CN116182744A - Gamma nonlinear error correction method for three-dimensional measurement of fringe projection - Google Patents
Gamma nonlinear error correction method for three-dimensional measurement of fringe projection Download PDFInfo
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- G—PHYSICS
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/25—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
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- G—PHYSICS
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- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
- G01B11/06—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness for measuring thickness ; e.g. of sheet material
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Abstract
The invention discloses a gamma nonlinear error correction method for three-dimensional measurement of stripe projection, which comprises the following steps: step S1: constructing a stripe projection three-dimensional measurement system, which comprises a projector and a camera; step S2: the projector sequentially projects phase-shift stripe patterns to the surface of the measured object, and the camera captures the stripe patterns distorted by the surface of the measured object; step S3: calculating the wrapping phase phi influenced by the gamma effect of the system by a three-step phase shift method g (x, y); step S4: wrapping phase phi to be affected by system gamma effect g (x, y) is converted into an expression form under a polar coordinate system, and then the polar diameters of all polar coordinates are drawn to obtain a spatial distribution diagram of the polar diameters; step S5: the polar paths are uniformly distributed in the polar coordinate system space through the included angle between the average adjacent polar paths; step S6: restoring the spatial distribution map of the equalized polar diameter to the corrected wrapping phase phi c (x, y); step S7: opposite correctionThe wrapping phase phi after c The (x, y) unwrapping obtains the absolute phase Φ (x, y) and then a three-dimensional reconstruction of the object surface is performed.
Description
Technical Field
The invention belongs to the technical field of three-dimensional measurement, and particularly relates to a gamma nonlinear error correction method for three-dimensional measurement of fringe projection.
Background
The stripe projection three-dimensional measurement method based on the structured light technology has the advantages of non-contact, high precision, high speed and the like, and is widely applied to various fields such as industrial detection, reverse engineering, virtual reality, human modeling, cultural relics protection and the like. The three-dimensional measuring method of stripe projection is characterized in that a group of coded stripe patterns are projected onto the surface of an object to be measured through a projector, then the stripe patterns distorted by the surface of the object are captured through a camera, and finally the three-dimensional shape of the surface of the object is reconstructed through calculating the phase information of the stripe images. However, the projectors and cameras currently in use have some gamma effect, resulting in unnecessary intensity variations in the fringe pattern captured by the camera and introducing serious phase errors in the reconstruction results. Therefore, in order to ensure the measurement accuracy of the reconstruction result, it is necessary to correct the nonlinear error caused by the gamma effect.
Currently, many methods have been proposed for correcting gamma non-linearity errors. These methods can be generally divided into three categories: the first method is to estimate the nonlinear error of the whole measurement system in advance according to some pre-calibration steps, and then directly compensate the error in the actual measurement result by using pre-calibration information, and the method corrects the error without slowing down the measurement speed, but needs to re-calibrate when the measurement environment changes (Optics Letters,2011,36 (2): 154-156); the second method is to obtain a phase diagram opposite to the original phase error curve by projecting an additional fringe image and average the phase diagram with the original phase so as to reduce the overall error, and the method has a certain correction effect, but the projection of the additional pattern reduces the measurement speed (IEEE Transactions On Instrumentation And Measurement,2021, 70:7006509); the third type of method is to obtain an additional phase map for error averaging using hilbert transform or other frequency domain transform on the original phase map, which, although not requiring a pre-calibration step and additional fringe images, can only process objects whose surface is relatively smooth (Optics Express,2015,23 (19): 25171-25181).
In summary, how to provide a gamma nonlinear error correction method with simple operation and convenient implementation while ensuring the measurement speed and measurement accuracy is still a problem to be solved.
