CN116138767A - Detection method for calculating cobb angle through fitting circle method - Google Patents
Detection method for calculating cobb angle through fitting circle method Download PDFInfo
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/103—Detecting, measuring or recording devices for testing the shape, pattern, colour, size or movement of the body or parts thereof, for diagnostic purposes
- A61B5/107—Measuring physical dimensions, e.g. size of the entire body or parts thereof
- A61B5/1071—Measuring physical dimensions, e.g. size of the entire body or parts thereof measuring angles, e.g. using goniometers
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/0059—Measuring for diagnostic purposes; Identification of persons using light, e.g. diagnosis by transillumination, diascopy, fluorescence
- A61B5/0062—Arrangements for scanning
- A61B5/0064—Body surface scanning
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/0059—Measuring for diagnostic purposes; Identification of persons using light, e.g. diagnosis by transillumination, diascopy, fluorescence
- A61B5/0077—Devices for viewing the surface of the body, e.g. camera, magnifying lens
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/103—Detecting, measuring or recording devices for testing the shape, pattern, colour, size or movement of the body or parts thereof, for diagnostic purposes
- A61B5/107—Measuring physical dimensions, e.g. size of the entire body or parts thereof
- A61B5/1077—Measuring of profiles
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/103—Detecting, measuring or recording devices for testing the shape, pattern, colour, size or movement of the body or parts thereof, for diagnostic purposes
- A61B5/107—Measuring physical dimensions, e.g. size of the entire body or parts thereof
- A61B5/1079—Measuring physical dimensions, e.g. size of the entire body or parts thereof using optical or photographic means
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/0002—Inspection of images, e.g. flaw detection
- G06T7/0012—Biomedical image inspection
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10028—Range image; Depth image; 3D point clouds
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
- G06T2207/30004—Biomedical image processing
- G06T2207/30008—Bone
- G06T2207/30012—Spine; Backbone
Abstract
The invention relates to a detection method for calculating cobb angle by fitting a circle method. The invention designs an improved Cobb angle calculation method, which uses the central angle of a fitting circle instead of the included angle of a curve tangent line, thereby reducing the error introduced by the curve tangent line method. The fitting curve of the invention adopts 7 times polynomial instead of B spline fitting, which can reduce random errors caused by operation and enhance the reliability of the curve. The invention can effectively obtain the internal vertebral body information of the body through the body surface of the tested person and further obtain the Cobb angle. The number of times that the testee shot X-rays can be effectively reduced, and the health of the testee is protected.
Description
Technical Field
The invention relates to the field of calculation of spine curves and cobb angles obtained from human body surfaces, in particular to a detection method for obtaining spine curves from body surfaces and calculating cobb angles through a fitting circle method.
Background
Curvature estimation is an important indicator for evaluating scoliosis. The standard curvature estimation method for quantitatively assessing the degree of spinal curvature is accomplished by measuring the Cobb angle. The Cobb angle reflects the curvature of the coronal plane of the spine. The traditional mode of calculating the Cobb angle is to calculate the intersection angle of two extension lines by a physician with abundant experience through judging the most complete upper and lower end surfaces of the cone body and drawing the extension lines of the upper and lower end surfaces.
However, existing measurement techniques. On the one hand, the patient is subjected to additional radioactive effects, which have a greater influence on the teenagers in the growth and development stage. The back point cloud of the patient is obtained by utilizing the binocular camera principle, and the two-dimensional spine curve is obtained by processing the back point cloud of the patient and two-dimensionally obtaining the back point cloud. A new method for extracting the spinal curve acting on the two-dimensional curve is provided.
Disclosure of Invention
The technical problem to be solved by the invention is to calculate the cobb angle by a detection method of calculating the cobb angle by a fitting circle method according to a human back point cloud picture.
A computing device for human back point cloud. The detection device is characterized by comprising a support frame, a darkroom, a scanner and a computer. The supporting frame can enable the tested person to keep a specific posture; the darkroom is used for shielding external stray light, providing darker background and protecting privacy of a tested person; the scanner is composed of a light supplementing system and two cameras, wherein the light supplementing system is used for enhancing the contrast ratio of images, and the cameras are used for collecting back pictures of human bodies; the computer is used for storing collected pictures, three-dimensional reconstruction, characteristic calculation and other tasks.
