A whole-eye 3D reconstruction method based on SS-OCT measurement system

Through the full-eye three-dimensional reconstruction method based on the SS-OCT measurement system, the three-dimensional original data of the eyes are collected and processed, and the surface fitting and refraction correction are combined with the principal element analysis method and the least squares method, the three-dimensional structure measurement of the eyes in the prior art is solved. The accuracy problem has achieved a more accurate three-dimensional structure reconstruction of the eye.

CN114947728BActive Publication Date: 2025-02-18HANGZHOU AITAIKE TECHNOLOGY HOLDINGS CO LTD
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Patent Information

Application Number
CN202210701794.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-06-21
Publication Date
2025-02-18
Estimated Expiration
2042-06-21

AI Technical Summary

Technical Problem

The prior art is difficult to accurately measure the three-dimensional structure of the eye, especially in OCT scans. Since light is refracted when passing through multiple media of the eye, the original image is affected by distortion. The existing correction methods are mostly carried out in two-dimensional planes and cannot be effective. Correct distortion in three-dimensional three-dimensional space.

Method used

The whole-eye three-dimensional reconstruction method based on the SS-OCT measurement system is adopted. By collecting the original three-dimensional eye data, grayscale correction and pixel correction are performed, OTUS Otsu algorithm is used for binarization and denoising, and surface fitting is used for least squares method. The surface normal vector is estimated through the principal element analysis method, and finally a layer-by-layer refraction correction is performed.

Benefits of technology

Accurate three-dimensional structural reconstruction of the eyes is achieved, and the true shape and biological parameters of the eyes can be restored more accurately, deviations in the two-dimensional correction methods are avoided, and the accuracy and reliability of measurement are improved.

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Abstract

The present invention discloses a method for three-dimensional reconstruction of the whole eye based on an SS-OCT measurement system, which relates to the fields of data simulation and biomedical imaging technology. The SS-OCT measurement system is a non-contact system, and the imaging depth can image the whole eye, and the acquisition speed is fast; it includes thresholding, denoising, deleting small-area objects, surface fitting, normal vector acquisition, and refraction correction parts; the principal component analysis method is used to estimate the surface normal vector, and this solution has strong robustness in eliminating data noise; the data is centrally processed to reduce the influence of deviation points, laying the foundation for the correct acquisition of deflection vectors for subsequent distortion correction; layered layer-by-layer correction is used, and the light deflection is calculated according to the law of optical refraction at the interface where the refractive index changes. The present invention considers the influence of the refraction effect of light in three-dimensional space, accurately restores the true shape of the eye, and realizes accurate measurement of the biomedical parameters of the eye.
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Description

Technical Field

[0001] The present invention relates to the fields of data simulation and biomedical imaging technology, and in particular to a whole-eye three-dimensional reconstruction method based on an SS-OCT measurement system. Background Art

[0002] The eye is an important organ of the human body, and people rely on vision to obtain most of the information from the outside world. Myopia is an important cause of visual impairment, and it has been gradually erupting in recent years. Although it has been studied for many years, its pathogenesis is still unclear. The three-dimensional structural parameters of the eye can characterize the function of the eye and are the basis of myopia-related research. At present, the technologies used in ophthalmic measurement include ultrasound, magnetic resonance imaging, and bioparameter measuring instruments. During ultrasound imaging, the ultrasound probe needs to contact the eyeball, causing discomfort to the person being measured. Magnetic resonance can image the entire eyeball, but due to the slow imaging speed, the measurement is interfered by eye movement artifacts. The ophthalmic bioparameter measuring instrument mainly measures distance parameters such as axial length. The measurement of parameters such as curvature is based on a specific two-dimensional plane, and it is impossible to obtain more comprehensive three-dimensional structural information of the eye.

