stripe image
Carrying out four-step phase shift for the second time, and calculating to obtain the phase value at (x, y)
Calculating the final phase value according to the phase value obtained by two times of four-step phase shifts
If the pixel point (x, y) is overexposed during the first four-step phase shift and is not overexposed during the second four-step phase shift, then
Get
If no overexposure occurs during the first four-step phase shift and overexposure occurs during the second four-step phase shift, then
Get
If the overexposure appears or does not appear in the two-time four-step phase shift, then
The average of the two phases is taken.
The method comprises the following specific steps:
step one, carrying out four-step phase shift for the first time, and solving a phase value and a phase error of a pixel point (x, y) on the sine stripe image.
And (3) moving the initial phase by pi/2 every time for photographing to obtain four sinusoidal stripe images when the initial phase is respectively 0, pi/2, pi and 3 pi/2, wherein the gray values of the four sinusoidal stripe images at (x, y) are respectively as follows:
solving the phase value at the pixel point (x, y) in the first four-step phase shift according to the following four formulas:
the phase error between the actual phase value and the ideal phase value of the overexposed area is
Wherein,
is an ideal phase value.
And step two, carrying out the phase shift for the second time, and solving the phase value and the phase error of the pixel point (x, y) on the sine stripe image. The initial phase of each step of the second four-step phase shift is more than pi/4 of that of the first four-step phase shift, and the gray values of the four acquired sine stripe images are as follows:
obtaining a phase value of
The phase error between the actual phase value and the ideal phase value of the exposure area is:
and step three, solving the final phase value of the pixel point (x, y) according to the phase value obtained by the two-time four-step phase shift.
Because the difference between the two four-step phase shifts is pi/4 offset, the situation of an overexposed area of an image acquired by each four-step phase shift is different, and for an image with 0-255 gray scales, the gray scale value of a pixel point (x, y) in a sine stripe image with two four-step phase shifts can be divided into the following four situations:
(1) in the four images acquired by the first four-step phase shift, the gray value is less than 255; in the four images acquired in the second four-step phase shift, the gray value is equal to 255 in at least one image.
(2) In the four images acquired in the first four-step phase shift, the gray value is equal to 255 in at least one image; in the four images acquired by the second four-step phase shift, the gray value is less than 255.
(3) In four images respectively acquired by two times of four-step phase shifting, the gray value is less than 255.
(4) In the four images acquired in each of the two four phase shifts, the gray value is equal to 255 in at least one image.
According to the above four cases, the final phase value is solved respectively:
(1) the overexposure does not occur in the first four-step phase shift, the overexposure occurs in the second four-step phase shift, the phase error in the first time is obviously smaller than that in the second time, and the final phase value is the phase value obtained by the first four-step phase shift:
(2) overexposure occurs in the first four-step phase shift, overexposure occurs in the second four-step phase shift, the phase error in the first time is obviously larger than that in the second time, and the final phase value is the phase value obtained by the second four-step phase shift:
(3) no overexposure occurs in both four phase shifts, and the final phase value is averaged over both phases:
therefore, the phase error caused by random noise can be effectively inhibited.
(4) Overexposure occurs in both of the two four-step phase shifts, and the final phase value is averaged over the two phases:
the above calculation is performed for all pixels of the sinusoidal fringe image, thereby obtaining the phase value of the entire sinusoidal fringe image.
Phase error analysis of the two-four-step phase shift method:
the phase error of the two-four-step phase shift method can be obtained by the following formula:
because the phase error of the two-time four-step phase shift is close to the sinusoidal periodic characteristic and has the offset of half period, the phase error of any overexposure point has opposite signs in the two-time four-step phase shift, C1、C2Close to, have | (C)1-C2)/2]＜C1Then there is a phase error
Therefore, in the overexposed area of the image, compared with the traditional method adopting one-time four-step phase shifting, the phase error is effectively reduced.
The root mean square of the phase errors is used as an evaluation index, and the smaller the root mean square of the phase errors is, the smaller the deviation degree is, and the more accurate the phase measurement is.