A method for obtaining a spinal body shape by using body surface attachment points. The method is characterized in that the using process of the invention comprises the following steps of
S1, the back of the tested person needs to be exposed to enter the darkroom. The entire test environment may not be too bright to take advantage of imaging.
S2, in order to display the bone position, white mark points are required to be stuck to the spinous process position of the back of the tester. In order to be able to describe the morphology of the spine as completely as possible and to reduce the time-consuming measurements. Each tested person needs to paste 14 mark points on the back, wherein 10 mark points are pasted on the spinous process for describing the shape of the spine, 2 mark points are pasted on the shoulders of the tested person for measuring the height difference of the two shoulders of the tested person, and 2 mark points are pasted on the posterior upper spine of the ilium.
S3, controlling the binocular camera to shoot through matched software, and reconstructing a point cloud image of the back of the patient in a computer.
S4, acquiring three-dimensional data of the back attachment points in a computer through image recognition software.
S5, calculating cobb angles according to the obtained three-dimensional spinal scattered points.
The binocular camera acquires a back point cloud image of a patient, and is characterized in that the specific substeps of adopting a binocular stereoscopic imaging technology in the step S3 are as follows:
binocular stereoscopic vision reconstructs three-dimensional information of a measured object based on observation, and the same target is observed through two different viewpoints to obtain perceived images under different vision. And calculating the position deviation between the pixels of the image by utilizing the triangle geometry principle so as to calculate the real three-dimensional information of the target.
The process of taking a picture by a camera is a process of mapping coordinate points in a three-dimensional world to a two-dimensional image plane. Specifically, a world coordinate system in three-dimensional vision is transformed into a camera coordinate system of a camera through rigid transformation, three-dimensional is transformed into an image physical coordinate system through perspective projection, and finally a picture pixel coordinate system is obtained through rigid transformation, so that two-dimensional position coordinates corresponding to an object in the three-dimensional world are obtained. The specific substeps are as follows:
s31, point P (X) w ，Y w ，Z w ) Conversion to a point P (X) c ，Y c ，Z c ) Ketong (Chinese character)Over translation and rotation, where r 1 ～r 9 For rotating matrix, t x 、t y 、t z Is a translation matrix.
S32, the origin of the image physical coordinate system is the intersection point of the camera optical axis and the imaging plane, and the X and y axes of the image physical coordinate system are respectively parallel to the X of the camera coordinate system c And Y c The axis, therefore, the point P (X) in the camera coordinate system can be deduced from the principle of triangle similarity c ，Y c ，Z c ) And the point P' (x, y) in the physical coordinate system of the image satisfy the following formula, where f is the focal length of the camera.
S33、O 1 Is the intersection point of the optical axis of the camera and the imaging plane, O 0 Is the origin of the pixel coordinate system, (u) 0 ,v 0 ) Is O 1 Assuming that the actual physical dimensions of each pixel in the u-axis and v-axis directions are d x And d y The relationship between the pixel coordinates P '(u, v) and the physical coordinates P' (x, y) can be obtained as follows.
S34, image coordinates (u, v) and world coordinates (X W ,Y W ,Z W ) The relationship between them is as follows.
Wherein s is a scale factor, (d) x ，d y ，u 0 ，v 0 F) is an internal reference of the camera, which is the phaseThe intrinsic parameters of the camera, (R, T) are external parameters of the camera, and represent the relation between the camera coordinate system and the world coordinate system, and the process of obtaining the parameters is called camera calibration.
The s scale factor is just an intermediate parameter and can be eliminated in the operation. The method is the prior art, and the specific method steps are shown in [1] Wu Linhui, namely, three-dimensional reconstruction research based on binocular stereo vision [ D ] Wuhan engineering university, 2022.DOI:10.27727/d.cnki.gwhxc.2022.000585.
S35, calculating the real three-dimensional coordinates of the target by using the pictures shot by the left and right two-phase camera. C1 and C2 cameras observe the P point at the same time, and P is obtained from the two-camera shooting pictures respectively 1 And P 2 And (5) a dot. Then the true P point coordinates are the straight line O 1 P 1 And straight line O 2 P 2 Of (wherein O 1 、O 2 Respectively the intersection of the optical axis of the two-phase camera and the imaging plane).