[0003] Optical coherence tomography (OCT) is a new type of biomedical imaging technology that was born in the early 1990s. It has the advantages of non-invasiveness, non-destructiveness, high spatial resolution, and three-dimensional real-time imaging. At present, OCT technology is mainly used in ophthalmic imaging. It can display the microscopic structure of the eye in real time and is an indispensable device for the diagnosis of ophthalmic diseases. With the development of high-speed swept source optical coherence tomography (SS-OCT), the line scanning speed of OCT has reached hundreds of kHz or even MHz. At the same time, its imaging depth and sensitivity have also been greatly improved, which can realize the rapid scanning of the three-dimensional structure of the eye. However, the original image directly obtained by OCT scanning is affected by the refraction of the eye (the light is refracted through the interface with changed refractive index), which will be distorted and deviate from the real structure. Therefore, accurate measurement of the three-dimensional structure of the eye requires distortion correction of the original image. Existing distortion correction is mostly performed on two-dimensional images, and these methods are suitable for special curved surfaces passing through the vertex of the eyeball. However, most of the refraction of the detection beam in OCT scanning occurs in three-dimensional space, and correcting it in a two-dimensional plane will inevitably produce deviations. In recent years, some research teams have tried stereoscopic correction based on three-dimensional space, but they are limited by two points: ① The detection depth of the hardware equipment is limited, and multiple scans and alignment are required to obtain the original image of the eyeball, which is complicated and affects the accuracy; ② The surface extraction and surface normal vector extraction algorithms lack robustness and are easily affected by image noise. After three-dimensional reconstruction, parameters such as corneal thickness, anterior and posterior corneal surface curvature radius, lens thickness, anterior and posterior lens surface curvature radius, vitreous depth, and axial length can be measured. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention designs a whole-eye three-dimensional reconstruction method based on the SS-OCT measurement system;

[0005] A whole-eye three-dimensional reconstruction method based on an SS-OCT measurement system specifically comprises the following steps:

[0006] Step 1: Collect the original 3D data of the eye using the SS-OCT measurement system;

[0007] The SS-OCT measurement system is based on the interferometer principle, using near-infrared weak coherent light to illuminate the tissue to be measured, generating interference based on the coherence of the light, and using superheterodyne detection technology to measure the intensity of the reflected light for imaging the superficial layer of the tissue;

[0008] The SS-OCT measurement system specifically includes: coupler 1, coupler 2, circulator 1, circulator 2, lens 1, lens 2, reflector 1, XY galvanometer, dichroic mirror, light source, balanced detector, acquisition card, target object;

[0009] Among them, one end of the coupler 1 is connected to the light source, and the other end is connected to the circulator 1, one end of the circulator 1 is connected to the collimator 1, and the collimator 1, the XY galvanometer, the lens 1, the dichroic mirror, and the eye form a sample arm; one end of the circulator 1 is connected to the coupler 2, and one end of the coupler 2 is connected to the balanced detector; one end of the coupler 1 is connected to the circulator 2, and the circulator 2 is connected to the collimator 2, and the collimator 2, the lens 2, and the reflector 1 form a reference arm;

[0010] The SS-OCT measurement system uses a swept-frequency light source in the 1060nm band. The central wavelength of the light source is longer than that used in the spectral domain and time domain. The axial resolution is reduced, but the depth range of tissue detection is wider. It is used for endoscopic OCT imaging of cardiovascular and cerebrovascular tissues. In SS-OCT, the imaging depth z max It is expressed as:

[0011]

[0012] In the above formula, λ0 represents the central wavelength of the light source, R λ It represents the resolution of the spectrometer expressed in wavelength, which is directly obtained through experiments. n is the average refractive index of the imaged tissue. The theoretical imaging depth of the SS-OCT system is more than ten centimeters. The axial length of the eye is a (a<3) centimeters, which is sufficient for whole-eye imaging. The value of a varies according to the axial length of the human eye.

[0013] The working process of the SS-OCT system to collect 3D raw data of the eye is as follows:

[0014] The light emitted by the light source is split by the coupler 1, part of the light is input into the reference arm, part of the light is input into the sample arm, the light enters the reference arm through the circulator 2, the light is collimated by the collimator 2, and converged to the reflector 1 through the lens 2; the light is input into the sample arm through the circulator 1, collimated by the collimator 1 and irradiated to the XY scanning galvanometer, and then the sample light is converged by the lens 1 and shot into the pupil of the subject, the light returning through the pupil and lens of the subject passes through the circulator 1 and the light returning from the reference arm passes through the circulator 2 to the coupler 2 to interfere, the interference signal is detected by the balanced detector BPD, and finally the interference signal is sampled and recorded by the data acquisition card DAQ and saved to the computer for subsequent processing;

[0015] Step 2: The three-dimensional raw data of the eye collected in step 1 is calculated and processed to obtain an eye image. The image is a cross-sectional view of each position of the eye. Grayscale correction and pixel correction are performed on the image. The image has pixel correction problems in three directions. The correspondence between the pixel size of the image and the real geometric distance is confirmed to restore the real size of the eyeball. Otherwise, the measurement result is incorrect, which affects the further correction of image distortion.

