An absolute phase unwrapping method based on geometric constraints and photometric information

Abstract

The present invention discloses an absolute phase unwrapping method based on geometric constraints and photometric information. This method can measure objects with a large depth range without the need for additional image acquisition or other cameras. The method sets a virtual reference plane behind the object to be measured and uses the absolute phase of the reference plane as a reference to obtain the object's initial absolute phase. Phase discontinuities in the initial absolute phase are detected and connected as boundaries, thereby dividing the object into independent regions. Using a projector as a point light source, according to Lambert's cosine law, simulated images of different 2π phase domain intervals in space are generated for each region in turn. The phase domain 2π interval corresponding to the region is determined by comparing the similarity between these simulated images and the modulated image, ultimately obtaining the entire absolute phase map of the object.

Description

Technical Field

[0001] The invention relates to an absolute phase unwrapping method based on geometric constraints and photometric information, and belongs to the technical field of optical three-dimensional measurement. Background Art

[0002] Fringe projection profilometry is a widely studied and applied optical 3D shape measurement technique within structured light vision measurement. It uses a projector to project a structured pattern (typically sinusoidal fringes) onto the object being measured. A camera then captures the deformed pattern and non-contactly calculates the 3D surface topography of the object. Fringe projection profilometry offers the advantages of high speed and high accuracy. Fringe projection profilometry typically uses phase information extracted from the fringe pattern to establish a pixel-level correspondence between the camera and projector, or directly establishes a phase-height mapping. There are two main methods for obtaining phase: phase shifting and Fourier transform. Both use tangent functions, resulting in the obtained phase being wrapped within the range [-π, π). However, high-precision measurements often require projecting high-frequency sinusoidal fringes, and the wrapped phase will differ from the desired absolute phase by an integer multiple of 2π. This multiple is often called the fringe order, so phase unwrapping is required to determine the fringe order for each pixel to eliminate periodic ambiguity in the wrapped phase.

[0003] Phase unwrapping can generally be divided into two categories: spatial domain phase unwrapping and time domain phase unwrapping. Spatial domain phase unwrapping is a direct unwrapping of the wrapped phase. It is simple to operate, but it cannot measure isolated objects with discontinuous surfaces, and can only unwrap the relative phase. Time domain phase unwrapping requires projecting additional patterns to assist in phase unwrapping. Common methods include Gray code, multi-frequency, and phase encoding. Although the time domain phase unwrapping method can obtain a relatively high-precision absolute phase, the additional projected pattern limits the measurement speed, making it unsuitable for the measurement of dynamic objects. In addition, some scholars have proposed a phase unwrapping method based on a reference plane, but it is necessary to limit the depth range of the object to be measured to the 2π interval in the phase domain adjacent to the reference plane, and the boundary of this interval changes pixel by pixel. It is difficult to intuitively grasp this constraint in actual operation. Summary of the Invention

[0004] To address the above problems, the present invention provides an absolute phase unwrapping method based on geometric constraints and photometric information. On the basis of the reference plane method, the phase of the object under test with a large depth range is directly unwrapped based only on the geometric constraints and photometric information of the structured light system.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] Step 1: Using the N-step phase shift method, a set of phase-shifted sinusoidal fringes is projected onto the object. The deformed fringe pattern is captured by a camera, and the object's wrapping phase φ and modulation index B are calculated using the following formulas:

[0007]

[0008]

[0009] Among them, (u c ,v c ) represents the corresponding camera pixel, n represents the serial number of the phase-shift fringe, and I represents the fringe pattern;

[0010] Step 2: Take the camera coordinate system as the world coordinate system, assume that a virtual reference plane z=z0 is set behind the object to be measured, and use the projection matrix P of the camera and projector obtained by calibration. c ,P p Absolute phase Φ of the reference plane z ; For each pixel of the camera, Φ z (u c ,v c )=2π·u p / M, where u p is the camera pixel (u c ,v c ) is the horizontal coordinate of the corresponding point of the projector DMD, M is the number of DMD pixels occupied by the sinusoidal signal of one cycle in the phase-shifted fringe; and can be obtained by the projection equation:

[0011]

[0012] Among them, (x, y, z0) is the spatial coordinate of the reference plane, and its projection pixel coordinates in the camera and projector are pixels (u c ,v c ) and (u p ,v p ), s c ,s p is the scale factor;

[0013] Step 3: Take the absolute phase Φ of the reference plane z As a reference, the object's wrapped phase is compared with it, and the initial fringe order k(u c ,v c ):

[0014]

[0015] And the initial absolute phase of the object is obtained from the order of each pixel:

[0016] Φ0(u c ,v c )=φ(u c ,v c )+2π·k(u c ,v c ) (5)

[0017] Step 4: Perform edge detection on the initial absolute phase of the object, detect discontinuities in the phase and boundaries with large jumps, and connect these boundaries to finally divide the object into multiple independent regions; the phase in each region changes continuously, there is no phase jump or step, and the depth range of each region corresponds to a 2π interval in the spatial phase domain; Step 5: Decrease the initial absolute phase of the object by 2π, 4π,... and other integer multiples of 2π to generate multiple candidate phase values; Based on each candidate phase value, a candidate point cloud in a different 2π interval in the spatial phase domain can be reconstructed for each independent region; these 2π intervals in the spatial phase domain are distributed sequentially from the reference plane toward the camera; the interval adjacent to the reference plane is defined as interval 0, and each 2π interval is numbered in sequence;

[0018] Step 6: Consider the projector as a point light source, and the position of the light source is the calibrated optical center position of the projector. Since the structured light system based on grating projection is mainly used to measure the Lambertian body of surface diffuse reflection, it is assumed that each segmented area has the same reflectivity, and according to the Lambert cosine theorem, a simulated image I is generated for each independent area under the point light source model. sn :

[0019]

[0020] Where sn is the serial number corresponding to the 2π interval; n is the normal vector of the point (x, y, z) in the object point cloud, which can be obtained by computing the generated candidate point cloud; s represents the incident direction of light at the point, which can be obtained from the point cloud and the coordinates of the light source; D represents the distance from the point to the light source.

[0021] Step 7: For each region, the simulated images I in different phase domains are taken into account. sn (u c ,v c ) is compared with the modulation image of the region for similarity; the similarity measure is expressed by the normalized mutual correlation coefficient ξ:

[0022]

[0023] Among them, Ω represents the pixel set of the area, and are the average grayscale values ​​of the modulation image and the simulated image of the region respectively; the simulated image with the highest similarity to the modulation image corresponds to the correct 2π interval of the region in space, and the absolute phase value corresponding to this interval is the accurate absolute phase of the region; finally, the absolute phases of each region are combined to obtain the complete absolute phase of the object.

[0024] Compared to existing technologies, the present invention, by employing the above technical solutions, offers the following advantages: The proposed phase unwrapping method, based on geometric constraints and photometric information, does not require the projection of additional images or other hardware assistance, is simple to operate, and has significant potential for application in dynamic measurement. The proposed method overcomes the depth limitations of existing reference plane methods, making it applicable to measuring objects with a wider depth range, effectively expanding its practical application range. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a flowchart of the absolute phase unwrapping method based on geometric constraints and photometric information;

[0026] Figure 2 Schematic diagram of the constructed structured light system and phase unwrapping based on the reference plane;

[0027] Figure 3 is the object's wrapping phase;

[0028] Figure 4 is the modulation image of the object;

[0029] Figure 5 is the initial absolute phase of the object;

[0030] Figure 6 The edge detection and segmentation results of the object's initial absolute phase;

[0031] Figure 7 is the final absolute phase of the object. DETAILED DESCRIPTION

[0032] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings:

[0033] Step 1: As attached Figure 2 As shown, a structured light system is first built using a camera and a projector and calibrated. The approximate measurement object distance is then determined by the system parameters, and the object to be measured is placed in the measurement field of view of the structured light system according to the object distance.

[0034] Step 2: Start the projector to project sinusoidal phase-shifted fringes onto the object, and use the camera to capture the image and calculate the object's wrapping phase φ (see attached figure). Figure 3 as shown) and modulation B (as shown in the attached Figure 4 shown);

[0035] Step 3: Using the measured object distance as a reference, set a virtual reference plane z = z0 behind the object and calculate the absolute phase Φ of the reference plane. z ;

[0036] Step 4: From the absolute phase Φ of the reference plane z The initial fringe order corresponding to each pixel is calculated using the object's wrapping phase φ:

[0037]

[0038] The initial absolute phase of the object is obtained from these orders, as shown in the following figure. Figure 5 As shown:

[0039] Φ0(u c ,v c )=φ(u c ,v c )+2π·k(u c ,v c ) (2)

[0040] Step 5: Use the Canny operator to perform edge detection on the initial absolute phase of the object, detect the discontinuities in the phase and the boundaries with large jumps, and connect these boundaries to finally divide the object into multiple independent regions, as shown in the following figure. Figure 6 As shown;

[0041] Step 5: Decrease the object's initial absolute phase by 2π, 4π, ..., and other integer multiples of 2π to generate multiple candidate phase values. Based on each candidate phase value, a candidate point cloud within a different 2π interval in the spatial phase domain can be reconstructed for each independent region.