A method for calculating cobb angle of human body by fitting circle. The method is characterized in that in the step S5, cobb angles are calculated on the basis of three-dimensional scattered point data by adopting the fitting circle method provided by the invention.
The method specifically comprises the following substeps:
and S51, projecting three-dimensional coordinates of the back mark points extracted from the three-dimensional point cloud picture to an XOY plane, and corresponding to the X-ray plane. Setting the coordinate of the mark point as gamma (x, y, z) and projecting to the XOY plane to obtain a changed two-dimensional coordinate gamma (x, y)
S52, fitting the body surface marking points into an approximate curve of the human spine by adopting a 7-degree polynomial fitting method.
The mathematical expression of the polynomial fit is as follows:
where M is the highest degree of the polynomial, x j Represents the power of x, w j Is x j Is a coefficient of (a). Compared with B spline fitting, the 7 th-degree polynomial fitting method can reduce random errors introduced by operation and enhance the reliability of the curve.
And S53, determining the starting and ending positions of the upper end face and the lower end face by the inflection point position of the curve. The inflection point of the curve is a point at which the convexity of the curve changes. Let the resulting spinal curve equation be y=p (t), where t, y are the abscissa and ordinate of the spinal curve, respectively. The solution of the inflection point of the spinal curve is as follows:
(1) P' (t) is found.
(2) Let P "(t) =0, solve for its real root over the entire spinal curve and find points where P" (t) is absent over the entire spinal curve.
(3) For each real root or point t where the second derivative does not exist solved in (2) 0 Check P' (t) at t 0 Symbols adjacent to the left and right sides, when the symbols are opposite, points (t 0 ,(t 0 ) Is an inflection point, when the signs are the same, a point (t 0 ,(t 0 ) Not an inflection point.
And S54, fitting the curves surrounded by all the adjacent endpoints calculated in the step S43 by using a Hyper Fit fitting method. The starting point of the C-curve is point a, the end point is point b, and the discrete spinal column point row forming the main C-curve is set as point p i (x i ,y i )(a<i<b) A. The invention relates to a method for producing a fibre-reinforced plastic composite For the point column p between C-turns a i Fitting a circle equation by adopting a least square method, wherein the equation of the fitted circle is as follows
(x-x 0 ) 2 +(y-y 0 ) 2 ＝R 2
Wherein x is 0 ，y 0 For the center of the fitting circle, R is the radius of the fitting circle. And traversing and calculating the circle center of the fitting circle between each two adjacent inflection points and the curvature radius of the fitting circle.
S55, calculating the curvature radius by using the S54, and searching the C-bend with the smallest curvature radius (namely, the largest curvature) as the main C-bend. The upper end point of the principal C-bend is (x) 1 ,y 1 ) The point and lower endpoint are (x) 2 ,y 2 ) The center of the circle is (a, b) and the central angle is
The beneficial effects of the invention are as follows:
the invention can effectively obtain the internal vertebral body information of the body through the body surface of the tested person and further obtain the Cobb angle. The number of times that the testee shot X-rays can be effectively reduced, and the health of the testee is protected. An improved Cobb angle calculation method is designed, and the error introduced by a curve tangent method is reduced by using the central angle of a fitting circle instead of the curve tangent included angle. The fitting curve of the invention adopts 7 times polynomial instead of B spline fitting, which can reduce random errors caused by operation and enhance the reliability of the curve.
Drawings
Fig. 1 is an overall flowchart.
Fig. 2 is a cobb angle calculation flowchart.
Detailed Description
In order to make the technical problems, technical solutions and advantages to be solved more apparent, the following detailed description will be given with reference to the accompanying drawings and specific embodiments.
The technical problem to be solved by the invention is to calculate the cobb angle by a detection method of calculating the cobb angle by a fitting circle method according to a human back point cloud picture.