[0016] Step 3: Use the OTUS Otsu algorithm to binarize, threshold segment, and denoise the image processed in step 2, perform image enhancement on the region, delete small area objects, so as to extract the interface of the eye tissue structure layer, and store the interface data of the eye tissue structure layer;

[0017] Step 4: Use the least square method to perform surface fitting on the data in the effective area of ​​the image processed in step 3. The data in the effective area is obtained by intercepting the effective data in the interface data of the eye tissue structure layer by masking. After the surface fitting, the principal component analysis method is used to estimate the surface normal vector;

[0018] The idea of ​​principal component analysis is to fit a plane to the N points of the K-nearest neighbors, that is, the plane passes through the centroid O i The plane is fitted with N points to obtain the plane normal vector; the least squares fitting is converted into the eigenvector corresponding to the minimum eigenvalue P of the covariance matrix of the effective area of ​​the image, that is, the SVD decomposition is performed on the effective area of ​​the image; the SVD solution is highly robust to data noise, and the key point is to centralize the data and move the origin of the covariance matrix coordinates to the center of gravity of the data; finally, according to the minimum eigenvalue P to the center of gravity O i The positive or negative sign of the normal vector is determined by the dot product of the formed vector and the plane normal vector, f(p)<0 is negative, and f(p)>0 is positive; Step 5: Perform refraction correction on the pixels of the image. Since the light passes through various tissue structures of the eye in sequence, the refractive index of the layered media is different. For example, the refractive indexes of the cornea, aqueous humor, lens and vitreous body are 1.375, 1.336, 1.416 and 1.336 respectively. Therefore, refraction will occur on the layered surface of structures such as the cornea, which will significantly affect the observed surface geometric features and be inconsistent with the actual parameters; in order to correct the influence of optical distortion, it is necessary to propagate along the direction vector of the light; when the light propagates through the refraction effect at each interface between two media with different refractive indices, it is propagated according to the direction vector after refraction, and corrected layer by layer to obtain a real volume image.

[0019] Beneficial technical effects of the present invention:

[0020] 1. A SS-OCT measurement system is used, which is a non-contact system. The imaging depth can image the whole eye and the acquisition speed is fast.

[0021] 2. The principal component analysis method is used to estimate the surface normal vector. This solution is highly robust to data noise. The data is centralized and the influence of deviation points is reduced. This lays the foundation for the correct determination of the deflection vector for subsequent distortion correction and more accurately restores the true shape of the model.

[0022] 3. Correction is performed layer by layer, from top to bottom. According to the law of optical refraction, deflection occurs at the interface with different refractive indices, and the refraction efficiency of light is considered in multiple directions. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Schematic diagram of refraction correction according to an embodiment of the present invention;

[0024] Figure 2 Schematic diagram of correction results of an embodiment of the present invention; Figure a is a two-dimensional correction; Figure b is a three-dimensional correction;

[0025] Figure 3 An embodiment of the present invention provides a swept-frequency optical coherence tomography system. DETAILED DESCRIPTION

[0026] The present invention will be further described below in conjunction with the accompanying drawings and embodiments;

[0027] The present invention proposes a new method for full-eye 3D reconstruction, which innovates the algorithms of each link in the process of eye 3D reconstruction. Figure 1 The refraction correction shown can achieve three-dimensional structure correction of the eye, more accurately restore the correct physical distance of the eye, the biological parameters and dimensions of each surface, and realize the detection of the whole eye and subsequent image processing without alignment and one-time measurement.