Example 1: as shown in fig. 4(a), in the single four-step phase shift, there is a case where the pixel is overexposed only in one image. The phase error of the two four-step phase shifts is shown in fig. 4(b), and it can be seen that the phase error values of the pixels where overexposure occurs in the two four-step phase shifts are different in sign. As shown in fig. 4(c), the phase error of the phase value obtained by the two-four-step phase shift method is significantly reduced compared to the phase error obtained by the single-four-step phase shift method. The root mean square of the phase errors of the single four-step phase shifting method is 0.0284, and the root mean square of the phase errors of the double four-step phase shifting method is 0.0007, which is reduced by 40 times, and the effect is obvious. As shown in fig. 4(d), comparing the degree of deviation between the phase value and the ideal phase value in the two-four-step phase shift method and the single-four-step phase shift method, the phase value obtained in the two-four-step phase shift method is closer to the ideal phase value. The double four-step phase shift method effectively improves the phase measurement precision.
Example 2: as shown in fig. 5(a), in the single four-step phase shift, there are two cases that the pixel is overexposed in one image and overexposed in two images simultaneously. The phase error of the two four-step phase shifts is shown in fig. 5(b), and it can be seen that the phase error values of the pixels with overexposure in the two four-step phase shifts are different in sign. As shown in fig. 5(c), the phase error of the phase value obtained by the two-four-step phase shift method is significantly reduced compared to the phase error obtained by the single-four-step phase shift method. Compared with the phase error root mean square, the phase error root mean square of the single four-step phase shifting method is 0.0600, and the phase error root mean square of the double four-step phase shifting method is 0.0097, which is reduced by 6 times. As shown in fig. 5(d), comparing the degree of deviation between the phase value and the ideal phase value in the two-four-step phase shift method and the single-four-step phase shift method, the phase value obtained in the two-four-step phase shift method is closer to the ideal phase value. The double four-step phase shift method effectively improves the phase measurement precision.
Example 3: as shown in fig. 6(a), there are two cases in a single four-step phase shift, where no overexposure occurs to a pixel and overexposure occurs in an image. The phase error of the two four-step phase shifts is shown in fig. 6(b), and it can be seen that the phase error values of the pixels with overexposure in the two four-step phase shifts are different in sign. As shown in fig. 6(c), the phase error of the phase value obtained by the two-four-step phase shift method is reduced by comparing the phase errors of the two-four-step phase shift method and the single-four-step phase shift method. Meanwhile, it can be seen from the figure that, where the phase error of the single four-step phase shift method is larger, the more the phase error is reduced after the double four-step phase shift method is used for processing, according to the step three, a certain pixel point is overexposed in one four-step phase shift, but is not overexposed in the other time, and the phase value without overexposure is taken, and certainly, the phase error is also reduced. Thus reducing the phase error of the overall overexposed area to a smaller level. Compared with the phase error root mean square, the phase error root mean square of the single four-step phase shifting method is 0.0062, and the phase error root mean square of the double four-step phase shifting method is 0.0020, which is reduced by 3 times. As shown in fig. 6(d), comparing the degree of deviation between the phase value and the ideal phase value in the two-four-step phase shift method and the single-four-step phase shift method, the phase value obtained in the two-four-step phase shift method is closer to the ideal phase value.
Claims (1)
1. A double four-step phase shift method for improving the phase measurement precision of an image overexposure area is characterized by comprising the following steps:
step one, carrying out four-step phase shift for the first time to obtain four sinusoidal stripe images with initial phases of 0, pi/2, pi and 3 pi/2 respectively, wherein gray values of the four sinusoidal stripe images at (x, y) are as follows:
solving the phase value at pixel point (x, y) in the first four-step phase shift
Step two, carrying out second four-step phase shift, wherein the initial phase of each step in the second four-step phase shift is pi/4 more than that of the first four-step phase shift, and the gray values of the four acquired sinusoidal fringe images are as follows:
obtaining the phase value at the pixel point (x, y) in the second four-step phase shift
Step three, calculating a final phase value according to the phase value obtained by the two-time four-step phase shift and the phase value obtained by the two-time four-step phase shift
If the pixel point (x, y) is overexposed during the first four-step phase shift and is not overexposed during the second four-step phase shift, then
Get
(ii) a If no overexposure occurs during the first four-step phase shift and overexposure occurs during the second four-step phase shift, then
Get
If the overexposure appears or does not appear in the two-time four-step phase shift, then
Get
And
average value of (a).
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