A computing device for human back point cloud. The detection device is characterized by comprising a support frame, a darkroom, a scanner and a computer. The supporting frame can enable the tested person to keep a specific posture; the darkroom is used for shielding external stray light, providing darker background and protecting privacy of a tested person; the scanner is composed of a light supplementing system and two cameras, wherein the light supplementing system is used for enhancing the contrast ratio of images, and the cameras are used for collecting back pictures of human bodies; the computer is used for storing collected pictures, three-dimensional reconstruction, characteristic calculation and other tasks.
A method for obtaining a spinal body shape by using body surface attachment points. The method is characterized in that the using process of the invention comprises the following steps of
S1, the back of the tested person needs to be exposed to enter the darkroom. The entire test environment may not be too bright to take advantage of imaging.
S2, in order to display the bone position, white mark points are required to be stuck to the spinous process position of the back of the tester. In order to be able to describe the morphology of the spine as completely as possible and to reduce the time-consuming measurements. Each tested person needs to paste 14 mark points on the back, wherein 10 mark points are pasted on the spinous process for describing the shape of the spine, 2 mark points are pasted on the shoulders of the tested person for measuring the height difference of the two shoulders of the tested person, and 2 mark points are pasted on the posterior upper spine of the ilium.
S3, controlling the binocular camera to shoot through matched software, and reconstructing a point cloud image of the back of the patient in a computer.
S4, acquiring three-dimensional data of the back attachment points in a computer through image recognition software.
S5, calculating cobb angles according to the obtained three-dimensional spinal scattered points.
The binocular camera acquires a back point cloud image of a patient, and is characterized in that the specific substeps of adopting a binocular stereoscopic imaging technology in the step S3 are as follows:
binocular stereoscopic vision reconstructs three-dimensional information of a measured object based on observation, and the same target is observed through two different viewpoints to obtain perceived images under different vision. And calculating the position deviation between the pixels of the image by utilizing the triangle geometry principle so as to calculate the real three-dimensional information of the target.
The process of taking a picture by a camera is a process of mapping coordinate points in a three-dimensional world to a two-dimensional image plane. Specifically, a world coordinate system in three-dimensional vision is transformed into a camera coordinate system of a camera through rigid transformation, three-dimensional is transformed into an image physical coordinate system through perspective projection, and finally a picture pixel coordinate system is obtained through rigid transformation, so that two-dimensional position coordinates corresponding to an object in the three-dimensional world are obtained. The specific substeps are as follows:
s31, point P (X) w ，Y w ，Z w ) Conversion to a point P (X) c ，Y c ，Z c ) Can be realized by translation and rotation, wherein r is as follows 1 ～r 9 For rotating matrix, t x 、t y 、t z Is a translation matrix.
S32, the origin of the physical coordinate system of the image is the optical axis and imaging of the cameraIntersection of planes, X and y axes of the physical coordinate system of the image are respectively parallel to X of the coordinate system of the camera c And Y c The axis, therefore, the point P (X) in the camera coordinate system can be deduced from the principle of triangle similarity c ，Y c ，Z c ) And the point P' (x, y) in the physical coordinate system of the image satisfy the following formula, where f is the focal length of the camera.
S33、O 1 Is the intersection point of the optical axis of the camera and the imaging plane, O 0 Is the origin of the pixel coordinate system, (u) 0 ,v 0 ) Is O 1 Assuming that the actual physical dimensions of each pixel in the u-axis and v-axis directions are d x And d y The relationship between the pixel coordinates P '(u, v) and the physical coordinates P' (x, y) can be obtained as follows.
S34, image coordinates (u, v) and world coordinates (X W ,Y W ,Z W ) The relationship between them is as follows.
Wherein s is a scale factor, (d) x ，d y ，u 0 ，v 0 F) is an internal parameter of the camera, is an intrinsic parameter of the camera, and (R, T) is an external parameter of the camera, and represents the relation between a camera coordinate system and a world coordinate system, and the process of obtaining the parameters is called camera calibration
S35, calculating the real three-dimensional coordinates of the target by using the pictures shot by the left and right two-phase camera. C1 and C2 cameras observe the P point at the same time, and P is obtained from the two-camera shooting pictures respectively 1 And P 2 And (5) a dot. Then the true P point coordinates are the straight line O 1 P 1 And straight line O 2 P 2 Of (wherein O 1 、O 2 Intersection point of optical axis and imaging plane of two-phase camera respectively
A method for calculating cobb angle of human body by fitting circle. The method is characterized in that in the step S5, cobb angles are calculated on the basis of three-dimensional scattered point data by adopting the fitting circle method provided by the invention.