[0028] A whole-eye three-dimensional reconstruction method based on an SS-OCT measurement system specifically comprises the following steps:

[0029] Step 1: Collect the original 3D data of the eye using the SS-OCT measurement system;

[0030] The SS-OCT measurement system is based on the interferometer principle, using near-infrared weak coherent light to illuminate the tissue to be measured, generating interference based on the coherence of the light, and using superheterodyne detection technology to measure the intensity of the reflected light for imaging the superficial layer of the tissue; the OCT system is composed of a low-coherence light source, a fiber Michelson interferometer, and a photoelectric detection system;

[0031] The SS-OCT measurement system specifically includes: coupler 1, coupler 2, circulator 1, circulator 2, lens 1, lens 2, reflector 1, XY galvanometer, dichroic mirror, light source, balanced detector, acquisition card, target; as shown in the attached Figure 3 As shown;

[0032] Among them, one end of the coupler 1 is connected to the light source, and the other end is connected to the circulator 1, one end of the circulator 1 is connected to the collimator 1, and the collimator 1, the XY galvanometer, the lens 1, the dichroic mirror, and the eye form a sample arm; one end of the circulator 1 is connected to the coupler 2, and one end of the coupler 2 is connected to the balanced detector; one end of the coupler 1 is connected to the circulator 2, and the circulator 2 is connected to the collimator 2, and the collimator 2, the lens 2, and the reflector 1 form a reference arm;

[0033] The SS-OCT measurement system uses a swept-frequency light source in the 1060nm band. The central wavelength of the light source is longer than that used in the spectral domain and time domain. The axial resolution is reduced, but the depth range of tissue detection is wider. It is used for endoscopic OCT imaging of cardiovascular and cerebrovascular tissues. In SS-OCT, the imaging depth z max It is expressed as:

[0034]

[0035] In the above formula, λ0 represents the central wavelength of the light source, R λ It represents the resolution of the spectrometer expressed in wavelength, which is directly obtained through experiments. n is the average refractive index of the imaged tissue. The theoretical imaging depth of the SS-OCT system is more than ten centimeters. The axial length of the eye is a (a<3) centimeters, which is sufficient for whole-eye imaging. The value of a varies according to the axial length of the human eye.

[0036] The working process of the SS-OCT system to collect 3D raw data of the eye is as follows:

[0037] The light emitted by the light source is split by the coupler 1, part of the light is input into the reference arm, part of the light is input into the sample arm, the light enters the reference arm through the circulator 2, the light is collimated by the collimator 2, and converged to the reflector 1 through the lens 2; the light is input into the sample arm through the circulator 1, collimated by the collimator 1 and irradiated to the XY scanning galvanometer, and then the sample light is converged by the lens 1 and shot into the pupil of the subject, the light returning through the pupil and lens of the subject passes through the circulator 1 and the light returning from the reference arm passes through the circulator 2 to the coupler 2 to interfere, the interference signal is detected by the balanced detector BPD, and finally the interference signal is sampled and recorded by the data acquisition card DAQ and saved to the computer for subsequent processing;

[0038] The SS-OCT measurement system is sufficient for full-eye imaging. In the actual application of the imaging system, the imaging depth is not only related to the performance of the light source, but also affected by the performance of the system signal detection device. The greater the tissue depth, the higher the signal frequency obtained. The effective signal has a certain bandwidth, which requires the balanced detector to have sufficient response bandwidth, and the bandwidth of the acquisition card must also meet the bandwidth requirements of the signal frequency at the maximum depth. Therefore, in terms of acquisition cards and photoelectric detection, higher-performance devices should be selected as much as possible to avoid affecting the imaging depth of the system.

[0039] Step 2: The three-dimensional raw data of the eye collected in step 1 is calculated and processed to obtain an eye image. The image is a cross-sectional view of each position of the eye. Grayscale correction and pixel correction are performed on the image. The image has pixel correction problems in three directions. The correspondence between the pixel size of the image and the real geometric distance is confirmed to restore the real size of the eyeball. Otherwise, the measurement result is incorrect, which affects the further correction of image distortion.