Disclosure of Invention
The invention provides a gamma nonlinear error correction method for three-dimensional measurement of fringe projection, which aims to solve the problems in the background technology.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: the gamma nonlinear error correction method for three-dimensional measurement of fringe projection specifically comprises the following steps:
step S1: setting up a fringe projection three-dimensional measurement system which comprises a projector and a camera, wherein the projector and the camera synchronously trigger starting operation, the projector, the camera and an object to be measured form a triangulation relation, and the system finishes the calibration of the conversion relation of the height-phase value;
step S2: the projector sequentially projects phase-shift stripe patterns onto the surface of the measured object, and the camera captures the stripe patterns distorted by the surface of the measured object; taking a three-step phase shift method as an example for describing a technical scheme, the light intensity of the three-step phase shift stripe pattern captured by the camera is expressed as follows:
I 1 (x,y)＝A(x,y)+B(x,y)cos[φ g (x,y)-2π/3]；
I 2 (x,y)＝A(x,y)+B(x,y)cos[φ g (x,y)]；
I 1 (x,y)＝A(x,y)+B(x,y)cos[φ g (x,y)+2π/3]；
wherein: (x, y) represents camera coordinates; i 1 (x,y)、I 2 (x,y)、I 3 (x, y) represents the three-step phase-shifted fringe pattern intensity; a (x, y) and B (x, y) respectively represent background light intensity and modulated light intensity; phi (phi) g (x, y) represents the wrapped phase affected by the system gamma effect;
step S3: calculating the wrapping phase phi influenced by the gamma effect of the system by a three-step phase shift method g (x,y)；
Step S4: wrapping phase phi to be affected by system gamma effect g (x, y) conversionThe method comprises the steps of (1) drawing the polar diameters of all polar coordinates to obtain a spatial distribution diagram of the polar diameters for the expression form under the polar coordinate system;
step S5: the polar paths are uniformly distributed in the polar coordinate system space through the included angle between the average adjacent polar paths;
step S6: restoring the spatial distribution map of the equalized polar diameter to the corrected wrapping phase phi c (x, y) having values which are completely uniformly distributed within 0 to 2 pi;
step S7: corrected phi using phase unwrapping algorithm c The (x, y) unwraps to obtain an absolute phase phi (x, y), then converts the absolute phase phi (x, y) into height information according to the height-phase value conversion relationship, and performs three-dimensional reconstruction of the object surface.
Further, the step S3 three-step phase shift method solves the wrapping phase phi influenced by the system gamma effect g (x, y) can be expressed as:
wherein: (x, y) represents camera coordinates; i 1 (x,y)、I 2 (x,y)、I 3 (x, y) represents the three-step phase-shifted fringe pattern intensity.
Further, in the expression form under the polar coordinate system in the step S4, the polar angle is a wrapped phase value, and the polar path lengths are all set to 1; the polar meridians are different from the polar meridians in the polar coordinate definition, the polar meridians in the polar coordinate definition are scalar quantities and only represent the distances between polar coordinate points and poles; the polar path refers to a connection line between a polar coordinate point and a pole, and the meaning of the polar path includes the length of the line segment and the spatial position in the polar coordinate system.
Further, in the step S5, the polar meridians are uniformly distributed in the polar coordinate system space, which means that the number of polar meridians included in any polar angle interval with equal length is the same.
Further, the unwrapping calculation in step S7 includes:
Φ(x,y)＝φ c (x,y)+2πK(x,y)；
wherein: k (x, y) represents the fringe order, which can be obtained by a phase unwrapping algorithm; the phase unwrapping algorithm is in the prior art and will not be described in detail.
Further, the method for averaging the included angle between the adjacent polar meridians in the step S5 may be divided into the following sub-steps:
step S51: extracting polar angle values in chord distribution diagram to form polar angle sequence theta i And according to the wrapping phase phi influenced by the gamma effect of the system g Sequence pair θ of (x, y) additions to chord distribution graph i Numbering is carried out; note that the numbering is used to restore the equalized chord distribution map to a parcel phase map;
step S52: for theta i Ascending order arrangement to obtain theta' i The method comprises the steps of carrying out a first treatment on the surface of the Note that the numbering will always record the sequence θ i Initial positions of the respective elements;
step S53: from theta' i Calculating the included angle value sequence delta theta 'of adjacent polar angles' i ：
Step S54: find Δθ' i Average value of (2):
wherein: m represents Δθ' i The total number of included angle values;
step S55: by means of
Generating polar angle sequences theta', with equal included angles i ：
Step S56: rearrange θ″ according to the number in step S51 i To restore the number to the original valueStarting the sequence;
step S57: according to the rearranged θ' in step S55 i Generating a uniform polar channel distribution map; wherein the polar coordinates S in the uniform polar warp distribution diagram 1 Should correspond to rearranged θ i The polar angle value of the middle number is 1, S 2 Should correspond to a polar value numbered 2, and so on.