The method specifically comprises the following substeps:
and S51, projecting three-dimensional coordinates of the back mark points extracted from the three-dimensional point cloud picture to an XOY plane, and corresponding to the X-ray plane. Setting the coordinate of the mark point as gamma (, y, z) and projecting to the XOY plane to obtain a changed two-dimensional coordinate gamma (, y)
S52, fitting the body surface marking points into an approximate curve of the human spine by adopting a 7-degree polynomial fitting method.
The mathematical expression of the polynomial fit is as follows:
where M is the highest degree of the polynomial, x j Represents the power of x, w j Is x j Is a coefficient of (a). Compared with B spline fitting, the 7 th-degree polynomial fitting method can reduce random errors introduced by operation and enhance the reliability of the curve.
And S53, determining the starting and ending positions of the upper end face and the lower end face by the inflection point position of the curve. The inflection point of the curve is a point at which the convexity of the curve changes. Let the resulting spinal curve equation be y=p (t), where t, y are the abscissa and ordinate of the spinal curve, respectively. The solution of the inflection point of the spinal curve is as follows:
(1) P' (t) is found.
(2) Let P "(t) =0, solve for its real root over the entire spinal curve and find points where P" (t) is absent over the entire spinal curve.
(3) For each real root or point t where the second derivative does not exist solved in (2) 0 Check P' (t) at t 0 Symbols adjacent to the left and right sides, when the symbols are opposite, points (t 0 ,(t 0 ) Is an inflection point, when the signs are the same, a point (t 0 ,(t 0 ) Not an inflection point.
And S54, fitting the curves surrounded by all the adjacent endpoints calculated in the step S43 by using a Hyper Fit fitting method. The starting point of the C-curve is point a, the end point is point b, and the discrete spinal column point row forming the main C-curve is set as point p i (x i ,y i )(a<i<b) A. The invention relates to a method for producing a fibre-reinforced plastic composite For the point column p between C-turns a i Fitting a circle equation by adopting a least square method, wherein the equation of the fitted circle is as follows
(x-x 0 ) 2 +(y-y 0 ) 2 ＝R 2
Wherein x is 0 ，y 0 For the center of the fitting circle, R is the radius of the fitting circle. And traversing and calculating the circle center of the fitting circle between each two adjacent inflection points and the curvature radius of the fitting circle.
S55, calculating the curvature radius by using the S54, and searching the C-bend with the smallest curvature radius (namely, the largest curvature) as the main C-bend. The upper end point of the principal C-bend is (x) 1 ,y 1 ) The point and lower endpoint are (x) 2 ,y 2 ) The center of the circle is (a, b) and the central angle is
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Claims (3)
1. The detection method for calculating cobb angle by fitting a circle method is characterized by comprising the following steps:
s1, a tested person needs to expose the back to enter a darkroom;
s2, in order to display the bone position, white mark points are required to be stuck to the spinous process position of the back of the tester; each tested person needs to paste 14 marking points on the back, wherein 10 marking points are pasted on the spinous process for describing the shape of the spine, 2 marking points are pasted on the shoulders of the tested person for measuring the height difference of the two shoulders of the tested person, and 2 marking points are pasted on the posterior upper spine of the ilium;
s3, controlling the binocular camera to shoot through matched software, and reconstructing a point cloud image of the back of the patient in a computer;
s4, acquiring three-dimensional data of the back attachment points in a computer through image recognition software;
s5, calculating cobb angles according to the obtained three-dimensional spinal scattered points.