[0040] Step 3: Use the OTUS Otsu algorithm to binarize, threshold segment, and denoise the image processed in step 2, perform image enhancement on the region, delete small area objects, so as to extract the interface of the eye tissue structure layer, and store the interface data of the eye tissue structure layer;

[0041] Step 4: Use the least square method to perform surface fitting on the data in the effective area of ​​the image processed in step 3. The data in the effective area is obtained by intercepting the effective data in the interface data of the eye tissue structure layer by masking. After the surface fitting, the principal component analysis method is used to estimate the surface normal vector;

[0042] The idea of ​​principal component analysis is to fit a plane to the N points of the K-nearest neighbors, that is, the plane passes through the centroid O i The plane is fitted with N points to obtain the plane normal vector; the least squares fitting is converted into the eigenvector corresponding to the minimum eigenvalue P of the covariance matrix of the effective area of ​​the image, that is, the SVD decomposition is performed on the effective area of ​​the image; the SVD solution is highly robust to data noise, and the key point is to centralize the data and move the origin of the covariance matrix coordinates to the center of gravity of the data; finally, according to the minimum eigenvalue P to the center of gravity O i The positive or negative sign of the normal vector is determined by the dot product of the formed vector and the plane normal vector, f(p)<0 is negative, and f(p)>0 is positive; Step 5: Perform refraction correction on the pixels of the image. Since the light passes through various tissue structures of the eye in sequence, the refractive index of the layered media is different. For example, the refractive indexes of the cornea, aqueous humor, lens and vitreous body are 1.375, 1.336, 1.416 and 1.336 respectively. Therefore, refraction will occur on the layered surface of structures such as the cornea, which will significantly affect the observed surface geometric features and be inconsistent with the actual parameters; in order to correct the influence of optical distortion, it is necessary to propagate along the direction vector of the light; when the light propagates through the refraction effect at each interface between two media with different refractive indices, it is propagated according to the direction vector after refraction, and corrected layer by layer to obtain a real volume image.

[0043] The specific process of refraction correction is as follows:

[0044] Assume that the light is incident vertically on the front surface of the cornea and intersects with the front surface of the cornea. At this time, the confluence point of the light and the front surface of the cornea is and the direction vector obtained using the surface normal vector obtained in step 4 and the incident light It's on point The distance where the surface intersects at the confluence point is Then, the light is refracted and its direction vector is changed If the light continues to travel through the back surface of the cornea, it will The geometric distance moved is given by Indicates. Figure 1 As shown;

[0045] Intersection Generalized vector form association according to the direction vector:

[0046]

[0047] The geometric distance of the eye is calculated using the optical path. However, in OCT image representation, the geometric distance cannot be seen because each A-Scan represents the optical path of a specific light ray. In general, the total path D of a specific light ray (i) is i It can be expressed as the sum of the partial optical paths of each medium through which the light passes, assuming that the medium is homogeneous and the optical path is simply the product of the geometric path and the refractive index value (see equation (2)).

[0048]

[0049] From the initial coordinates and the initial direction vector To begin with, we can estimate the continuous coordinates (space and direction ), considering this point The position is actually the geometric distance measured along the ray (See equation (1)). Once the light passes through the first surface, if the refractive index of the continuous medium is different from that of air, the light will be refracted. To calculate the direction in which the light will travel after refraction, the vector refraction equation needs to be applied:

[0050]

[0051] Attached Figure 2 Figures a and b in the figure are the images of the same position of the model eye after two-dimensional and three-dimensional correction. Because two-dimensional correction only considers the influence of one plane, the position and curvature of the correction of each interface of the eye are not accurate enough, while three-dimensional correction considers all directions for the real shape and geometric distance of the eye, especially the fundus, and there is a big difference between the two. After comparing with the model eye data, it is found that the image after three-dimensional correction can better restore the real shape of the eye.

Claims

1. A whole-eye three-dimensional reconstruction method based on SS-OCT measurement system, characterized in that: The specific steps include: Step 1: Collect the original 3D data of the eye using the SS-OCT measurement system; Step 2: The three-dimensional raw data of the eye collected in step 1 is calculated and processed to obtain an eye image. The image is a cross-sectional view of each position of the eye. Grayscale correction and pixel correction are performed on the image. The image has pixel correction problems in three directions. The correspondence between the pixel size of the image and the real geometric distance is confirmed to restore the real size of the eyeball. Otherwise, the measurement result is incorrect, which affects the further correction of image distortion. Step 3: Use the OTUS Otsu algorithm to binarize, threshold segment, and denoise the image processed in step 2, perform image enhancement on the region, delete small area objects, so as to extract the interface of the eye tissue structure layer, and store the interface data of the eye tissue structure layer; Step 4: Use the least square method to perform surface fitting on the data in the effective area of ​​the image processed in step 3. The data in the effective area is obtained by intercepting the effective data in the interface data of the eye tissue structure layer by masking. After the surface fitting, the principal component analysis method is used to estimate the surface normal vector; Step 5: Set the incident light, and use the surface normal vector obtained after surface fitting in step 4 to perform refraction correction on the pixels of the image to obtain a real volume image of the eye; the refraction correction is: when the light propagates through the refraction effect occurring at each interface between two media with different refractive indices, the pixels of the image are corrected layer by layer according to the direction vector propagation after refraction to obtain a real volume image.