The beneficial effects of adopting above technical scheme are:
1. the gamma nonlinear error correction method for the three-dimensional measurement of the fringe projection provided by the invention can effectively improve the precision of the three-dimensional measurement result of the fringe projection without slowing down the measurement speed.
2. The gamma nonlinear error correction method for three-dimensional measurement of stripe projection provided by the invention can correct errors caused by the gamma effect of the system without any pre-calibration step, is convenient and quick in error correction process, and has a wider application range compared with other methods.
3. According to the gamma nonlinear error correction method for three-dimensional measurement of stripe projection, provided by the invention, the probability distribution of the wrapping phase value is corrected by equalizing the polar channel distribution diagram of the wrapping phase under the polar coordinate system, so that compared with methods such as frequency domain transformation, the method does not introduce extra edge contour errors when measuring complex objects or objects with large surface height differences.
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FIG. 1 is a schematic diagram of a three-dimensional measurement system with fringe projection;
FIG. 2 is a schematic representation of the expression of the wrapping phase in a polar coordinate system and the polar distribution;
FIG. 3 is a graph showing polar distribution versus phase for different wraps;
FIG. 4 is a flow chart of pole distributed equalization;
Detailed Description
The following detailed description of the embodiments of the invention, given by way of example only, is presented in the accompanying drawings to aid in a more complete, accurate and thorough understanding of the concepts and aspects of the invention, and to aid in its practice, by those skilled in the art.
As shown in fig. 1 to 4, the present invention is a gamma nonlinear error correction method for three-dimensional measurement of fringe projection, taking a three-step phase shift method as an example, and specifically comprising the following steps:
example 1:
step S1: constructing a fringe projection three-dimensional measurement system, as shown in fig. 1, wherein the system comprises a projector, a camera and an object to be measured, the projector is used for projecting three-step phase-shift fringe patterns onto the object to be measured, and the camera is used for capturing the phase-shift fringe patterns distorted by the surface of the object to be measured; the projector and the camera synchronously trigger the starting operation, the projector, the camera and the measured object form a triangulation relation, and the system finishes the calibration of the conversion relation of the height-phase value;
step S2: the projector sequentially projects three-step phase-shift fringe patterns to the surface of the measured object, and meanwhile, the camera captures the fringe patterns distorted by the surface of the measured object; taking a three-step phase shift method as an example for describing a technical scheme, a three-step phase shift fringe pattern projected by a projector is generated by a computer, and the intensity of the three-step phase shift fringe pattern can be expressed as follows:
wherein: (x) p ,y p ) Representing pixel coordinates of the projector; f represents the number of cycles of the stripes in an image; a. b is a constant for adjusting the stripe intensity; preferably, in this embodiment, a=b=0.5;
the light intensity of the three-step phase-shifted fringe pattern captured by the camera is expressed as:
I 1 (x,y)＝A(x,y)+B(x,y)cos[φ g (x,y)-2π/3]；
I 2 (x,y)＝A(x,y)+B(x,y)cos[φ g (x,y)]；
I 1 (x,y)＝A(x,y)+B(x,y)cos[φ g (x,y)+2π/3]；
wherein: (x, y) represents camera coordinates; i 1 (x,y)、I 2 (x,y)、I 3 (x, y) represents the three-step phase-shifted fringe pattern intensity; a (x, y) and B (x, y) respectively represent background light intensity and modulated light intensity; phi (phi) g (x, y) represents the wrapped phase affected by the system gamma effect;
step S3: calculating the wrapping phase phi influenced by the gamma effect of the system by a three-step phase shift method g (x, y); wherein, the step S3 three-step phase shift method solves the wrapping phase phi influenced by the system gamma effect g (x, y) can be expressed as:
step S4: wrapping phase phi to be affected by system gamma effect g (x, y) into an expression form in a polar coordinate system, as shown in fig. 2 (1), wherein: θ represents the polar angle whose value is equal to the wrapped phase value, point S i (1,θ i ) Represent phi g Polar coordinates corresponding to (x, y), OS i Representing polar coordinate point S i (1,θ i ) R represents the pole length and is set to 1 for ease of calculation, ox represents the pole axis; preferably, the counter-clockwise direction is taken as the positive polar coordinate direction, and the polar angle value at the polar axis OX is set to 0;
then, the wrapping phase phi influenced by the system gamma effect is sequentially carried out g (x, y) is added into a polar coordinate system, and a spatial distribution diagram of polar channels obtained by polar channels of all polar coordinates is drawn, as shown in fig. 2 (2); preferably, the wrapping phase φ, in turn, will be affected by the system gamma effect g (x, y) is added to the polar coordinate system by prioritizing the wrapping phases phi in columns g (x, y) added to the polar coordinate system, i.e. S i (1,θ i ) And phi g The correspondence of (x, y) satisfies:
through the step, the distribution condition of the wrapping phase value in 0 to 2 pi can be converted into the spatial distribution condition of polar channels in a polar coordinate system; specifically, as shown in fig. 3: FIG. 3 (1) is an ideal parcel phase diagram, and FIG. 3 (2) is a corresponding polar channel diagram thereof; FIG. 3 (3) is a wrapped phase diagram of the effect of gamma effect, and FIG. 3 (4) is a corresponding polar channel distribution diagram;
step S5: the polar meridians are uniformly distributed in the polar coordinate system space by averaging the included angles between the adjacent polar meridians; the method for adopting the included angle between the average adjacent polar meridians is shown in a figure (4), and the method can be divided into the following sub-steps:
step S51: extracting polar angle values in chord distribution diagram to form polar angle sequence theta i And according to the wrapping phase phi influenced by the gamma effect of the system g Sequence pair θ of (x, y) additions to chord distribution graph i Numbering is carried out; note that the numbering is used to restore the equalized chord distribution map to a parcel phase map;
step S52: for theta i Ascending order arrangement to obtain theta' i The method comprises the steps of carrying out a first treatment on the surface of the Note that the numbering will always record the sequence θ i Initial positions of the respective elements;
step S53: from theta' i Calculating the included angle value sequence delta theta 'of adjacent polar angles' i ：
Step S54: find Δθ' i Average value of (2):
wherein: m represents Δθ' i The total number of included angle values;
step S55: by means of
Generating polar angle sequences theta', with equal included angles i ：
Step S56: rearrange θ″ according to the number in step S51 i Restoring the numbers to the initial order;
step S57: according to the rearranged θ' in step S55 i Generating a uniform polar channel distribution map; wherein the polar coordinates S in the uniform polar warp distribution diagram 1 Should correspond to rearranged θ i The polar angle value of the middle number is 1, S 2 Should correspond to a polar value numbered 2, and so on.
Step S6: restoring the spatial distribution map of the equalized polar diameter into corrected wrapping phase phi according to the sequence of priority c (x, y) having values which are completely uniformly distributed within 0 to 2 pi; wherein: the wrapping phase phi c Phi in (x, y) c (1, 1) should correspond to polar coordinate S in the equalized chord distribution graph 1 ，φ c (2, 1) should correspond to polar coordinate S 2 ，φ c (x, y) should correspond to polar coordinate S i (i＝x+(y-1)×col)；
Step S7: phase unwrapping algorithm is used to unwrap corrected wrapped phase phi c Unwrapping (x, y) to obtain an absolute phase phi (x, y), then converting the absolute phase phi (x, y) into height information according to a conversion relation of the height-phase value, and performing three-dimensional reconstruction on the surface of the object; wherein: the calculation process of the unwrapped package is as follows:
Φ(x,y)＝φ c (x,y)+2πK(x,y)；
wherein: k (x, y) represents the fringe order, which can be obtained by a phase unwrapping algorithm.
While the invention has been described above by way of example with reference to the accompanying drawings, it is to be understood that the invention is not limited to the particular embodiments described, but is capable of numerous insubstantial modifications of the inventive concept and solution; or the invention is not improved, and the conception and the technical scheme are directly applied to other occasions and are all within the protection scope of the invention.