[0042] Step 6: Consider the projector as a point light source. The position of the light source is the calibrated optical center of the projector. Assuming that each segmented area has the same reflectivity, generate a simulated image I for each independent area under the point light source model according to Lambert's cosine theorem. sn :

[0043]

[0044] Step 7: For each region, the simulated images I in different phase domains are taken into account. sn (u c ,v c ) is compared with the modulation image of the region for similarity; the similarity measure is expressed by the normalized mutual correlation coefficient ξ:

[0045]

[0046] The simulated image with the highest similarity to the modulation image corresponds to the correct 2π interval of the region in space. The absolute phase value corresponding to this interval is the accurate absolute phase of the region. Finally, the absolute phase of each region is combined to obtain the complete absolute phase of the object, as shown in the attached figure. Figure 7 shown.

[0047] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person familiar with the technology can understand and think of any changes or replacements within the technical scope disclosed by the present invention, which should be included in the scope of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. An absolute phase unwrapping method based on geometric constraints and photometric information, characterized in that: This method achieves direct unwrapping of absolute phase without the need for additional projection patterns or other hardware, utilizing only the geometric constraints and photometric information in the structured light system. The method includes the following steps: Step 1: Using the N-step phase shift method, a set of phase-shifted sinusoidal fringes is projected onto the object. The deformed fringe pattern is captured by a camera, and the object's wrapping phase φ and modulation index B are calculated using the following formulas: Among them, (u c ,v c ) represents the corresponding camera pixel, n represents the serial number of the phase-shift fringe, and I represents the fringe pattern; Step 2: Take the camera coordinate system as the world coordinate system, assume that a virtual reference plane z=z0 is set behind the object to be measured, and use the projection matrix P of the camera and projector obtained by calibration. c ,P p Absolute phase Φ of the reference plane z ; For each pixel of the camera, Φ z (u c ,v c )=2π·u p / M, where u p is the camera pixel (u c ,v c ) is the horizontal coordinate of the corresponding point of the projector DMD, M is the number of DMD pixels occupied by the sinusoidal signal of one cycle in the phase-shifted fringe; and the projection equations are combined to obtain: Among them, (x, y, z0) is the spatial coordinate of the reference plane, and its projection pixel coordinates in the camera and projector are pixels (u c ,v c ) and (u p ,v p ), s c ,s p is the scale factor; Step 3: Take the absolute phase Φ of the reference plane z As a reference, the object's wrapped phase is compared with it, and the initial fringe order k(u c ,v c ): And the initial absolute phase of the object is obtained from the order of each pixel: Φ0(u c ,v c )=φ(u c ,v c )+2π·k(u c ,v c ) (5) Step 4: Perform edge detection on the object's initial absolute phase, detecting discontinuities and boundaries with large phase jumps, and connecting these boundaries to ultimately segment the object into multiple independent regions. The phase in each region changes continuously, without phase jumps or steps, and the depth range of each region corresponds to a 2π interval in the spatial phase domain. Step 5: Decrease the object's initial absolute phase by multiples of 2π to generate multiple candidate phase values. Based on each candidate phase value, reconstruct a candidate point cloud for each independent region within a different 2π interval in the spatial phase domain. These 2π intervals in the spatial phase domain are distributed sequentially from the reference plane toward the camera. The interval immediately adjacent to the reference plane is defined as interval 0, and the 2π intervals are numbered sequentially. Step 6: Consider the projector as a point light source, and the position of the light source is the calibrated optical center position of the projector. Since the structured light system based on grating projection is mainly used to measure the Lambertian body of surface diffuse reflection, it is assumed that each segmented area has the same reflectivity, and according to the Lambert cosine theorem, a simulated image I is generated for each independent area under the point light source model. sn : Where sn is the serial number corresponding to the 2π interval; n is the normal vector of the point (x, y, z) in the object point cloud, which is calculated by the generated candidate point cloud; s represents the incident direction of the light at the point, which is obtained from the point cloud and the coordinates of the light source; D represents the distance from the point to the light source. Step 7: For each region, the simulated images I in different phase domain intervals are taken in turn. sn (u c ,v c ) is compared with the modulation image of the region for similarity; the similarity metric is expressed by the normalized mutual correlation coefficient ξ: Among them, Ω represents the pixel set of the area, and are the average grayscale values ​​of the modulation image and the simulated image of the region respectively; the simulated image with the highest similarity to the modulation image corresponds to the correct 2π interval of the region in space, and the absolute phase value corresponding to this interval is the accurate absolute phase of the region; finally, the absolute phases of each region are combined to obtain the complete absolute phase of the object.

Images