2. The detection method according to claim 1, wherein the specific sub-steps of the binocular stereo imaging technique adopted in step S3 are as follows:
the specific substeps are as follows:
s31, point P (X) w ，Y w ，Z w ) Conversion to a point P (X) c ，Y c ，Z c ) The method comprises the steps of carrying out a first treatment on the surface of the By translation and rotation, where r 1 ～r 9 For rotating matrix, t x 、t y 、t z Is a translation matrix;
s32, the origin of the image physical coordinate system is the intersection point of the camera optical axis and the imaging plane, and the X and y axes of the image physical coordinate system are respectively parallel to the X of the camera coordinate system c And Y c The axis, therefore, the point P (X) in the camera coordinate system can be deduced from the principle of triangle similarity c ，Y c ，Z c ) And a point P' (x, y) in the physical coordinate system of the image, wherein f is the focal length of the camera;
S33、O 1 is the intersection point of the optical axis of the camera and the imaging plane, O 0 Is the origin of the pixel coordinate system, (u) 0 ,v 0 ) Is O 1 Assuming that the actual physical dimensions of each pixel in the u-axis and v-axis directions are d x And d y The relationship between the pixel coordinates P '(u, v) and the physical coordinates P' (x, y) can be obtained as follows;
s34, image coordinates (u, v) and world coordinates (X W ,Y W ,Z W ) The relationship between them is as follows;
wherein s is a scale factor, (d) x ，d y ，u 0 ，v 0 F) is an internal parameter of the camera, is an intrinsic parameter of the camera, and (R, T) is an external parameter of the camera, and represents the relation between a camera coordinate system and a world coordinate system, and the process of obtaining the parameters is called camera calibration;
s35, calculating real three-dimensional coordinates of the target by using pictures shot by the left camera and the right camera; c1 and C2 cameras observe the P point at the same time, and P is obtained from the two-camera shooting pictures respectively 1 And P 2 A dot; then the true P point coordinates are the straight line O 1 P 1 And straight line O 2 P 2 Wherein O is 1 、O 2 Respectively the intersection point of the optical axis of the two-phase camera and the imaging plane.
3. The detection method according to claim 1, wherein S5 specifically comprises the sub-steps of:
s51, projecting three-dimensional coordinates of a back mark point extracted from the three-dimensional point cloud picture to an XOY plane to correspond to the X-ray plane; setting the coordinate of the mark point as gamma (, y, z) and projecting to the XOY plane to obtain a changed two-dimensional coordinate gamma (, y)
S52, fitting the body surface marking points into an approximate curve of the human spine by adopting a 7-time polynomial fitting method;
the mathematical expression of the polynomial fit is as follows:
where M is the highest degree of the polynomial, x j Represents the power of x, w j Is x j Coefficients of (2);
s53, determining starting and ending positions of the upper end face and the lower end face by inflection point positions of a curve; the inflection point of the curve is a point at which the convexity and convexity of the curve change; setting the obtained spinal curve equation as y=p (t), wherein t and y are respectively the abscissa and the ordinate of the spinal curve; the solution of the inflection point of the spinal curve is as follows:
(1) Solving for P' (t);
(2) Let P "(t) =0, solve for its real root over the entire spinal curve and find points where P" (t) does not exist over the entire spinal curve;
(3) For each real root or point t where the second derivative does not exist solved in (2) 0 Check P' (t) at t 0 Symbols adjacent to the left and right sides, when the symbols are opposite, points (t 0 ,P(t 0 ) Is an inflection point, when the signs are the same, a point (t 0 ,P(t 0 ) Not an inflection point;
s54, fitting the curves surrounded by all the adjacent endpoints calculated in the S43 by using a Hyper Fit fitting method; the starting point of the C-curve is point a, the end point is point b, and the discrete spinal column point row forming the main C-curve is set as point p i (x i ,y i ) (a < i < b); for the point column p between C-turns a i Fitting a circle equation by adopting a least square method, wherein the equation of the fitted circle is as follows
(x-x 0 ) 2 +(y-y 0 ) 2 ＝R 2
Wherein x is 0 ，y 0 R is the radius of the fitting circle for the circle center of the fitting circle; traversing and calculating the circle center of a fitting circle and the curvature radius of the fitting circle between every two adjacent inflection points;
s55, calculating the curvature radius by using the S54, and searching the C-bend with the smallest curvature radius, namely the largest curvature, as a main C-bend; the upper end point of the principal C-bend is (x) 1 ,y 1 ) The point and lower endpoint are (x) 2 ,y 2 ) The center of the circle is (a, b) and the central angle is
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