Claims (6)
1. A gamma nonlinear error correction method for three-dimensional measurement of fringe projection is characterized by comprising the following steps of: the method specifically comprises the following steps:
step S1: setting up a fringe projection three-dimensional measurement system which comprises a projector and a camera, wherein the projector and the camera synchronously trigger starting operation, the projector, the camera and an object to be measured form a triangulation relation, and the system finishes the calibration of the conversion relation of the height-phase value;
step S2: the projector sequentially projects phase-shift stripe patterns onto the surface of the measured object, and the camera captures the stripe patterns distorted by the surface of the measured object;
step S3: calculating the wrapping phase phi influenced by the gamma effect of the system by a three-step phase shift method g (x,y)；
Step S4: wrapping phase phi to be affected by system gamma effect g (x, y) is converted into an expression form under a polar coordinate system, and then a polar channel space distribution diagram of all polar coordinates is drawn;
step S5: the polar meridians are uniformly distributed in the polar coordinate system space by averaging the included angles between the adjacent polar meridians;
step S6: restoring the equalized polar spatial distribution map to the corrected wrapping phase phi c (x, y) having values which are completely uniformly distributed within 0 to 2 pi;
step S7: phase unwrapping algorithm is used to unwrap corrected wrapped phase phi c The (x, y) unwraps to obtain an absolute phase phi (x, y), then converts the absolute phase phi (x, y) into height information according to the height-phase value conversion relationship, and performs three-dimensional reconstruction of the object surface.
2. Gamma non-linear error correction for fringe projection three-dimensional measurement as recited in claim 1The method is characterized in that: the three-step phase shift method in the step S3 solves the wrapping phase phi influenced by the system gamma effect g (x, y) can be expressed as:
wherein: (x, y) represents camera coordinates; i 1 (x,y)、I 2 (x,y)、I 3 (x, y) represents the three-step phase-shifted fringe pattern intensity.
3. The gamma non-linear error correction method for fringe projection three-dimensional measurement of claim 1, wherein: the polar angle in the expression form under the polar coordinate system in the step S4 is a wrapping phase value, and the polar warp length is set to be 1; the polar meridians are different from the polar meridians in the polar coordinate definition, the polar meridians in the polar coordinate definition are scalar quantities and only represent the distances between polar coordinate points and poles; the polar path refers to a connection line between a polar coordinate point and a pole, and the meaning of the polar path includes the length of the line segment and the spatial position in the polar coordinate system.
4. The gamma non-linear error correction method for fringe projection three-dimensional measurement of claim 1, wherein: the step S5 of uniformly distributing the polar meridians in the polar coordinate system space means that the number of polar meridians included in any polar angle section of equal length is the same.
5. The gamma non-linear error correction method for fringe projection three-dimensional measurement of claim 1, wherein: the unwrapping calculation in step S7 includes:
Φ(x,y)＝φ c (x,y)+2πK(x,y)；
wherein: k (x, y) represents the fringe order, which can be obtained by a phase unwrapping algorithm.
6. The gamma non-linear error correction method for fringe projection three-dimensional measurement of claim 1, wherein: the method for averaging the included angle between the adjacent polar meridians in the step S5 can be divided into the following sub-steps:
step S51: extracting polar angle values in chord distribution diagram to form polar angle sequence theta i And according to the wrapping phase phi influenced by the gamma effect of the system g Sequence pair θ of (x, y) additions to chord distribution graph i Numbering is carried out; note that the numbering is used to restore the equalized chord distribution map to a parcel phase map;
step S52: for theta i Ascending order arrangement to obtain theta i 'A'; note that the numbering will always record the sequence θ i Initial positions of the respective elements;
step S53: from theta i ' calculating the sequence of included angle values delta theta of adjacent polar angles i '：
Step S54: calculate delta theta i Average of:
wherein: m represents Δθ i Total number of included angle values in';
step S55: by means of
Generating polar angle sequences theta with equal included angles i ”：
Step S56: rearranging θ according to the number in step S51 i ", restore the numbering to the original order;
step S57: according to the rearrangement in step S55θ of (2) i "generate a uniform polar channel profile; wherein the polar coordinates S in the uniform polar warp distribution diagram 1 Should correspond to rearranged theta i "polar angle value of 1, S 2 Should correspond to a polar value numbered 2, and so on.
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