2. A whole-eye three-dimensional reconstruction method based on SS-OCT measurement system according to claim 1, characterized in that: The SS-OCT measurement system described in step 1 is based on the interferometer principle, which uses near-infrared weak coherent light to illuminate the tissue to be measured, generates interference based on the coherence of the light, and uses superheterodyne detection technology to measure the intensity of the reflected light for imaging the superficial layer of the tissue; The SS-OCT measurement system specifically includes: coupler 1, coupler 2, circulator 1, circulator 2, lens 1, lens 2, reflector 1, XY galvanometer, dichroic mirror, light source, balanced detector, acquisition card, target object; Among them, one end of the coupler 1 is connected to the light source, and the other end is connected to the circulator 1, one end of the circulator 1 is connected to the collimator 1, and the collimator 1, the XY galvanometer, the lens 1, the dichroic mirror, and the eye form a sample arm; one end of the circulator 1 is connected to the coupler 2, and one end of the coupler 2 is connected to the balanced detector; one end of the coupler 1 is connected to the circulator 2, and the circulator 2 is connected to the collimator 2, and the collimator 2, the lens 2, and the reflector 1 form a reference arm; The SS-OCT measurement system uses a swept-frequency light source in the 1060nm band. The central wavelength of the light source is longer than that used in the spectral domain and time domain. The axial resolution is reduced, but the depth range of tissue detection is wider, which is used for endoscopic OCT imaging of cardiovascular and cerebrovascular tissues. In SS-OCT, the imaging depth z max It is expressed as: In the above formula, λ0 represents the central wavelength of the light source, R λ It represents the resolution of the spectrometer expressed in wavelength, which is directly obtained through experiments. n is the average refractive index of the imaged tissue. The theoretical imaging depth of the SS-OCT system is more than ten centimeters. The axial length of the eye is a, and a<3 cm, which is sufficient for whole-eye imaging. The value of a varies according to the axial length of the human eye.

3. The whole-eye three-dimensional reconstruction method based on the SS-OCT measurement system according to claim 1, characterized in that: Step 1 The working process of the SS-OCT system to collect 3D data of the eye is as follows: The light emitted by the light source is split by coupler 1, part of the light is input into the reference arm, and part of the light is input into the sample arm. The light enters the reference arm through circulator 2, is collimated by collimator 2, and is converged to reflector 1 through lens 2; the light is input into the sample arm through circulator 1, is collimated by collimator 1 and irradiated to the XY scanning galvanometer, and then the sample light is converged by lens 1 and emitted into the pupil of the subject. The light returned through the pupil and lens of the subject passes through circulator 1 and the light returned from the reference arm passes through circulator 2 to coupler 2 to interfere, and the interference signal is detected by the balanced detector BPD. Finally, the interference signal is sampled, recorded and saved to the computer by the data acquisition card DAQ for subsequent processing.

4. The whole-eye three-dimensional reconstruction method based on the SS-OCT measurement system according to claim 1, characterized in that: The idea of ​​the principal component analysis method described in step 4 is to fit a plane to the N points of the K-nearest neighbors, that is, the plane passes through the centroid O i The plane is fitted with N points to obtain the plane normal vector; the least squares fitting is converted into the eigenvector corresponding to the minimum eigenvalue P of the covariance matrix of the effective area of ​​the image, that is, the SVD decomposition is performed on the effective area of ​​the image; the SVD solution is highly robust to data noise, and the key point is to centralize the data and move the origin of the covariance matrix coordinates to the center of gravity of the data; finally, according to the minimum eigenvalue P to the center of gravity O i The positive or negative sign of the normal vector is determined by the dot product of the formed vector and the plane normal vector. If f(p)<0, it is negative, and if f(p)>0, it is positive.

Citation Information

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